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Commit 79b24318 authored by Helene31's avatar Helene31
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...@@ -9,10 +9,9 @@ ...@@ -9,10 +9,9 @@
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" /> <meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="author" content="Hélène Raynal" />
<title>Exercice 3 Module 2</title> <title>journalHelene31.utf8</title>
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to <script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
// be compatible with the behavior of Pandoc < 2.8). // be compatible with the behavior of Pandoc < 2.8).
...@@ -375,9 +374,6 @@ summary { ...@@ -375,9 +374,6 @@ summary {
<h1 class="title toc-ignore">Exercice 3 Module 2</h1>
<h4 class="author">Hélène Raynal</h4>
<h4 class="date">21 avril 2020</h4>
</div> </div>
...@@ -515,18 +511,6 @@ summary { ...@@ -515,18 +511,6 @@ summary {
</tbody> </tbody>
</table> </table>
</div> </div>
<div id="suivi-des-data-coronavirus" class="section level2">
<h2>Suivi des data coronavirus</h2>
<pre class="r"><code>setwd(&quot;C:/Users/hraynal/EspaceTravailBadet/FORMATION_PERSO/2020-Reproductibilite/moocrr-reproducibility-study/module2/exo4&quot;)
library(ggplot2)
monDataset &lt;- read.csv(&quot;covid19-du-2020-03-04-au-2020-03-25.csv&quot;, sep=&quot;;&quot;)
#summary(monDataset)
ggplot(monDataset) +
geom_point(aes(x = Date, y = Occitanie),
color = &quot;darkgreen&quot;)</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="module-1-cahier-de-notes-cahier-de-laboratoire" class="section level2"> <div id="module-1-cahier-de-notes-cahier-de-laboratoire" class="section level2">
<h2>Module 1: Cahier de notes cahier de laboratoire</h2> <h2>Module 1: Cahier de notes cahier de laboratoire</h2>
<div id="nous-utilisons-tous-des-cahiers-de-notes-cahier-de-laboratoire" class="section level3"> <div id="nous-utilisons-tous-des-cahiers-de-notes-cahier-de-laboratoire" class="section level3">
......
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# le titre de la premiere section
## le titre de la 2eme ss section
_italique_ *italique*
__gras__ **gras**
échasse fixeé 'chasse fixe' `chasse fixe`
--barré-- ~~barrer~~
un hyperline [Élaboration et conversion de documents avec Markdown et Pandoc](https://enacit1.epfl.ch/markdown-pandoc/)
<!-- un commentaire -->
![une photo de chat](https://upload.wikimedia.org/wikipedia/commons/thumb/6/64/Collage_of_Six_Cats-02.jpg/290px-Collage_of_Six_Cats-02.jpg)
liste à puce
- +1er élément
- 2 eme element
- 3 eme element
numérotation
1. premier
2. deuxieme
3. ...
Je peux imbriquer
1. ff
- a
- b
2. ggg
3. on continu
1. au début
2. ensuite
on va s'arrêter là
# Nouvelle Section de Niveau 1
- liste de Voitures
1. Porsche
2. Ferrari
- Liste d'éditeurs
1. Notepad++
2. TextEdit
## Nouvelle Section de Niveau 2
Bonjour, c'est ma nouvelle Section de niveau 2,
qui permet de créer un heading de niveau 2 en HTML.
### C'est un paragraphe formé de plusieurs lignes
<p> Ligne 1 du paragraphe <br> <hr>Ligne 2 du paragraphe <br> <hr> Ligne 3 du paragraphe
</p>
<br>
*Texte en Italique* <br>
__texte en gras__ <br>
___texte en italique et gras___
<br>
[Lien vers Google](https://www.google.fr/)
<br>
![Image ](http://animtoit.fr/exemple-chien/)
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---
title: "Your title"
author: "Your name"
date: "Today's date"
output: html_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## Some explanations
This is an R Markdown document that you can easily export to HTML, PDF, and MS Word formats. For more information on R Markdown, see <http://rmarkdown.rstudio.com>.
When you click on the button **Knit**, the document will be compiled in order to re-execute the R code and to include the results into the final document. As we have shown in the video, R code is inserted as follows:
```{r cars}
summary(cars)
```
It is also straightforward to include figures. For example:
```{r pressure, echo=FALSE}
plot(pressure)
```
Note the parameter `echo = FALSE` that indicates that the code will not appear in the final version of the document. We recommend not to use this parameter in the context of this MOOC, because we want your data analyses to be perfectly transparent and reproducible.
Since the results are not stored in Rmd files, you should generate an HTML or PDF version of your exercises and commit them. Otherwise reading and checking your analysis will be difficult for anyone else but you.
Now it's your turn! You can delete all this information and replace it by your computational document.
module2/exo1/toy_document_fr.Rmd deleted 100644 → 0
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---
title: "À propos du calcul de pi"
author: "Isaac KABRE"
date: "10 avril 2020"
output: html_document
---
## En demandant à la lib maths
Mon ordinateur m'indique que $\pi$ vaut approximativement
```
pi
```
## En utilisant la méthode des aiguilles de Buffon
Mais calculé avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation** :
```{r }
set.seed(42)
N = 100000
x = runif(N)
theta = pi/2*runif(N)
2/(mean(x+sin(theta)>1))
```
## Avec un argument “fréquentiel” de surface
Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d’appel à la fonction sinus se base sur le fait que si
$X \sim U(0,1)$ et
$Y \sim U(0,1)$ alors
$P[X^{2} + Y^{2} \le 1]= \pi /4$
(voir [méthode de Monte Carlo sur Wikipedia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80). Le code suivant illustre ce fait:
```{r }
set.seed(42)
N = 1000
df = data.frame(X = runif(N), Y = runif(N))
df$Accept = (df$X**2 + df$Y**2 <=1)
library(ggplot2)
ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw()
```
Il est alors aisé d’obtenir une approximation (pas terrible) de π en comptant combien de fois, en moyenne, $X{2}+Y{2}$ est inférieur à 1:
```{r }
4*mean(df$Accept)
```
\ No newline at end of file
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---
title: "À Propos du calcul de pi"
author: "Arnaud Legrand"
date: "06/25/2020"
output: html_document
---
## En demandant à la lib maths
Mon ordinateur m'indique que \pi vaut *approximativement*
```{r}
pi
```
## En tulisant la méthode des aiguilles de Buffon
Mais calculer avec la **méthode** des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon), on obtiendrait comme **approximation** :
```{r}
set.seed(42)
N = 100000
x = runif(N)
theta = pi/2*runif(N)
2/(mean(x+sin(theta)>1))
```
## Avec un argument “fréquentiel” de surface
Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d’appel à la fonction sinus se base sur le fait que si X∼U(0,1) et Y∼U(0,1) alors P[X2+Y2≤1]=\pi/4 (voir [méthode de Monte Carlo sur Wikipedia](https://fr.wikipedia.org/wiki/Méthode_de_Monte-Carlo#Détermination_de_la_valeur_de_π)). Le code suivant illustre ce fait:
```{r}
set.seed(42)
N = 1000
df = data.frame(X = runif(N), Y = runif(N))
df$Accept = (df$X**2 + df$Y**2 <=1)
library(ggplot2)
ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw()
```
Il est alors aisé d’obtenir une approximation (pas terrible) de \pi en comptant combien de fois, en moyenne, X2+Y2 est inférieur à 1:
```{r}
4*mean(df$Accept)
```
\ No newline at end of file
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#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, R code is included as follows (and is
exxecuted by typing ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
And now the same but in an R session. This is the most frequent
situation, because R is really an interactive language. With a
session, R's state, i.e. the values of all the variables, remains
persistent from one code block to the next. The code is still executed
using ~C-c C-c~.
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Finally, an example for graphical output:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cars.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in R by typing ~<r~ or ~<R~ followed by
~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
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#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
R. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclut du code
R de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
Voici la même chose, mais avec une session R (c'est le cas le
plus courant, R étant vraiment un langage interactif), donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Et enfin, voici un exemple de sortie graphique:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cars.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, pour les prochains exercices, nous ne vous fournirons pas
forcément de fichier de départ, ça sera à vous de le créer, par
exemple en repartant de ce document et de le commiter vers
gitlab. N'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code R (en
faisant ~<r~ ou ~<R~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module2/exo1/toy_document_orgmode_python_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, Python code is included as follows (and
is exxecuted by typing ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
And now the same but in an Python session. With a session, Python's
state, i.e. the values of all the variables, remains persistent from
one code block to the next. The code is still executed using ~C-c
C-c~.
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Finally, an example for graphical output:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cosxsx.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in Python by typing ~<p~, ~<P~ or ~<PP~
followed by ~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
module2/exo1/toy_document_orgmode_python_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
python. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclue du code
python de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
Voici la même chose, mais avec une session python, donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Et enfin, voici un exemple de sortie graphique:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cosxsx.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, n'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code python (en
faisant ~<p~, ~<P~ ou ~<PP~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module2/exo1/toy_notebook_en.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo1/toy_notebook_fr.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo3/exercice.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo3/exercice_R_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, R code is included as follows (and is
exxecuted by typing ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
And now the same but in an R session. This is the most frequent
situation, because R is really an interactive language. With a
session, R's state, i.e. the values of all the variables, remains
persistent from one code block to the next. The code is still executed
using ~C-c C-c~.
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Finally, an example for graphical output:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cars.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in R by typing ~<r~ or ~<R~ followed by
~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
module2/exo3/exercice_R_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
R. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclut du code
R de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
Voici la même chose, mais avec une session R (c'est le cas le
plus courant, R étant vraiment un langage interactif), donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Et enfin, voici un exemple de sortie graphique:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cars.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, pour les prochains exercices, nous ne vous fournirons pas
forcément de fichier de départ, ça sera à vous de le créer, par
exemple en repartant de ce document et de le commiter vers
gitlab. N'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code R (en
faisant ~<r~ ou ~<R~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module2/exo3/exercice_en.Rmd deleted 100644 → 0
View file @ ecd554d7
---
title: "Your title"
author: "Your name"
date: "Today's date"
output: html_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## Some explanations
This is an R Markdown document that you can easily export to HTML, PDF, and MS Word formats. For more information on R Markdown, see <http://rmarkdown.rstudio.com>.
When you click on the button **Knit**, the document will be compiled in order to re-execute the R code and to include the results into the final document. As we have shown in the video, R code is inserted as follows:
```{r cars}
summary(cars)
```
It is also straightforward to include figures. For example:
```{r pressure, echo=FALSE}
plot(pressure)
```
Note the parameter `echo = FALSE` that indicates that the code will not appear in the final version of the document. We recommend not to use this parameter in the context of this MOOC, because we want your data analyses to be perfectly transparent and reproducible.
Since the results are not stored in Rmd files, you should generate an HTML or PDF version of your exercises and commit them. Otherwise reading and checking your analysis will be difficult for anyone else but you.
Now it's your turn! You can delete all this information and replace it by your computational document.
module2/exo3/exercice_en.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo3/exercice_fr.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo3/exercice_python_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, Python code is included as follows (and
is exxecuted by typing ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
And now the same but in an Python session. With a session, Python's
state, i.e. the values of all the variables, remains persistent from
one code block to the next. The code is still executed using ~C-c
C-c~.
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Finally, an example for graphical output:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cosxsx.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in Python by typing ~<p~, ~<P~ or ~<PP~
followed by ~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
module2/exo3/exercice_python_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
python. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclue du code
python de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
Voici la même chose, mais avec une session python, donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Et enfin, voici un exemple de sortie graphique:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cosxsx.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, n'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code python (en
faisant ~<p~, ~<P~ ou ~<PP~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module2/exo4/exercice.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo4/exercice_R_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, R code is included as follows (and is
exxecuted by typing ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
And now the same but in an R session. This is the most frequent
situation, because R is really an interactive language. With a
session, R's state, i.e. the values of all the variables, remains
persistent from one code block to the next. The code is still executed
using ~C-c C-c~.
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Finally, an example for graphical output:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cars.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in R by typing ~<r~ or ~<R~ followed by
~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
module2/exo4/exercice_R_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
R. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclut du code
R de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
Voici la même chose, mais avec une session R (c'est le cas le
plus courant, R étant vraiment un langage interactif), donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Et enfin, voici un exemple de sortie graphique:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cars.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, pour les prochains exercices, nous ne vous fournirons pas
forcément de fichier de départ, ça sera à vous de le créer, par
exemple en repartant de ce document et de le commiter vers
gitlab. N'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code R (en
faisant ~<r~ ou ~<R~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module2/exo4/exercice_en.Rmd deleted 100644 → 0
View file @ ecd554d7
---
title: "Your title"
author: "Your name"
date: "Today's date"
output: html_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## Some explanations
This is an R Markdown document that you can easily export to HTML, PDF, and MS Word formats. For more information on R Markdown, see <http://rmarkdown.rstudio.com>.
When you click on the button **Knit**, the document will be compiled in order to re-execute the R code and to include the results into the final document. As we have shown in the video, R code is inserted as follows:
```{r cars}
summary(cars)
```
It is also straightforward to include figures. For example:
```{r pressure, echo=FALSE}
plot(pressure)
```
Note the parameter `echo = FALSE` that indicates that the code will not appear in the final version of the document. We recommend not to use this parameter in the context of this MOOC, because we want your data analyses to be perfectly transparent and reproducible.
Since the results are not stored in Rmd files, you should generate an HTML or PDF version of your exercises and commit them. Otherwise reading and checking your analysis will be difficult for anyone else but you.
Now it's your turn! You can delete all this information and replace it by your computational document.
module2/exo4/exercice_en.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo4/exercice_fr.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo4/exercice_python_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, Python code is included as follows (and
is exxecuted by typing ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
And now the same but in an Python session. With a session, Python's
state, i.e. the values of all the variables, remains persistent from
one code block to the next. The code is still executed using ~C-c
C-c~.
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Finally, an example for graphical output:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cosxsx.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in Python by typing ~<p~, ~<P~ or ~<PP~
followed by ~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
module2/exo4/exercice_python_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
python. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclue du code
python de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
Voici la même chose, mais avec une session python, donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Et enfin, voici un exemple de sortie graphique:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cosxsx.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, n'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code python (en
faisant ~<p~, ~<P~ ou ~<PP~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module2/exo4/journalHelene31.Rmd deleted 100644 → 0
View file @ ecd554d7
---
title: "Exercice 3 Module 2"
author: "Hélène Raynal"
date: "21 avril 2020"
output: html_document
---
<img src="https://images-na.ssl-images-amazon.com/images/I/41w3Kf%2BAzBL._SX331_BO1,204,203,200_.jpg" width="100"/>
# Journal Hélène 31
*Objet de ce document*
ce que vous apprenez dans ce MOOC:
les références qui vous paraissent utiles, etc.
des données quotidiennes qui vous intéressent (temps, etc.). Vous les utiliserez par la suite dans le module 2.
## Data
| date | weather | temperature | hours |
|:----------|:------------:|------------:|------:|
|23/03/2020 | sunny | 14 | 1 |
|24/03/2020 | windy | 14 | 1 |
|25/03/2020 | windy | 15 | 2 |
|26/03/2020 | cloudy | 10 | 3 |
|27/03/2020 | sunny | 18 | 0 |
|28/03/2020 | sunny | 18 | 0 |
|29/03/2020 | cloudy | 12 | 0 |
|30/03/2020 | melted snow | 4 | 2 |
|31/03/2020 | melted snow | 4 | 2 |
|01/04/2020 | melted snow | 4 | 2 |
|02/04/2020 | sunny | 15 | 0 |
|03/04/2020 | sunny | 15 | 0 |
|04/04/2020 | sunny | 15 | 0 |
|05/04/2020 | sunny | 18 | 0 |
|06/04/2020 | sunny | 15 | 2 |
|15/04/2020 | sunny | 16 | 1 |
|16/04/2020 | sunny | 15 | 3 |
|20/04/2020 | rain | 10 | 2 |
|21/04/2020 | rain | 7 | 3 |
## Suivi des data coronavirus
```{r }
setwd("C:/Users/hraynal/EspaceTravailBadet/FORMATION_PERSO/2020-Reproductibilite/moocrr-reproducibility-study/module2/exo4")
library(ggplot2)
monDataset <- read.csv("covid19-du-2020-03-04-au-2020-03-25.csv", sep=";")
#summary(monDataset)
max(monDataset$Occitanie)
ggplot(monDataset) +
geom_point(aes(x = Date, y = Occitanie),
color = "darkgreen")
```
## Module 1: Cahier de notes cahier de laboratoire
### Nous utilisons tous des cahiers de notes, cahier de laboratoire
### Un aperçu historique de la prise de note
### Du fichier texte au langage balisage léger
- Tutoriel trés complet sur markdown et pandoc
[https://enacit.epfl.ch/cours/markdown-pandoc/]
- R Markdown: The Definitive Guide
[https://bookdown.org/yihui/rmarkdown/]
-- Exemple Rmarkdown généré avec Rstudio[https://app-learninglab.inria.fr/moocrr/gitlab/moocrr-session3/moocrr-reproducibility-study/blob/master/testmarkdown.Rmd] - (Fichier html généré avec R studio)[SortieTestRmarkdown.html]
-- Résultat en html, fichier html généré avec Rstudio [https://app-learninglab.inria.fr/moocrr/gitlab/moocrr-session3/moocrr-reproducibility-study/blob/master/SortieTestRmarkdown.html]
- Pandoc sur mon PC:
-- installation sur poste de travail, puis ouvrir ligne de commande
```
C:\Users\hraynal\EspaceTravailBadet\FORMATION_PERSO\2020-Reproductibilite>pandoc -o carnet.pdf journalHelene31.md
```
### Pérennité et évolutivité des notes avec gitlab
- question sur client git pour windows:
*Trois outils sont proposés en semaine 2. Les trois outils permettent d’utiliser Git.
La solution avec RStudio me semble la plus simple à mettre en œuvre : RStudio / Utiliser Git avec RStudio (cf. onglet 3. RStudio : installation, documentation).*
- Manip à faire pour versionner avec git depuis RStudio
<<<<<<< HEAD
-- Créer un projet
-- (Bon tutoriel pour installation) [https://jennybc.github.io/2014-05-12-ubc/ubc-r/session03_git.html]
-- (Autre tuto envoyé par Eric)[happygitwithr.com/]
-- Pb "git: 'credential-cache' is not a git command" Faire:To remove the message, "git: 'credential-cache' is not a git command.", run "git config --global --unset credential.helper"
-- Depuis l'interface : cocher à droite le fichier dont on veut faire le commit
-- Bouton en haut "Git"
-- Commit - compléter le message de commit
-- Push
-- Pb je n'arrivais pas à le faire en utilisant l'interface graphique car au départ il y avait des accents dans le nom du fichier. Je le fais en ligne de commande: git commit fichier, git push
-- Pb j'ai l'impression qu'il faut que je sois connectée à gitlab, et que j'ai fait un Save As du fichier.
-- Créer un projet
-- (Bon tutoriel pour installation) [https://jennybc.github.io/2014-05-12-ubc/ubc-r/session03_git.html]
-- Pb "git: 'credential-cache' is not a git command" Faire:To remove the message, "git: 'credential-cache' is not a git command.", run "git config --global --unset credential.helper"
-- Depuis l'interface : cocher à droite le fichier dont on veut faire le commit
-- Bouton en haut "Git"
-- Commit
-- Push
-- Pb je n'arrive pas à le faire en utilisant l'interface graphique. Je le fais en ligne de commande:
--- git commit fichier Puis git push
### les étiquettes et logiciel d'indexation pour s'y retrouver
### Supports de cours
### exercices
\ No newline at end of file
module2/exo5/exo5_R_en.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analysis of the risk of failure of the O-rings on the Challenger shuttle"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On January 27, 1986, the day before the takeoff of the shuttle _Challenger_, had\n",
"a three-hour teleconference was held between \n",
"Morton Thiokol (the manufacturer of one of the engines) and NASA. The\n",
"discussion focused on the consequences of the\n",
"temperature at take-off of 31°F (just below\n",
"0°C) for the success of the flight and in particular on the performance of the\n",
"O-rings used in the engines. Indeed, no test\n",
"had been performed at this temperature.\n",
"\n",
"The following study takes up some of the analyses carried out that\n",
"night with the objective of assessing the potential influence of\n",
"the temperature and pressure to which the O-rings are subjected\n",
"on their probability of malfunction. Our starting point is \n",
"the results of the experiments carried out by NASA engineers\n",
"during the six years preceding the launch of the shuttle\n",
"Challenger."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loading the data\n",
"We start by loading this data:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<caption>A data.frame: 23 × 5</caption>\n",
"<thead>\n",
"\t<tr><th scope=col>Date</th><th scope=col>Count</th><th scope=col>Temperature</th><th scope=col>Pressure</th><th scope=col>Malfunction</th></tr>\n",
"\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
"</thead>\n",
"<tbody>\n",
"\t<tr><td>4/12/81 </td><td>6</td><td>66</td><td> 50</td><td>0</td></tr>\n",
"\t<tr><td>11/12/81 </td><td>6</td><td>70</td><td> 50</td><td>1</td></tr>\n",
"\t<tr><td>3/22/82 </td><td>6</td><td>69</td><td> 50</td><td>0</td></tr>\n",
"\t<tr><td>11/11/82 </td><td>6</td><td>68</td><td> 50</td><td>0</td></tr>\n",
"\t<tr><td>4/04/83 </td><td>6</td><td>67</td><td> 50</td><td>0</td></tr>\n",
"\t<tr><td>6/18/82 </td><td>6</td><td>72</td><td> 50</td><td>0</td></tr>\n",
"\t<tr><td>8/30/83 </td><td>6</td><td>73</td><td>100</td><td>0</td></tr>\n",
"\t<tr><td>11/28/83 </td><td>6</td><td>70</td><td>100</td><td>0</td></tr>\n",
"\t<tr><td>2/03/84 </td><td>6</td><td>57</td><td>200</td><td>1</td></tr>\n",
"\t<tr><td>4/06/84 </td><td>6</td><td>63</td><td>200</td><td>1</td></tr>\n",
"\t<tr><td>8/30/84 </td><td>6</td><td>70</td><td>200</td><td>1</td></tr>\n",
"\t<tr><td>10/05/84 </td><td>6</td><td>78</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>11/08/84 </td><td>6</td><td>67</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>1/24/85 </td><td>6</td><td>53</td><td>200</td><td>2</td></tr>\n",
"\t<tr><td>4/12/85 </td><td>6</td><td>67</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>4/29/85 </td><td>6</td><td>75</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>6/17/85 </td><td>6</td><td>70</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>7/29/85</td><td>6</td><td>81</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>8/27/85 </td><td>6</td><td>76</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>10/03/85 </td><td>6</td><td>79</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>10/30/85 </td><td>6</td><td>75</td><td>200</td><td>2</td></tr>\n",
"\t<tr><td>11/26/85 </td><td>6</td><td>76</td><td>200</td><td>0</td></tr>\n",
"\t<tr><td>1/12/86 </td><td>6</td><td>58</td><td>200</td><td>1</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"A data.frame: 23 × 5\n",
"\\begin{tabular}{r|lllll}\n",
" Date & Count & Temperature & Pressure & Malfunction\\\\\n",
" <fct> & <int> & <int> & <int> & <int>\\\\\n",
"\\hline\n",
"\t 4/12/81 & 6 & 66 & 50 & 0\\\\\n",
"\t 11/12/81 & 6 & 70 & 50 & 1\\\\\n",
"\t 3/22/82 & 6 & 69 & 50 & 0\\\\\n",
"\t 11/11/82 & 6 & 68 & 50 & 0\\\\\n",
"\t 4/04/83 & 6 & 67 & 50 & 0\\\\\n",
"\t 6/18/82 & 6 & 72 & 50 & 0\\\\\n",
"\t 8/30/83 & 6 & 73 & 100 & 0\\\\\n",
"\t 11/28/83 & 6 & 70 & 100 & 0\\\\\n",
"\t 2/03/84 & 6 & 57 & 200 & 1\\\\\n",
"\t 4/06/84 & 6 & 63 & 200 & 1\\\\\n",
"\t 8/30/84 & 6 & 70 & 200 & 1\\\\\n",
"\t 10/05/84 & 6 & 78 & 200 & 0\\\\\n",
"\t 11/08/84 & 6 & 67 & 200 & 0\\\\\n",
"\t 1/24/85 & 6 & 53 & 200 & 2\\\\\n",
"\t 4/12/85 & 6 & 67 & 200 & 0\\\\\n",
"\t 4/29/85 & 6 & 75 & 200 & 0\\\\\n",
"\t 6/17/85 & 6 & 70 & 200 & 0\\\\\n",
"\t 7/29/85 & 6 & 81 & 200 & 0\\\\\n",
"\t 8/27/85 & 6 & 76 & 200 & 0\\\\\n",
"\t 10/03/85 & 6 & 79 & 200 & 0\\\\\n",
"\t 10/30/85 & 6 & 75 & 200 & 2\\\\\n",
"\t 11/26/85 & 6 & 76 & 200 & 0\\\\\n",
"\t 1/12/86 & 6 & 58 & 200 & 1\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 23 × 5\n",
"\n",
"| Date &lt;fct&gt; | Count &lt;int&gt; | Temperature &lt;int&gt; | Pressure &lt;int&gt; | Malfunction &lt;int&gt; |\n",
"|---|---|---|---|---|\n",
"| 4/12/81 | 6 | 66 | 50 | 0 |\n",
"| 11/12/81 | 6 | 70 | 50 | 1 |\n",
"| 3/22/82 | 6 | 69 | 50 | 0 |\n",
"| 11/11/82 | 6 | 68 | 50 | 0 |\n",
"| 4/04/83 | 6 | 67 | 50 | 0 |\n",
"| 6/18/82 | 6 | 72 | 50 | 0 |\n",
"| 8/30/83 | 6 | 73 | 100 | 0 |\n",
"| 11/28/83 | 6 | 70 | 100 | 0 |\n",
"| 2/03/84 | 6 | 57 | 200 | 1 |\n",
"| 4/06/84 | 6 | 63 | 200 | 1 |\n",
"| 8/30/84 | 6 | 70 | 200 | 1 |\n",
"| 10/05/84 | 6 | 78 | 200 | 0 |\n",
"| 11/08/84 | 6 | 67 | 200 | 0 |\n",
"| 1/24/85 | 6 | 53 | 200 | 2 |\n",
"| 4/12/85 | 6 | 67 | 200 | 0 |\n",
"| 4/29/85 | 6 | 75 | 200 | 0 |\n",
"| 6/17/85 | 6 | 70 | 200 | 0 |\n",
"| 7/29/85 | 6 | 81 | 200 | 0 |\n",
"| 8/27/85 | 6 | 76 | 200 | 0 |\n",
"| 10/03/85 | 6 | 79 | 200 | 0 |\n",
"| 10/30/85 | 6 | 75 | 200 | 2 |\n",
"| 11/26/85 | 6 | 76 | 200 | 0 |\n",
"| 1/12/86 | 6 | 58 | 200 | 1 |\n",
"\n"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"1 4/12/81 6 66 50 0 \n",
"2 11/12/81 6 70 50 1 \n",
"3 3/22/82 6 69 50 0 \n",
"4 11/11/82 6 68 50 0 \n",
"5 4/04/83 6 67 50 0 \n",
"6 6/18/82 6 72 50 0 \n",
"7 8/30/83 6 73 100 0 \n",
"8 11/28/83 6 70 100 0 \n",
"9 2/03/84 6 57 200 1 \n",
"10 4/06/84 6 63 200 1 \n",
"11 8/30/84 6 70 200 1 \n",
"12 10/05/84 6 78 200 0 \n",
"13 11/08/84 6 67 200 0 \n",
"14 1/24/85 6 53 200 2 \n",
"15 4/12/85 6 67 200 0 \n",
"16 4/29/85 6 75 200 0 \n",
"17 6/17/85 6 70 200 0 \n",
"18 7/29/85 6 81 200 0 \n",
"19 8/27/85 6 76 200 0 \n",
"20 10/03/85 6 79 200 0 \n",
"21 10/30/85 6 75 200 2 \n",
"22 11/26/85 6 76 200 0 \n",
"23 1/12/86 6 58 200 1 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = read.csv(\"shuttle.csv\",header=T)\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data set shows us the date of each test, the number of O-rings (there are 6 on the main launcher), the temperature (in Fahrenheit) and pressure (in psi), and finally the number of identified malfunctions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Graphical inspection\n",
"Flights without incidents do not provide any information\n",
"on the influence of temperature or pressure on malfunction.\n",
"We thus focus on the experiments in which at least one O-ring\n",
"was defective."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<caption>A data.frame: 7 × 5</caption>\n",
"<thead>\n",
"\t<tr><th></th><th scope=col>Date</th><th scope=col>Count</th><th scope=col>Temperature</th><th scope=col>Pressure</th><th scope=col>Malfunction</th></tr>\n",
"\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
"</thead>\n",
"<tbody>\n",
"\t<tr><th scope=row>2</th><td>11/12/81</td><td>6</td><td>70</td><td> 50</td><td>1</td></tr>\n",
"\t<tr><th scope=row>9</th><td>2/03/84 </td><td>6</td><td>57</td><td>200</td><td>1</td></tr>\n",
"\t<tr><th scope=row>10</th><td>4/06/84 </td><td>6</td><td>63</td><td>200</td><td>1</td></tr>\n",
"\t<tr><th scope=row>11</th><td>8/30/84 </td><td>6</td><td>70</td><td>200</td><td>1</td></tr>\n",
"\t<tr><th scope=row>14</th><td>1/24/85 </td><td>6</td><td>53</td><td>200</td><td>2</td></tr>\n",
"\t<tr><th scope=row>21</th><td>10/30/85</td><td>6</td><td>75</td><td>200</td><td>2</td></tr>\n",
"\t<tr><th scope=row>23</th><td>1/12/86 </td><td>6</td><td>58</td><td>200</td><td>1</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"A data.frame: 7 × 5\n",
"\\begin{tabular}{r|lllll}\n",
" & Date & Count & Temperature & Pressure & Malfunction\\\\\n",
" & <fct> & <int> & <int> & <int> & <int>\\\\\n",
"\\hline\n",
"\t2 & 11/12/81 & 6 & 70 & 50 & 1\\\\\n",
"\t9 & 2/03/84 & 6 & 57 & 200 & 1\\\\\n",
"\t10 & 4/06/84 & 6 & 63 & 200 & 1\\\\\n",
"\t11 & 8/30/84 & 6 & 70 & 200 & 1\\\\\n",
"\t14 & 1/24/85 & 6 & 53 & 200 & 2\\\\\n",
"\t21 & 10/30/85 & 6 & 75 & 200 & 2\\\\\n",
"\t23 & 1/12/86 & 6 & 58 & 200 & 1\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 7 × 5\n",
"\n",
"| <!--/--> | Date &lt;fct&gt; | Count &lt;int&gt; | Temperature &lt;int&gt; | Pressure &lt;int&gt; | Malfunction &lt;int&gt; |\n",
"|---|---|---|---|---|---|\n",
"| 2 | 11/12/81 | 6 | 70 | 50 | 1 |\n",
"| 9 | 2/03/84 | 6 | 57 | 200 | 1 |\n",
"| 10 | 4/06/84 | 6 | 63 | 200 | 1 |\n",
"| 11 | 8/30/84 | 6 | 70 | 200 | 1 |\n",
"| 14 | 1/24/85 | 6 | 53 | 200 | 2 |\n",
"| 21 | 10/30/85 | 6 | 75 | 200 | 2 |\n",
"| 23 | 1/12/86 | 6 | 58 | 200 | 1 |\n",
"\n"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"2 11/12/81 6 70 50 1 \n",
"9 2/03/84 6 57 200 1 \n",
"10 4/06/84 6 63 200 1 \n",
"11 8/30/84 6 70 200 1 \n",
"14 1/24/85 6 53 200 2 \n",
"21 10/30/85 6 75 200 2 \n",
"23 1/12/86 6 58 200 1 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = data[data$Malfunction>0,]\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have a high temperature variability but\n",
"the pressure is almost always 200, which should\n",
"simplify the analysis.\n",
"\n",
"How does the frequency of failure vary with temperature?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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9cvK3J/KJoojpBgGU8hPWUuPpxcfTnU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\nRTZ+AAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At first glance, the dependence does not look very important, but let's try to\n",
"estimate the impact of temperature $t$ on the probability of O-ring malfunction."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation of the temperature influence\n",
"\n",
"Suppose that each of the six O-rings is damaged with the same\n",
"probability and independently of the others and that this probability\n",
"depends only on the temperature. If $p(t)$ is this probability, the\n",
"number $D$ of malfunctioning O-rings during a flight at\n",
"temperature $t$ follows a binomial law with parameters $n=6$ and\n",
"$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a\n",
"logistic regression."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = Malfunction/Count ~ Temperature, family = binomial(link = \"logit\"), \n",
" data = data, weights = Count)\n",
"\n",
"Deviance Residuals: \n",
" 2 9 10 11 14 21 23 \n",
"-0.3015 -0.2836 -0.2919 -0.3015 0.6891 0.6560 -0.2850 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|)\n",
"(Intercept) -1.389528 3.195752 -0.435 0.664\n",
"Temperature 0.001416 0.049773 0.028 0.977\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 1.3347 on 6 degrees of freedom\n",
"Residual deviance: 1.3339 on 5 degrees of freedom\n",
"AIC: 18.894\n",
"\n",
"Number of Fisher Scoring iterations: 4\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count, \n",
" family=binomial(link='logit'))\n",
"summary(logistic_reg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The most likely estimator of the temperature parameter is 0.0014\n",
"and the standard error of this estimator is 0.122, in other words we\n",
"cannot distinguish any particular impact and we must take our\n",
"estimates with caution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation of the probability of O-ring malfunction\n",
"\n",
"The expected temperature on the take-off day is 31°F. Let's try to\n",
"estimate the probability of O-ring malfunction at\n",
"this temperature from the model we just built:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tempv = seq(from=30, to=90, by = .5)\n",
"rmv <- predict(logistic_reg,list(Temperature=tempv),type=\"response\")\n",
"plot(tempv,rmv,type=\"l\",ylim=c(0,1))\n",
"points(data=data, Malfunction/Count ~ Temperature)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"As expected from the initial data, the\n",
"temperature has no significant impact on the probability of failure of the\n",
"O-rings. It will be about 0.2, as in the tests\n",
"where we had a failure of at least one joint. Let's get back\n",
"to the initial dataset to estimate the probability of failure:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"0.0652173913043478"
],
"text/latex": [
"0.0652173913043478"
],
"text/markdown": [
"0.0652173913043478"
],
"text/plain": [
"[1] 0.06521739"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data_full = read.csv(\"shuttle.csv\",header=T)\n",
"sum(data_full$Malfunction)/sum(data_full$Count)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This probability is thus about $p=0.065$. Knowing that there is\n",
"a primary and a secondary O-ring on each of the three parts of the\n",
"launcher, the probability of failure of both joints of a launcher\n",
"is $p^2 \\approx 0.00425$. The probability of failure of any one of the\n",
"launchers is $1-(1-p^2)^3 \\approx 1.2\\%$. That would really be\n",
"bad luck.... Everything is under control, so the takeoff can happen\n",
"tomorrow as planned.\n",
"\n",
"But the next day, the Challenger shuttle exploded and took away\n",
"with her the seven crew members. The public was shocked and in\n",
"the subsequent investigation, the reliability of the\n",
"O-rings was questioned. Beyond the internal communication problems\n",
"of NASA, which have a lot to do with this fiasco, the previous analysis\n",
"includes (at least) a small problem.... Can you find it?\n",
"You are free to modify this analysis and to look at this dataset\n",
"from all angles in order to to explain what's wrong."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"celltoolbar": "Hide code",
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo5/exo5_R_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Analysis of the risk of failure of the O-rings on the Challenger shuttle
#+AUTHOR: Arnaud Legrand
#+LANGUAGE: en
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
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#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
#+LATEX_HEADER: \usepackage[utf8]{inputenc}
#+LATEX_HEADER: \usepackage[T1]{fontenc}
#+LATEX_HEADER: \usepackage[a4paper,margin=.8in]{geometry}
#+LATEX_HEADER: \usepackage[french]{babel}
# #+PROPERTY: header-args :session :exports both
On January 27, 1986, the day before the takeoff of the shuttle /Challenger/, had
a three-hour teleconference was held between
Morton Thiokol (the manufacturer of one of the engines) and NASA. The
discussion focused on the consequences of the
temperature at take-off of 31°F (just below
0°C) for the success of the flight and in particular on the performance of the
O-rings used in the engines. Indeed, no test
had been performed at this temperature.
The following study takes up some of the analyses carried out that
night with the objective of assessing the potential influence of
the temperature and pressure to which the O-rings are subjected
on their probability of malfunction. Our starting point is
the results of the experiments carried out by NASA engineers
during the six years preceding the launch of the shuttle
Challenger.
* Loading the data
We start by loading this data:
#+begin_src R :results output :session *R* :exports both
data = read.csv("shuttle.csv",header=T)
data
#+end_src
#+RESULTS:
#+begin_example
Date Count Temperature Pressure Malfunction
1 4/12/81 6 66 50 0
2 11/12/81 6 70 50 1
3 3/22/82 6 69 50 0
4 11/11/82 6 68 50 0
5 4/04/83 6 67 50 0
6 6/18/82 6 72 50 0
7 8/30/83 6 73 100 0
8 11/28/83 6 70 100 0
9 2/03/84 6 57 200 1
10 4/06/84 6 63 200 1
11 8/30/84 6 70 200 1
12 10/05/84 6 78 200 0
13 11/08/84 6 67 200 0
14 1/24/85 6 53 200 2
15 4/12/85 6 67 200 0
16 4/29/85 6 75 200 0
17 6/17/85 6 70 200 0
18 7/29/85 6 81 200 0
19 8/27/85 6 76 200 0
20 10/03/85 6 79 200 0
21 10/30/85 6 75 200 2
22 11/26/85 6 76 200 0
23 1/12/86 6 58 200 1
#+end_example
The data set shows us the date of each test, the number of O-rings
(there are 6 on the main launcher), the
temperature (in Fahrenheit) and pressure (in psi), and finally the
number of identified malfunctions.
* Graphical inspection
Flights without incidents do not provide any information
on the influence of temperature or pressure on malfunction.
We thus focus on the experiments in which at least one O-ring was defective.
#+begin_src R :results output :session *R* :exports both
data = data[data$Malfunction>0,]
data
#+end_src
#+RESULTS:
: Date Count Temperature Pressure Malfunction
: 2 11/12/81 6 70 50 1
: 9 2/03/84 6 57 200 1
: 10 4/06/84 6 63 200 1
: 11 8/30/84 6 70 200 1
: 14 1/24/85 6 53 200 2
: 21 10/30/85 6 75 200 2
: 23 1/12/86 6 58 200 1
We have a high temperature variability but
the pressure is almost always 200, which should
simplify the analysis.
How does the frequency of failure vary with temperature?
#+begin_src R :results output graphics :file "freq_temp.png" :exports both :width 600 :height 400 :session *R*
plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))
#+end_src
#+RESULTS:
[[file:freq_temp.png]]
At first glance, the dependence does not look very important, but let's try to
estimate the impact of temperature $t$ on the probability of O-ring malfunction.
* Estimation of the temperature influence
Suppose that each of the six O-rings is damaged with the same
probability and independently of the others and that this probability
depends only on the temperature. If $p(t)$ is this probability, the
number $D$ of malfunctioning O-rings during a flight at
temperature $t$ follows a binomial law with parameters $n=6$ and
$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a
logistic regression.
#+begin_src R :results output :session *R* :exports both
logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count,
family=binomial(link='logit'))
summary(logistic_reg)
#+end_src
#+RESULTS:
#+begin_example
Call:
glm(formula = Malfunction/Count ~ Temperature, family = binomial(link = "logit"),
data = data, weights = Count)
Deviance Residuals:
2 9 10 11 14 21 23
-0.3015 -0.2836 -0.2919 -0.3015 0.6891 0.6560 -0.2850
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.389528 3.195752 -0.435 0.664
Temperature 0.001416 0.049773 0.028 0.977
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1.3347 on 6 degrees of freedom
Residual deviance: 1.3339 on 5 degrees of freedom
AIC: 18.894
Number of Fisher Scoring iterations: 4
#+end_example
The most likely estimator of the temperature parameter is 0.001416
and the standard error of this estimator is 0.049, in other words we
cannot distinguish any particular impact and we must take our
estimates with caution.
* Estimation of the probability of O-ring malfunction
The expected temperature on the take-off day is 31°F. Let's try to
estimate the probability of O-ring malfunction at
this temperature from the model we just built:
#+begin_src R :results output graphics :file "proba_estimate.png" :exports both :width 600 :height 400 :session *R*
# shuttle=shuttle[shuttle$r!=0,]
tempv = seq(from=30, to=90, by = .5)
rmv <- predict(logistic_reg,list(Temperature=tempv),type="response")
plot(tempv,rmv,type="l",ylim=c(0,1))
points(data=data, Malfunction/Count ~ Temperature)
#+end_src
#+RESULTS:
[[file:proba_estimate.png]]
As expected from the initial data, the
temperature has no significant impact on the probability of failure of the
O-rings. It will be about 0.2, as in the tests
where we had a failure of at least one joint. Let's get back to the initial dataset to estimate the probability of failure:
#+begin_src R :results output :session *R* :exports both
data_full = read.csv("shuttle.csv",header=T)
sum(data_full$Malfunction)/sum(data_full$Count)
#+end_src
#+RESULTS:
: [1] 0.06521739
This probability is thus about $p=0.065$. Knowing that there is
a primary and a secondary O-ring on each of the three parts of the
launcher, the probability of failure of both joints of a launcher
is $p^2 \approx 0.00425$. The probability of failure of any one of the
launchers is $1-(1-p^2)^3 \approx 1.2%$. That would really be
bad luck.... Everything is under control, so the takeoff can happen
tomorrow as planned.
But the next day, the Challenger shuttle exploded and took away
with her the seven crew members. The public was shocked and in
the subsequent investigation, the reliability of the
O-rings was questioned. Beyond the internal communication problems
of NASA, which have a lot to do with this fiasco, the previous analysis
includes (at least) a small problem.... Can you find it?
You are free to modify this analysis and to look at this dataset
from all angles in order to to explain what's wrong.
module2/exo5/exo5_R_fr.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analyse du risque de défaillance des joints toriques de la navette Challenger"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le 27 Janvier 1986, veille du décollage de la navette _Challenger_, eu\n",
"lieu une télé-conférence de trois heures entre les ingénieurs de la\n",
"Morton Thiokol (constructeur d'un des moteurs) et de la NASA. La\n",
"discussion portait principalement sur les conséquences de la\n",
"température prévue au moment du décollage de 31°F (juste en dessous de\n",
"0°C) sur le succès du vol et en particulier sur la performance des\n",
"joints toriques utilisés dans les moteurs. En effet, aucun test\n",
"n'avait été effectué à cette température.\n",
"\n",
"L'étude qui suit reprend donc une partie des analyses effectuées cette\n",
"nuit là et dont l'objectif était d'évaluer l'influence potentielle de\n",
"la température et de la pression à laquelle sont soumis les joints\n",
"toriques sur leur probabilité de dysfonctionnement. Pour cela, nous\n",
"disposons des résultats des expériences réalisées par les ingénieurs\n",
"de la NASA durant les 6 années précédant le lancement de la navette\n",
"Challenger."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Chargement des données\n",
"Nous commençons donc par charger ces données :"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<thead><tr><th scope=col>Date</th><th scope=col>Count</th><th scope=col>Temperature</th><th scope=col>Pressure</th><th scope=col>Malfunction</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td>4/12/81 </td><td>6 </td><td>66 </td><td> 50 </td><td>0 </td></tr>\n",
"\t<tr><td>11/12/81</td><td>6 </td><td>70 </td><td> 50 </td><td>1 </td></tr>\n",
"\t<tr><td>3/22/82 </td><td>6 </td><td>69 </td><td> 50 </td><td>0 </td></tr>\n",
"\t<tr><td>11/11/82</td><td>6 </td><td>68 </td><td> 50 </td><td>0 </td></tr>\n",
"\t<tr><td>4/04/83 </td><td>6 </td><td>67 </td><td> 50 </td><td>0 </td></tr>\n",
"\t<tr><td>6/18/82 </td><td>6 </td><td>72 </td><td> 50 </td><td>0 </td></tr>\n",
"\t<tr><td>8/30/83 </td><td>6 </td><td>73 </td><td>100 </td><td>0 </td></tr>\n",
"\t<tr><td>11/28/83</td><td>6 </td><td>70 </td><td>100 </td><td>0 </td></tr>\n",
"\t<tr><td>2/03/84 </td><td>6 </td><td>57 </td><td>200 </td><td>1 </td></tr>\n",
"\t<tr><td>4/06/84 </td><td>6 </td><td>63 </td><td>200 </td><td>1 </td></tr>\n",
"\t<tr><td>8/30/84 </td><td>6 </td><td>70 </td><td>200 </td><td>1 </td></tr>\n",
"\t<tr><td>10/05/84</td><td>6 </td><td>78 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>11/08/84</td><td>6 </td><td>67 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>1/24/85 </td><td>6 </td><td>53 </td><td>200 </td><td>2 </td></tr>\n",
"\t<tr><td>4/12/85 </td><td>6 </td><td>67 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>4/29/85 </td><td>6 </td><td>75 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>6/17/85 </td><td>6 </td><td>70 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>7/29/85 </td><td>6 </td><td>81 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>8/27/85 </td><td>6 </td><td>76 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>10/03/85</td><td>6 </td><td>79 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>10/30/85</td><td>6 </td><td>75 </td><td>200 </td><td>2 </td></tr>\n",
"\t<tr><td>11/26/85</td><td>6 </td><td>76 </td><td>200 </td><td>0 </td></tr>\n",
"\t<tr><td>1/12/86 </td><td>6 </td><td>58 </td><td>200 </td><td>1 </td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"\\begin{tabular}{r|lllll}\n",
" Date & Count & Temperature & Pressure & Malfunction\\\\\n",
"\\hline\n",
"\t 4/12/81 & 6 & 66 & 50 & 0 \\\\\n",
"\t 11/12/81 & 6 & 70 & 50 & 1 \\\\\n",
"\t 3/22/82 & 6 & 69 & 50 & 0 \\\\\n",
"\t 11/11/82 & 6 & 68 & 50 & 0 \\\\\n",
"\t 4/04/83 & 6 & 67 & 50 & 0 \\\\\n",
"\t 6/18/82 & 6 & 72 & 50 & 0 \\\\\n",
"\t 8/30/83 & 6 & 73 & 100 & 0 \\\\\n",
"\t 11/28/83 & 6 & 70 & 100 & 0 \\\\\n",
"\t 2/03/84 & 6 & 57 & 200 & 1 \\\\\n",
"\t 4/06/84 & 6 & 63 & 200 & 1 \\\\\n",
"\t 8/30/84 & 6 & 70 & 200 & 1 \\\\\n",
"\t 10/05/84 & 6 & 78 & 200 & 0 \\\\\n",
"\t 11/08/84 & 6 & 67 & 200 & 0 \\\\\n",
"\t 1/24/85 & 6 & 53 & 200 & 2 \\\\\n",
"\t 4/12/85 & 6 & 67 & 200 & 0 \\\\\n",
"\t 4/29/85 & 6 & 75 & 200 & 0 \\\\\n",
"\t 6/17/85 & 6 & 70 & 200 & 0 \\\\\n",
"\t 7/29/85 & 6 & 81 & 200 & 0 \\\\\n",
"\t 8/27/85 & 6 & 76 & 200 & 0 \\\\\n",
"\t 10/03/85 & 6 & 79 & 200 & 0 \\\\\n",
"\t 10/30/85 & 6 & 75 & 200 & 2 \\\\\n",
"\t 11/26/85 & 6 & 76 & 200 & 0 \\\\\n",
"\t 1/12/86 & 6 & 58 & 200 & 1 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"Date | Count | Temperature | Pressure | Malfunction | \n",
"|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
"| 4/12/81 | 6 | 66 | 50 | 0 | \n",
"| 11/12/81 | 6 | 70 | 50 | 1 | \n",
"| 3/22/82 | 6 | 69 | 50 | 0 | \n",
"| 11/11/82 | 6 | 68 | 50 | 0 | \n",
"| 4/04/83 | 6 | 67 | 50 | 0 | \n",
"| 6/18/82 | 6 | 72 | 50 | 0 | \n",
"| 8/30/83 | 6 | 73 | 100 | 0 | \n",
"| 11/28/83 | 6 | 70 | 100 | 0 | \n",
"| 2/03/84 | 6 | 57 | 200 | 1 | \n",
"| 4/06/84 | 6 | 63 | 200 | 1 | \n",
"| 8/30/84 | 6 | 70 | 200 | 1 | \n",
"| 10/05/84 | 6 | 78 | 200 | 0 | \n",
"| 11/08/84 | 6 | 67 | 200 | 0 | \n",
"| 1/24/85 | 6 | 53 | 200 | 2 | \n",
"| 4/12/85 | 6 | 67 | 200 | 0 | \n",
"| 4/29/85 | 6 | 75 | 200 | 0 | \n",
"| 6/17/85 | 6 | 70 | 200 | 0 | \n",
"| 7/29/85 | 6 | 81 | 200 | 0 | \n",
"| 8/27/85 | 6 | 76 | 200 | 0 | \n",
"| 10/03/85 | 6 | 79 | 200 | 0 | \n",
"| 10/30/85 | 6 | 75 | 200 | 2 | \n",
"| 11/26/85 | 6 | 76 | 200 | 0 | \n",
"| 1/12/86 | 6 | 58 | 200 | 1 | \n",
"\n",
"\n"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"1 4/12/81 6 66 50 0 \n",
"2 11/12/81 6 70 50 1 \n",
"3 3/22/82 6 69 50 0 \n",
"4 11/11/82 6 68 50 0 \n",
"5 4/04/83 6 67 50 0 \n",
"6 6/18/82 6 72 50 0 \n",
"7 8/30/83 6 73 100 0 \n",
"8 11/28/83 6 70 100 0 \n",
"9 2/03/84 6 57 200 1 \n",
"10 4/06/84 6 63 200 1 \n",
"11 8/30/84 6 70 200 1 \n",
"12 10/05/84 6 78 200 0 \n",
"13 11/08/84 6 67 200 0 \n",
"14 1/24/85 6 53 200 2 \n",
"15 4/12/85 6 67 200 0 \n",
"16 4/29/85 6 75 200 0 \n",
"17 6/17/85 6 70 200 0 \n",
"18 7/29/85 6 81 200 0 \n",
"19 8/27/85 6 76 200 0 \n",
"20 10/03/85 6 79 200 0 \n",
"21 10/30/85 6 75 200 2 \n",
"22 11/26/85 6 76 200 0 \n",
"23 1/12/86 6 58 200 1 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = read.csv(\"shuttle.csv\",header=T)\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le jeu de données nous indique la date de l'essai, le nombre de joints\n",
"toriques mesurés (il y en a 6 sur le lançeur principal), la\n",
"température (en Farenheit) et la pression (en psi), et enfin le\n",
"nombre de dysfonctionnements relevés."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inspection graphique des données\n",
"Les vols où aucun incident n'est relevé n'apportant aucun information\n",
"sur l'influence de la température ou de la pression sur les\n",
"dysfonctionnements, nous nous concentrons sur les expériences où au\n",
"moins un joint a été défectueux."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table>\n",
"<caption>A data.frame: 7 × 5</caption>\n",
"<thead>\n",
"\t<tr><th></th><th scope=col>Date</th><th scope=col>Count</th><th scope=col>Temperature</th><th scope=col>Pressure</th><th scope=col>Malfunction</th></tr>\n",
"\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
"</thead>\n",
"<tbody>\n",
"\t<tr><th scope=row>2</th><td>11/12/81</td><td>6</td><td>70</td><td> 50</td><td>1</td></tr>\n",
"\t<tr><th scope=row>9</th><td>2/03/84 </td><td>6</td><td>57</td><td>200</td><td>1</td></tr>\n",
"\t<tr><th scope=row>10</th><td>4/06/84 </td><td>6</td><td>63</td><td>200</td><td>1</td></tr>\n",
"\t<tr><th scope=row>11</th><td>8/30/84 </td><td>6</td><td>70</td><td>200</td><td>1</td></tr>\n",
"\t<tr><th scope=row>14</th><td>1/24/85 </td><td>6</td><td>53</td><td>200</td><td>2</td></tr>\n",
"\t<tr><th scope=row>21</th><td>10/30/85</td><td>6</td><td>75</td><td>200</td><td>2</td></tr>\n",
"\t<tr><th scope=row>23</th><td>1/12/86 </td><td>6</td><td>58</td><td>200</td><td>1</td></tr>\n",
"</tbody>\n",
"</table>\n"
],
"text/latex": [
"A data.frame: 7 × 5\n",
"\\begin{tabular}{r|lllll}\n",
" & Date & Count & Temperature & Pressure & Malfunction\\\\\n",
" & <fct> & <int> & <int> & <int> & <int>\\\\\n",
"\\hline\n",
"\t2 & 11/12/81 & 6 & 70 & 50 & 1\\\\\n",
"\t9 & 2/03/84 & 6 & 57 & 200 & 1\\\\\n",
"\t10 & 4/06/84 & 6 & 63 & 200 & 1\\\\\n",
"\t11 & 8/30/84 & 6 & 70 & 200 & 1\\\\\n",
"\t14 & 1/24/85 & 6 & 53 & 200 & 2\\\\\n",
"\t21 & 10/30/85 & 6 & 75 & 200 & 2\\\\\n",
"\t23 & 1/12/86 & 6 & 58 & 200 & 1\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"A data.frame: 7 × 5\n",
"\n",
"| <!--/--> | Date &lt;fct&gt; | Count &lt;int&gt; | Temperature &lt;int&gt; | Pressure &lt;int&gt; | Malfunction &lt;int&gt; |\n",
"|---|---|---|---|---|---|\n",
"| 2 | 11/12/81 | 6 | 70 | 50 | 1 |\n",
"| 9 | 2/03/84 | 6 | 57 | 200 | 1 |\n",
"| 10 | 4/06/84 | 6 | 63 | 200 | 1 |\n",
"| 11 | 8/30/84 | 6 | 70 | 200 | 1 |\n",
"| 14 | 1/24/85 | 6 | 53 | 200 | 2 |\n",
"| 21 | 10/30/85 | 6 | 75 | 200 | 2 |\n",
"| 23 | 1/12/86 | 6 | 58 | 200 | 1 |\n",
"\n"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"2 11/12/81 6 70 50 1 \n",
"9 2/03/84 6 57 200 1 \n",
"10 4/06/84 6 63 200 1 \n",
"11 8/30/84 6 70 200 1 \n",
"14 1/24/85 6 53 200 2 \n",
"21 10/30/85 6 75 200 2 \n",
"23 1/12/86 6 58 200 1 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = data[data$Malfunction>0,]\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Très bien, nous avons une variabilité de température importante mais\n",
"la pression est quasiment toujours égale à 200, ce qui devrait\n",
"simplifier l'analyse.\n",
"\n",
"Comment la fréquence d'échecs varie-t-elle avec la température ?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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9cvK3J/KJoojpBgGU8hPWUuPpxcfTnU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\nRTZ+AAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"À première vue, ce n'est pas flagrant mais bon, essayons quand même\n",
"d'estimer l'impact de la température $t$ sur la probabilité de\n",
"dysfonctionnements d'un joint."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation de l'influence de la température\n",
"\n",
"Supposons que chacun des 6 joints toriques est endommagé avec la même\n",
"probabilité et indépendamment des autres et que cette probabilité ne\n",
"dépend que de la température. Si on note $p(t)$ cette probabilité, le\n",
"nombre de joints $D$ dysfonctionnant lorsque l'on effectue le vol à\n",
"température $t$ suit une loi binomiale de paramètre $n=6$ et\n",
"$p=p(t)$. Pour relier $p(t)$ à $t$, on va donc effectuer une\n",
"régression logistique."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = Malfunction/Count ~ Temperature, family = binomial(link = \"logit\"), \n",
" data = data, weights = Count)\n",
"\n",
"Deviance Residuals: \n",
" 2 9 10 11 14 21 23 \n",
"-0.3015 -0.2836 -0.2919 -0.3015 0.6891 0.6560 -0.2850 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|)\n",
"(Intercept) -1.389528 3.195752 -0.435 0.664\n",
"Temperature 0.001416 0.049773 0.028 0.977\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 1.3347 on 6 degrees of freedom\n",
"Residual deviance: 1.3339 on 5 degrees of freedom\n",
"AIC: 18.894\n",
"\n",
"Number of Fisher Scoring iterations: 4\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count, \n",
" family=binomial(link='logit'))\n",
"summary(logistic_reg)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"L'estimateur le plus probable du paramètre de température est 0.001416\n",
"et l'erreur standard de cet estimateur est de 0.049, autrement dit on\n",
"ne peut pas distinguer d'impact particulier et il faut prendre nos\n",
"estimations avec des pincettes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation de la probabilité de dysfonctionnant des joints toriques\n",
"\n",
"La température prévue le jour du décollage est de 31°F. Essayons\n",
"d'estimer la probabilité de dysfonctionnement des joints toriques à\n",
"cette température à partir du modèle que nous venons de construire :"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tempv = seq(from=30, to=90, by = .5)\n",
"rmv <- predict(logistic_reg,list(Temperature=tempv),type=\"response\")\n",
"plot(tempv,rmv,type=\"l\",ylim=c(0,1))\n",
"points(data=data, Malfunction/Count ~ Temperature)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"Comme on pouvait s'attendre au vu des données initiales, la\n",
"température n'a pas d'impact notable sur la probabilité d'échec des\n",
"joints toriques. Elle sera d'environ 0.2, comme dans les essais\n",
"précédents où nous il y a eu défaillance d'au moins un joint. Revenons\n",
"à l'ensemble des données initiales pour estimer la probabilité de\n",
"défaillance d'un joint :"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"0.0652173913043478"
],
"text/latex": [
"0.0652173913043478"
],
"text/markdown": [
"0.0652173913043478"
],
"text/plain": [
"[1] 0.06521739"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data_full = read.csv(\"shuttle.csv\",header=T)\n",
"sum(data_full$Malfunction)/sum(data_full$Count)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cette probabilité est donc d'environ $p=0.065$, sachant qu'il existe\n",
"un joint primaire un joint secondaire sur chacune des trois parties du\n",
"lançeur, la probabilité de défaillance des deux joints d'un lançeur\n",
"est de $p^2 \\approx 0.00425$. La probabilité de défaillance d'un des\n",
"lançeur est donc de $1-(1-p^2)^3 \\approx 1.2%$. Ça serait vraiment\n",
"pas de chance... Tout est sous contrôle, le décollage peut donc avoir\n",
"lieu demain comme prévu.\n",
"\n",
"Seulement, le lendemain, la navette Challenger explosera et emportera\n",
"avec elle ses sept membres d'équipages. L'opinion publique est\n",
"fortement touchée et lors de l'enquête qui suivra, la fiabilité des\n",
"joints toriques sera directement mise en cause. Au delà des problèmes\n",
"de communication interne à la NASA qui sont pour beaucoup dans ce\n",
"fiasco, l'analyse précédente comporte (au moins) un petit\n",
"problème... Saurez-vous le trouver ? Vous êtes libre de modifier cette\n",
"analyse et de regarder ce jeu de données sous tous les angles afin\n",
"d'expliquer ce qui ne va pas."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"celltoolbar": "Hide code",
"kernelspec": {
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"name": "ir"
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"version": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo5/exo5_R_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Analyse du risque de défaillance des joints toriques de la navette Challenger
#+AUTHOR: Arnaud Legrand
#+LANGUAGE: fr
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#+LATEX_HEADER: \usepackage[utf8]{inputenc}
#+LATEX_HEADER: \usepackage[T1]{fontenc}
#+LATEX_HEADER: \usepackage[a4paper,margin=.8in]{geometry}
#+LATEX_HEADER: \usepackage[french]{babel}
# #+PROPERTY: header-args :session :exports both
Le 27 Janvier 1986, veille du décollage de la navette /Challenger/, eu
lieu une télé-conférence de trois heures entre les ingénieurs de la
Morton Thiokol (constructeur d'un des moteurs) et de la NASA. La
discussion portait principalement sur les conséquences de la
température prévue au moment du décollage de 31°F (juste en dessous de
0°C) sur le succès du vol et en particulier sur la performance des
joints toriques utilisés dans les moteurs. En effet, aucun test
n'avait été effectué à cette température.
L'étude qui suit reprend donc une partie des analyses effectuées cette
nuit là et dont l'objectif était d'évaluer l'influence potentielle de
la température et de la pression à laquelle sont soumis les joints
toriques sur leur probabilité de dysfonctionnement. Pour cela, nous
disposons des résultats des expériences réalisées par les ingénieurs
de la NASA durant les 6 années précédant le lancement de la navette
Challenger.
* Chargement des données
Nous commençons donc par charger ces données:
#+begin_src R :results output :session *R* :exports both
data = read.csv("shuttle.csv",header=T)
data
#+end_src
#+RESULTS:
#+begin_example
Date Count Temperature Pressure Malfunction
1 4/12/81 6 66 50 0
2 11/12/81 6 70 50 1
3 3/22/82 6 69 50 0
4 11/11/82 6 68 50 0
5 4/04/83 6 67 50 0
6 6/18/82 6 72 50 0
7 8/30/83 6 73 100 0
8 11/28/83 6 70 100 0
9 2/03/84 6 57 200 1
10 4/06/84 6 63 200 1
11 8/30/84 6 70 200 1
12 10/05/84 6 78 200 0
13 11/08/84 6 67 200 0
14 1/24/85 6 53 200 2
15 4/12/85 6 67 200 0
16 4/29/85 6 75 200 0
17 6/17/85 6 70 200 0
18 7/29/85 6 81 200 0
19 8/27/85 6 76 200 0
20 10/03/85 6 79 200 0
21 10/30/85 6 75 200 2
22 11/26/85 6 76 200 0
23 1/12/86 6 58 200 1
#+end_example
Le jeu de données nous indique la date de l'essai, le nombre de joints
toriques mesurés (il y en a 6 sur le lançeur principal), la
température (en Fahrenheit) et la pression (en psi), et enfin le
nombre de dysfonctionnements relevés.
* Inspection graphique des données
Les vols où aucun incident n'est relevé n'apportant aucune information
sur l'influence de la température ou de la pression sur les
dysfonctionnements, nous nous concentrons sur les expériences où au
moins un joint a été défectueux.
#+begin_src R :results output :session *R* :exports both
data = data[data$Malfunction>0,]
data
#+end_src
#+RESULTS:
: Date Count Temperature Pressure Malfunction
: 2 11/12/81 6 70 50 1
: 9 2/03/84 6 57 200 1
: 10 4/06/84 6 63 200 1
: 11 8/30/84 6 70 200 1
: 14 1/24/85 6 53 200 2
: 21 10/30/85 6 75 200 2
: 23 1/12/86 6 58 200 1
Très bien, nous avons une variabilité de température importante mais
la pression est quasiment toujours égale à 200, ce qui devrait
simplifier l'analyse.
Comment la fréquence d'échecs varie-t-elle avec la température ?
#+begin_src R :results output graphics :file "freq_temp.png" :exports both :width 600 :height 400 :session *R*
plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))
#+end_src
#+RESULTS:
[[file:freq_temp.png]]
À première vue, ce n'est pas flagrant mais bon, essayons quand même
d'estimer l'impact de la température $t$ sur la probabilité de
dysfonctionnements d'un joint.
* Estimation de l'influence de la température
Supposons que chacun des 6 joints toriques est endommagé avec la même
probabilité et indépendamment des autres et que cette probabilité ne
dépend que de la température. Si on note $p(t)$ cette probabilité, le
nombre de joints $D$ dysfonctionnant lorsque l'on effectue le vol à
température $t$ suit une loi binomiale de paramètre $n=6$ et
$p=p(t)$. Pour relier $p(t)$ à $t$, on va donc effectuer une
régression logistique.
#+begin_src R :results output :session *R* :exports both
logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count,
family=binomial(link='logit'))
summary(logistic_reg)
#+end_src
#+RESULTS:
#+begin_example
Call:
glm(formula = Malfunction/Count ~ Temperature, family = binomial(link = "logit"),
data = data, weights = Count)
Deviance Residuals:
2 9 10 11 14 21 23
-0.3015 -0.2836 -0.2919 -0.3015 0.6891 0.6560 -0.2850
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.389528 3.195752 -0.435 0.664
Temperature 0.001416 0.049773 0.028 0.977
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1.3347 on 6 degrees of freedom
Residual deviance: 1.3339 on 5 degrees of freedom
AIC: 18.894
Number of Fisher Scoring iterations: 4
#+end_example
L'estimateur le plus probable du paramètre de température est 0.001416
et l'erreur standard de cet estimateur est de 0.049, autrement dit on
ne peut pas distinguer d'impact particulier et il faut prendre nos
estimations avec des pincettes.
* Estimation de la probabilité de dysfonctionnant des joints toriques
La température prévue le jour du décollage est de 31°F. Essayons
d'estimer la probabilité de dysfonctionnement des joints toriques à
cette température à partir du modèle que nous venons de construire:
#+begin_src R :results output graphics :file "proba_estimate.png" :exports both :width 600 :height 400 :session *R*
# shuttle=shuttle[shuttle$r!=0,]
tempv = seq(from=30, to=90, by = .5)
rmv <- predict(logistic_reg,list(Temperature=tempv),type="response")
plot(tempv,rmv,type="l",ylim=c(0,1))
points(data=data, Malfunction/Count ~ Temperature)
#+end_src
#+RESULTS:
[[file:proba_estimate.png]]
Comme on pouvait s'attendre au vu des données initiales, la
température n'a pas d'impact notable sur la probabilité d'échec des
joints toriques. Elle sera d'environ 0.2, comme dans les essais
précédents où nous il y a eu défaillance d'au moins un joint. Revenons
à l'ensemble des données initiales pour estimer la probabilité de
défaillance d'un joint:
#+begin_src R :results output :session *R* :exports both
data_full = read.csv("shuttle.csv",header=T)
sum(data_full$Malfunction)/sum(data_full$Count)
#+end_src
#+RESULTS:
: [1] 0.06521739
Cette probabilité est donc d'environ $p=0.065$, sachant qu'il existe
un joint primaire un joint secondaire sur chacune des trois parties du
lançeur, la probabilité de défaillance des deux joints d'un lançeur
est de $p^2 \approx 0.00425$. La probabilité de défaillance d'un des
lançeur est donc de $1-(1-p^2)^3 \approx 1.2%$. Ça serait vraiment
pas de chance... Tout est sous contrôle, le décollage peut donc avoir
lieu demain comme prévu.
Seulement, le lendemain, la navette Challenger explosera et emportera
avec elle ses sept membres d'équipages. L'opinion publique est
fortement touchée et lors de l'enquête qui suivra, la fiabilité des
joints toriques sera directement mise en cause. Au delà des problèmes
de communication interne à la NASA qui sont pour beaucoup dans ce
fiasco, l'analyse précédente comporte (au moins) un petit
problème... Saurez-vous le trouver ? Vous êtes libre de modifier cette
analyse et de regarder ce jeu de données sous tous les angles afin
d'expliquer ce qui ne va pas.
module2/exo5/exo5_en.Rmd deleted 100644 → 0
View file @ ecd554d7
---
title: "Analysis of the risk of failure of the O-rings on the Challenger shuttle"
author: "Arnaud Legrand"
date: "28 juin 2018"
output: html_document
---
On January 27, 1986, the day before the takeoff of the shuttle _Challenger_, had
a three-hour teleconference was held between
Morton Thiokol (the manufacturer of one of the engines) and NASA. The
discussion focused on the consequences of the
temperature at take-off of 31°F (just below
0°C) for the success of the flight and in particular on the performance of the
O-rings used in the engines. Indeed, no test
had been performed at this temperature.
The following study takes up some of the analyses carried out that
night with the objective of assessing the potential influence of
the temperature and pressure to which the O-rings are subjected
on their probability of malfunction. Our starting point is
the results of the experiments carried out by NASA engineers
during the six years preceding the launch of the shuttle
Challenger.
# Loading the data
We start by loading this data:
```{r}
data = read.csv("shuttle.csv",header=T)
data
```
The data set shows us the date of each test, the number of O-rings
(there are 6 on the main launcher), the
temperature (in Fahrenheit) and pressure (in psi), and finally the
number of identified malfunctions.
# Graphical inspection
Flights without incidents do not provide any information
on the influence of temperature or pressure on malfunction.
We thus focus on the experiments in which at least one O-ring was defective.
```{r}
data = data[data$Malfunction>0,]
data
```
We have a high temperature variability but
the pressure is almost always 200, which should
simplify the analysis.
How does the frequency of failure vary with temperature?
```{r}
plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))
```
At first glance, the dependence does not look very important, but let's try to
estimate the impact of temperature $t$ on the probability of O-ring malfunction.
# Estimation of the temperature influence
Suppose that each of the six O-rings is damaged with the same
probability and independently of the others and that this probability
depends only on the temperature. If $p(t)$ is this probability, the
number $D$ of malfunctioning O-rings during a flight at
temperature $t$ follows a binomial law with parameters $n=6$ and
$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a
logistic regression.
```{r}
logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count,
family=binomial(link='logit'))
summary(logistic_reg)
```
The most likely estimator of the temperature parameter is 0.001416
and the standard error of this estimator is 0.049, in other words we
cannot distinguish any particular impact and we must take our
estimates with caution.
# Estimation of the probability of O-ring malfunction
The expected temperature on the take-off day is 31°F. Let's try to
estimate the probability of O-ring malfunction at
this temperature from the model we just built:
```{r}
# shuttle=shuttle[shuttle$r!=0,]
tempv = seq(from=30, to=90, by = .5)
rmv <- predict(logistic_reg,list(Temperature=tempv),type="response")
plot(tempv,rmv,type="l",ylim=c(0,1))
points(data=data, Malfunction/Count ~ Temperature)
```
As expected from the initial data, the
temperature has no significant impact on the probability of failure of the
O-rings. It will be about 0.2, as in the tests
where we had a failure of at least one joint. Let's get back to the initial dataset to estimate the probability of failure:
```{r}
data_full = read.csv("shuttle.csv",header=T)
sum(data_full$Malfunction)/sum(data_full$Count)
```
This probability is thus about $p=0.065$. Knowing that there is
a primary and a secondary O-ring on each of the three parts of the
launcher, the probability of failure of both joints of a launcher
is $p^2 \approx 0.00425$. The probability of failure of any one of the
launchers is $1-(1-p^2)^3 \approx 1.2%$. That would really be
bad luck.... Everything is under control, so the takeoff can happen
tomorrow as planned.
But the next day, the Challenger shuttle exploded and took away
with her the seven crew members. The public was shocked and in
the subsequent investigation, the reliability of the
O-rings was questioned. Beyond the internal communication problems
of NASA, which have a lot to do with this fiasco, the previous analysis
includes (at least) a small problem.... Can you find it?
You are free to modify this analysis and to look at this dataset
from all angles in order to to explain what's wrong.
module2/exo5/exo5_en.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analysis of the risk of failure of the O-rings on the Challenger shuttle"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On January 27, 1986, the day before the takeoff of the shuttle _Challenger_, had\n",
"a three-hour teleconference was held between \n",
"Morton Thiokol (the manufacturer of one of the engines) and NASA. The\n",
"discussion focused on the consequences of the\n",
"temperature at take-off of 31°F (just below\n",
"0°C) for the success of the flight and in particular on the performance of the\n",
"O-rings used in the engines. Indeed, no test\n",
"had been performed at this temperature.\n",
"\n",
"The following study takes up some of the analyses carried out that\n",
"night with the objective of assessing the potential influence of\n",
"the temperature and pressure to which the O-rings are subjected\n",
"on their probability of malfunction. Our starting point is \n",
"the results of the experiments carried out by NASA engineers\n",
"during the six years preceding the launch of the shuttle\n",
"Challenger."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loading the data\n",
"We start by loading this data:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
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" <td>53</td>\n",
" <td>200</td>\n",
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" <td>4/12/85</td>\n",
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"</table>\n",
"</div>"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"0 4/12/81 6 66 50 0\n",
"1 11/12/81 6 70 50 1\n",
"2 3/22/82 6 69 50 0\n",
"3 11/11/82 6 68 50 0\n",
"4 4/04/83 6 67 50 0\n",
"5 6/18/82 6 72 50 0\n",
"6 8/30/83 6 73 100 0\n",
"7 11/28/83 6 70 100 0\n",
"8 2/03/84 6 57 200 1\n",
"9 4/06/84 6 63 200 1\n",
"10 8/30/84 6 70 200 1\n",
"11 10/05/84 6 78 200 0\n",
"12 11/08/84 6 67 200 0\n",
"13 1/24/85 6 53 200 2\n",
"14 4/12/85 6 67 200 0\n",
"15 4/29/85 6 75 200 0\n",
"16 6/17/85 6 70 200 0\n",
"17 7/29/85 6 81 200 0\n",
"18 8/27/85 6 76 200 0\n",
"19 10/03/85 6 79 200 0\n",
"20 10/30/85 6 75 200 2\n",
"21 11/26/85 6 76 200 0\n",
"22 1/12/86 6 58 200 1"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"data = pd.read_csv(\"shuttle.csv\")\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The data set shows us the date of each test, the number of O-rings (there are 6 on the main launcher), the temperature (in Fahrenheit) and pressure (in psi), and finally the number of identified malfunctions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Graphical inspection\n",
"Flights without incidents do not provide any information\n",
"on the influence of temperature or pressure on malfunction.\n",
"We thus focus on the experiments in which at least one O-ring\n",
"was defective."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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" vertical-align: top;\n",
" }\n",
"\n",
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" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Count</th>\n",
" <th>Temperature</th>\n",
" <th>Pressure</th>\n",
" <th>Malfunction</th>\n",
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" <th>10</th>\n",
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" <tr>\n",
" <th>13</th>\n",
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" <td>6</td>\n",
" <td>53</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
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" <th>20</th>\n",
" <td>10/30/85</td>\n",
" <td>6</td>\n",
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" <td>2</td>\n",
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" <th>22</th>\n",
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" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"1 11/12/81 6 70 50 1\n",
"8 2/03/84 6 57 200 1\n",
"9 4/06/84 6 63 200 1\n",
"10 8/30/84 6 70 200 1\n",
"13 1/24/85 6 53 200 2\n",
"20 10/30/85 6 75 200 2\n",
"22 1/12/86 6 58 200 1"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = data[data.Malfunction>0]\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have a high temperature variability but\n",
"the pressure is almost always 200, which should\n",
"simplify the analysis.\n",
"\n",
"How does the frequency of failure vary with temperature?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n",
"import matplotlib.pyplot as plt\n",
"\n",
"data[\"Frequency\"]=data.Malfunction/data.Count\n",
"data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At first glance, the dependence does not look very important, but let's try to\n",
"estimate the impact of temperature $t$ on the probability of O-ring malfunction."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation of the temperature influence\n",
"\n",
"Suppose that each of the six O-rings is damaged with the same\n",
"probability and independently of the others and that this probability\n",
"depends only on the temperature. If $p(t)$ is this probability, the\n",
"number $D$ of malfunctioning O-rings during a flight at\n",
"temperature $t$ follows a binomial law with parameters $n=6$ and\n",
"$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a\n",
"logistic regression."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>Generalized Linear Model Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Frequency</td> <th> No. Observations: </th> <td> 7</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLM</td> <th> Df Residuals: </th> <td> 5</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model Family:</th> <td>Binomial</td> <th> Df Model: </th> <td> 1</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Link Function:</th> <td>logit</td> <th> Scale: </th> <td> 1.0000</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>IRLS</td> <th> Log-Likelihood: </th> <td> -2.5250</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Sat, 13 Apr 2019</td> <th> Deviance: </th> <td> 0.22231</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>19:12:05</td> <th> Pearson chi2: </th> <td> 0.236</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Iterations:</th> <td>4</td> <th> Covariance Type: </th> <td>nonrobust</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>z</th> <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> -1.3895</td> <td> 7.828</td> <td> -0.178</td> <td> 0.859</td> <td> -16.732</td> <td> 13.953</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Temperature</th> <td> 0.0014</td> <td> 0.122</td> <td> 0.012</td> <td> 0.991</td> <td> -0.238</td> <td> 0.240</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 7\n",
"Model: GLM Df Residuals: 5\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -2.5250\n",
"Date: Sat, 13 Apr 2019 Deviance: 0.22231\n",
"Time: 19:12:05 Pearson chi2: 0.236\n",
"No. Iterations: 4 Covariance Type: nonrobust\n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept -1.3895 7.828 -0.178 0.859 -16.732 13.953\n",
"Temperature 0.0014 0.122 0.012 0.991 -0.238 0.240\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"data[\"Success\"]=data.Count-data.Malfunction\n",
"data[\"Intercept\"]=1\n",
"\n",
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The most likely estimator of the temperature parameter is 0.0014\n",
"and the standard error of this estimator is 0.122, in other words we\n",
"cannot distinguish any particular impact and we must take our\n",
"estimates with caution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation of the probability of O-ring malfunction\n",
"\n",
"The expected temperature on the take-off day is 31°F. Let's try to\n",
"estimate the probability of O-ring malfunction at\n",
"this temperature from the model we just built:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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5KgqSDz7YzSHPPLnf9RSHS1tfE2awbHy57KYS1ErUSNTUQI1ErYQENTUdt0WNoLZmb7u9j8nuqylaRo0K5teI2hoxvOPxUr4sAFFbky1b+bq7PK5omWv68HSUFfSSLgC+B9QCd0fEXxbd/3VgPtAKvAH8SUT8qg/19Nk+r/qljgAKjhpKvcruEzzFO0vnEUL2uP0dtaz/TSvvvbRjnzCIotvdBl3Rq3rbfu7b35HBPvOLQ6rLkcq+Ry7dHYE1N3/AyFVPdd7X2ZcSwVNYb9fneyD/Qnpp3UsH9PDC8FBhQOThURwEtTXZziyU7/D7Pr62RojC8MkeO6y2hkOG7Q2cjmDqWEbn8vL17vztbzn6qCP3CaWOdvvczutUPr+wPqlrqGX9UNewLFFDTan11AhREKI1RcuVgL3PRZdw7QjfGvHsM88we/YZBbUL1RQ9FwXPrfLlVotb+vCYHoNeUi1wB3Ae0ASskrQsIjYWNFsDnBoRH0j6r8BfAVfsb7nbm9s596//uXQQlArtff716Ro8Q9Lavrz2ltbxh93lFb9oR+g86ug4AqnpLmz2hkoWGnuPHrJ1lA6O2jwUJHizpoWjfv/wLjt58Tpqa9Sl9pJHPwV9KWyX9TN7LHmfawtrrum6jNqa7LkR+4ZNjYAuobdvUBTWvnrV85x+2qx9gqXrkV/R9ig6EhzK4dHY2EhDw8mDXUa/+djIGj4+ZuRglzGklHNEPxPYGhGvAkh6ELgY6Az6iHiqoP2zwBd6WujwGlH/e2M6d8CSQdBNKOzdWfNQoGvoFR/xFP6bpOLbRUc1xUddxQGyN/T2hlvx0UiNxIurVzNr1oyCYN7fkR37HAWpKJiGmiwspg12Gf2iaXQNnxg3erDLMKuYcoJ+AvB6wXQTMGs/7b8E/GOpOyQtABYAjB8/nssmvFdmmX0Q+U8FteU/5RirD2ja+EJlCxhCmpubaWxsHOwy+kXKfQP372BUTtCXOpwsGaGSvgCcCvxhqfsjYjGwGKC+vj4aGhrKq7IKZUe8DYNdRr9JuX8p9w3cv4NROUHfBBxTMD0R2FHcSNK5wP8E/jAiPqxMeWZmdqDK+cDUKmCKpMmSRgBXAssKG0iaBtwFzI2InZUv08zM+qrHoI+IVuBaYAWwCVgSERsk3Sxpbt5sEXAo8BNJayUt62ZxZmY2wMq6jj4ilgPLi+Z9q+D2uRWuy6zXlq7ZzqIVm9nxTgtHH17Hwjn1APvMu2TahAGtoT/X1xvfXLqeB557na+dsIcv3bCcebOO4ZZLThzssmwA+JOxloSla7ZzwyPradmTXRe1/Z0WFv7kJRDsaYvOeTc8sh6gX8K3VA39ub7e+ObS9fzw2dc6p9siOqcd9unzoGaWhEUrNncGbIc97dEZ8h1a9rSxaMXmAauhP9fXGw8893qv5ltaHPSWhB3vtPRL20rU0F/r6422bsab6G6+pcVBb0k4+vC6fmlbiRr6a329UdvNp6u7m29pcdBbEhbOqadueG2XecNrxPDarkFWN7y2803agaihP9fXG/NmHdOr+ZYWvxlrSeh4s3Mwr7rprobBfiMW9r7h2nFOvlbyVTcHEQe9JeOSaRNKhupABm13NQwFt1xyIrdcciKNjY3821UNg12ODSCfujEzS5yD3swscQ56M7PEOejNzBLnoDczS5yD3swscQ56M7PEOejNzBLnoDczS5yD3swscQ56M7PEOejNzBLnoDczS5yD3swscQ56M7PEOejNzBLnoDczS5yD3swscQ56M7PEOejNzBLnoDczS5yD3swscQ56M7PEOejNzBLnoDczS5yD3swscQ56M7PEOejNzBJXVtBLukDSZklbJX2jxP2HSHoov/85SZMqXaiZmfVNj0EvqRa4A7gQOB6YJ+n4omZfAt6OiH8HfBf4X5Uu1MzM+qacI/qZwNaIeDUiPgIeBC4uanMx8A/57YeBz0hS5co0M7O+GlZGmwnA6wXTTcCs7tpERKukd4FxwJuFjSQtABbkkx9KerkvRVeJIynqf2JS7l/KfQP3r9rV9/YB5QR9qSPz6EMbImIxsBhA0uqIOLWM9Vcl9696pdw3cP+qnaTVvX1MOadumoBjCqYnAju6ayNpGDAW+F1vizEzs8orJ+hXAVMkTZY0ArgSWFbUZhnwx/ntS4F/ioh9jujNzGzg9XjqJj/nfi2wAqgF7o2IDZJuBlZHxDLgHuB+SVvJjuSvLGPdiw+g7mrg/lWvlPsG7l+163X/5ANvM7O0+ZOxZmaJc9CbmSVuQIJe0khJz0t6SdIGSd/O50/Oh0zYkg+hMGIg6ukPkmolrZH0s3w6pb5tk7Re0tqOS7skHSHp8bx/j0v62GDX2VeSDpf0sKT/J2mTpNNT6Z+k+ny7dfy8J+lrCfXvv+WZ8rKkB/KsSWnf+/O8bxskfS2f1+ttN1BH9B8C50TEycBU4AJJp5ENlfDdiJgCvE02lEK1+nNgU8F0Sn0DODsiphZcn/wN4Mm8f0/m09Xqe8DPI+I44GSy7ZhE/yJic77dpgKnAB8Aj5JA/yRNAK4DTo2IE8guFrmSRPY9SScAXyYbneBk4HOSptCXbRcRA/oDjAJeJPt07ZvAsHz+6cCKga6nQn2amD/h5wA/I/sAWRJ9y+vfBhxZNG8zcFR++yhg82DX2ce+HQb8kvzChNT6V9Sn84GnU+kfez+RfwTZFYQ/A+aksu8BlwF3F0z/BfA/+rLtBuwcfX5qYy2wE3gc+DfgnYhozZs0kW24anQ72QZoz6fHkU7fIPuU80pJL+TDWAD8XkT8GiD//fFBq+7AfBJ4A/j7/NTb3ZJGk07/Cl0JPJDfrvr+RcR24DbgNeDXwLvAC6Sz770MnCVpnKRRwGfJPpja6203YEEfEW2R/fs4kexfkU+XajZQ9VSKpM8BOyPihcLZJZpWXd8KzI6I6WQjmP6ZpLMGu6AKGgZMB+6MiGnA+1ThaYye5Oep5wI/GexaKiU/N30xMBk4GhhN9jdarCr3vYjYRHYa6nHg58BLQOt+H9SNAb/qJiLeARqB04DD8yEToPTQCtVgNjBX0jaykT3PITvCT6FvAETEjvz3TrLzuzOB30o6CiD/vXPwKjwgTUBTRDyXTz9MFvyp9K/DhcCLEfHbfDqF/p0L/DIi3oiIPcAjwBmkte/dExHTI+Issg+jbqEP226grroZL+nw/HYd2QbaBDxFNmQCZEMoPDYQ9VRSRNwQERMjYhLZv8b/FBFXkUDfACSNljSm4zbZed6X6TrsRdX2LyJ+A7wuqWNEwM8AG0mkfwXmsfe0DaTRv9eA0ySNyodF79h2Sex7AJI+nv8+FviPZNuw19tuQD4ZK+kksvHqa8leXJZExM2SPkl2FHwEsAb4QkR82O8F9RNJDcD1EfG5VPqW9+PRfHIY8OOIuFXSOGAJcCzZDndZRFTlQHaSpgJ3AyOAV4Evkv+dkkb/RpG9afnJiHg3n5fE9ssv1b6C7JTGGmA+2Tn5qt/3ACT9C9l7fnuAr0fEk33Zdh4Cwcwscf5krJlZ4hz0ZmaJc9CbmSXOQW9mljgHvZlZ4sr5cnCzAZVfPvZkPvn7QBvZMAUAMyPio0EpbD8k/QmwPL8u32xI8eWVNqRJuglojojbhkAttRHR1s19/wpcGxFre7G8YQVjspj1G5+6saoi6Y+VfbfBWkl/I6lG0jBJ70haJOlFSSskzZL0z5JelfTZ/LHzJT2a379Z0jfLXO4tkp4HZkr6tqRV+Rjhf6vMFWTDbz+UP36EpKaCT4OfJumJ/PYtku6S9DjZQGrDJP11vu51kuYP/LNqqXPQW9XIx+f+PHBGPkDeMPZ+Ef1YYGU++NpHwE1kH4m/DLi5YDEz88dMB/6zpKllLPfFiJgZEc8A34uIGcCJ+X0XRMRDwFrgisjGfu/p1NI04KKI+CNgAdmgeDOBGWSDxh3bl+fHrDs+R2/V5FyyMFydDW1CHdlH+wFaIuLx/PZ64N2IaJW0HphUsIwVEfE2gKSlwH8g2w+6W+5H7B0CAuAzkhYCI4EjyYbF/cde9uOxiNid3z4f+LSkwheWKWQfbTerCAe9VRMB90bEX3SZmY1UWHgU3U72rWYdtwv/zovflIoeltsS+RtZ+Zgx/xeYHhHbJd1CFviltLL3P+biNu8X9elPI+JJzPqJT91YNXkCuFzSkZBdndOH0xznK/uO2FFkY5k/3Yvl1pG9cLyZj+j5nwru2wWMKZjeRvbVfRS1K7YC+NOOYXWVfcdrXS/7ZLZfPqK3qhER6/PRCp+QVEM2ot9/oXfjjf8r8GPgD4D7O66SKWe5EfGWpH8gG6b5V8BzBXf/PXC3pBay9wFuAv5O0m+A5/dTz11koxCuzU8b7SR7ATKrGF9eaQeN/IqWEyLia4Ndi9lA8qkbM7PE+YjezCxxPqI3M0ucg97MLHEOejOzxDnozcwS56A3M0vc/wcowwoTqhaBUgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n",
"data_pred['Frequency'] = logmodel.predict(data_pred[['Intercept','Temperature']])\n",
"data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n",
"plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"As expected from the initial data, the\n",
"temperature has no significant impact on the probability of failure of the\n",
"O-rings. It will be about 0.2, as in the tests\n",
"where we had a failure of at least one joint. Let's get back\n",
"to the initial dataset to estimate the probability of failure:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.06521739130434782\n"
]
}
],
"source": [
"data = pd.read_csv(\"shuttle.csv\")\n",
"print(np.sum(data.Malfunction)/np.sum(data.Count))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This probability is thus about $p=0.065$. Knowing that there is\n",
"a primary and a secondary O-ring on each of the three parts of the\n",
"launcher, the probability of failure of both joints of a launcher\n",
"is $p^2 \\approx 0.00425$. The probability of failure of any one of the\n",
"launchers is $1-(1-p^2)^3 \\approx 1.2%$. That would really be\n",
"bad luck.... Everything is under control, so the takeoff can happen\n",
"tomorrow as planned.\n",
"\n",
"But the next day, the Challenger shuttle exploded and took away\n",
"with her the seven crew members. The public was shocked and in\n",
"the subsequent investigation, the reliability of the\n",
"O-rings was questioned. Beyond the internal communication problems\n",
"of NASA, which have a lot to do with this fiasco, the previous analysis\n",
"includes (at least) a small problem.... Can you find it?\n",
"You are free to modify this analysis and to look at this dataset\n",
"from all angles in order to to explain what's wrong."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"celltoolbar": "Hide code",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module2/exo5/exo5_fr.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Analyse du risque de défaillance des joints toriques de la navette Challenger"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le 27 Janvier 1986, veille du décollage de la navette *Challenger*, eu\n",
"lieu une télé-conférence de trois heures entre les ingénieurs de la\n",
"Morton Thiokol (constructeur d'un des moteurs) et de la NASA. La\n",
"discussion portait principalement sur les conséquences de la\n",
"température prévue au moment du décollage de 31°F (juste en dessous de\n",
"0°C) sur le succès du vol et en particulier sur la performance des\n",
"joints toriques utilisés dans les moteurs. En effet, aucun test\n",
"n'avait été effectué à cette température.\n",
"\n",
"L'étude qui suit reprend donc une partie des analyses effectuées cette\n",
"nuit là et dont l'objectif était d'évaluer l'influence potentielle de\n",
"la température et de la pression à laquelle sont soumis les joints\n",
"toriques sur leur probabilité de dysfonctionnement. Pour cela, nous\n",
"disposons des résultats des expériences réalisées par les ingénieurs\n",
"de la NASA durant les 6 années précédant le lancement de la navette\n",
"Challenger.\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Chargement des données\n",
"Nous commençons donc par charger ces données:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Count</th>\n",
" <th>Temperature</th>\n",
" <th>Pressure</th>\n",
" <th>Malfunction</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>4/12/81</td>\n",
" <td>6</td>\n",
" <td>66</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>11/12/81</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>50</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>3/22/82</td>\n",
" <td>6</td>\n",
" <td>69</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>11/11/82</td>\n",
" <td>6</td>\n",
" <td>68</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>4/04/83</td>\n",
" <td>6</td>\n",
" <td>67</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>6/18/82</td>\n",
" <td>6</td>\n",
" <td>72</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>8/30/83</td>\n",
" <td>6</td>\n",
" <td>73</td>\n",
" <td>100</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>11/28/83</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>100</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>2/03/84</td>\n",
" <td>6</td>\n",
" <td>57</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>4/06/84</td>\n",
" <td>6</td>\n",
" <td>63</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>8/30/84</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>10/05/84</td>\n",
" <td>6</td>\n",
" <td>78</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>11/08/84</td>\n",
" <td>6</td>\n",
" <td>67</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>1/24/85</td>\n",
" <td>6</td>\n",
" <td>53</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>4/12/85</td>\n",
" <td>6</td>\n",
" <td>67</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>4/29/85</td>\n",
" <td>6</td>\n",
" <td>75</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>6/17/85</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>7/29/85</td>\n",
" <td>6</td>\n",
" <td>81</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>8/27/85</td>\n",
" <td>6</td>\n",
" <td>76</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>10/03/85</td>\n",
" <td>6</td>\n",
" <td>79</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>10/30/85</td>\n",
" <td>6</td>\n",
" <td>75</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>21</th>\n",
" <td>11/26/85</td>\n",
" <td>6</td>\n",
" <td>76</td>\n",
" <td>200</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>1/12/86</td>\n",
" <td>6</td>\n",
" <td>58</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"0 4/12/81 6 66 50 0\n",
"1 11/12/81 6 70 50 1\n",
"2 3/22/82 6 69 50 0\n",
"3 11/11/82 6 68 50 0\n",
"4 4/04/83 6 67 50 0\n",
"5 6/18/82 6 72 50 0\n",
"6 8/30/83 6 73 100 0\n",
"7 11/28/83 6 70 100 0\n",
"8 2/03/84 6 57 200 1\n",
"9 4/06/84 6 63 200 1\n",
"10 8/30/84 6 70 200 1\n",
"11 10/05/84 6 78 200 0\n",
"12 11/08/84 6 67 200 0\n",
"13 1/24/85 6 53 200 2\n",
"14 4/12/85 6 67 200 0\n",
"15 4/29/85 6 75 200 0\n",
"16 6/17/85 6 70 200 0\n",
"17 7/29/85 6 81 200 0\n",
"18 8/27/85 6 76 200 0\n",
"19 10/03/85 6 79 200 0\n",
"20 10/30/85 6 75 200 2\n",
"21 11/26/85 6 76 200 0\n",
"22 1/12/86 6 58 200 1"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"data = pd.read_csv(\"shuttle.csv\")\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le jeu de données nous indique la date de l'essai, le nombre de joints\n",
"toriques mesurés (il y en a 6 sur le lançeur principal), la\n",
"température (en Farenheit) et la pression (en psi), et enfin le\n",
"nombre de dysfonctionnements relevés. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Inspection graphique des données\n",
"Les vols où aucun incident n'est relevé n'apportant aucun information\n",
"sur l'influence de la température ou de la pression sur les\n",
"dysfonctionnements, nous nous concentrons sur les expériences où au\n",
"moins un joint a été défectueux.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
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" }\n",
"\n",
" .dataframe thead th {\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Count</th>\n",
" <th>Temperature</th>\n",
" <th>Pressure</th>\n",
" <th>Malfunction</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>11/12/81</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
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" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>2/03/84</td>\n",
" <td>6</td>\n",
" <td>57</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>4/06/84</td>\n",
" <td>6</td>\n",
" <td>63</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>8/30/84</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>200</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>1/24/85</td>\n",
" <td>6</td>\n",
" <td>53</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>10/30/85</td>\n",
" <td>6</td>\n",
" <td>75</td>\n",
" <td>200</td>\n",
" <td>2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>22</th>\n",
" <td>1/12/86</td>\n",
" <td>6</td>\n",
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" <td>200</td>\n",
" <td>1</td>\n",
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],
"text/plain": [
" Date Count Temperature Pressure Malfunction\n",
"1 11/12/81 6 70 50 1\n",
"8 2/03/84 6 57 200 1\n",
"9 4/06/84 6 63 200 1\n",
"10 8/30/84 6 70 200 1\n",
"13 1/24/85 6 53 200 2\n",
"20 10/30/85 6 75 200 2\n",
"22 1/12/86 6 58 200 1"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = data[data.Malfunction>0]\n",
"data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Très bien, nous avons une variabilité de température importante mais\n",
"la pression est quasiment toujours égale à 200, ce qui devrait\n",
"simplifier l'analyse.\n",
"\n",
"Comment la fréquence d'échecs varie-t-elle avec la température ?\n"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n",
"import matplotlib.pyplot as plt\n",
"\n",
"data[\"Frequency\"]=data.Malfunction/data.Count\n",
"data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"À première vue, ce n'est pas flagrant mais bon, essayons quand même\n",
"d'estimer l'impact de la température $t$ sur la probabilité de\n",
"dysfonctionnements d'un joint. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation de l'influence de la température\n",
"\n",
"Supposons que chacun des 6 joints toriques est endommagé avec la même\n",
"probabilité et indépendamment des autres et que cette probabilité ne\n",
"dépend que de la température. Si on note $p(t)$ cette probabilité, le\n",
"nombre de joints $D$ dysfonctionnant lorsque l'on effectue le vol à\n",
"température $t$ suit une loi binomiale de paramètre $n=6$ et\n",
"$p=p(t)$. Pour relier $p(t)$ à $t$, on va donc effectuer une\n",
"régression logistique."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>Generalized Linear Model Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>Frequency</td> <th> No. Observations: </th> <td> 7</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>GLM</td> <th> Df Residuals: </th> <td> 5</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model Family:</th> <td>Binomial</td> <th> Df Model: </th> <td> 1</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Link Function:</th> <td>logit</td> <th> Scale: </th> <td> 1.0000</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>IRLS</td> <th> Log-Likelihood: </th> <td> -2.5250</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Sat, 13 Apr 2019</td> <th> Deviance: </th> <td> 0.22231</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>19:11:24</td> <th> Pearson chi2: </th> <td> 0.236</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Iterations:</th> <td>4</td> <th> Covariance Type: </th> <td>nonrobust</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>z</th> <th>P>|z|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> -1.3895</td> <td> 7.828</td> <td> -0.178</td> <td> 0.859</td> <td> -16.732</td> <td> 13.953</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Temperature</th> <td> 0.0014</td> <td> 0.122</td> <td> 0.012</td> <td> 0.991</td> <td> -0.238</td> <td> 0.240</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" Generalized Linear Model Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Frequency No. Observations: 7\n",
"Model: GLM Df Residuals: 5\n",
"Model Family: Binomial Df Model: 1\n",
"Link Function: logit Scale: 1.0000\n",
"Method: IRLS Log-Likelihood: -2.5250\n",
"Date: Sat, 13 Apr 2019 Deviance: 0.22231\n",
"Time: 19:11:24 Pearson chi2: 0.236\n",
"No. Iterations: 4 Covariance Type: nonrobust\n",
"===============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"-------------------------------------------------------------------------------\n",
"Intercept -1.3895 7.828 -0.178 0.859 -16.732 13.953\n",
"Temperature 0.0014 0.122 0.012 0.991 -0.238 0.240\n",
"===============================================================================\n",
"\"\"\""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"data[\"Success\"]=data.Count-data.Malfunction\n",
"data[\"Intercept\"]=1\n",
"\n",
"logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n",
"\n",
"logmodel.summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"L'estimateur le plus probable du paramètre de température est 0.0014\n",
"et l'erreur standard de cet estimateur est de 0.122, autrement dit on\n",
"ne peut pas distinguer d'impact particulier et il faut prendre nos\n",
"estimations avec des pincettes.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Estimation de la probabilité de dysfonctionnant des joints toriques\n",
"La température prévue le jour du décollage est de 31°F. Essayons\n",
"d'estimer la probabilité de dysfonctionnement des joints toriques à\n",
"cette température à partir du modèle que nous venons de construire:\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n",
"data_pred['Frequency'] = logmodel.predict(data_pred[['Intercept','Temperature']])\n",
"data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n",
"plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {
"hideCode": false,
"hidePrompt": false,
"scrolled": true
},
"source": [
"Comme on pouvait s'attendre au vu des données initiales, la\n",
"température n'a pas d'impact notable sur la probabilité d'échec des\n",
"joints toriques. Elle sera d'environ 0.2, comme dans les essais\n",
"précédents où nous il y a eu défaillance d'au moins un joint. Revenons\n",
"à l'ensemble des données initiales pour estimer la probabilité de\n",
"défaillance d'un joint:\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.06521739130434782\n"
]
}
],
"source": [
"data = pd.read_csv(\"shuttle.csv\")\n",
"print(np.sum(data.Malfunction)/np.sum(data.Count))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Cette probabilité est donc d'environ $p=0.065$, sachant qu'il existe\n",
"un joint primaire un joint secondaire sur chacune des trois parties du\n",
"lançeur, la probabilité de défaillance des deux joints d'un lançeur\n",
"est de $p^2 \\approx 0.00425$. La probabilité de défaillance d'un des\n",
"lançeur est donc de $1-(1-p^2)^3 \\approx 1.2%$. Ça serait vraiment\n",
"pas de chance... Tout est sous contrôle, le décollage peut donc avoir\n",
"lieu demain comme prévu.\n",
"\n",
"Seulement, le lendemain, la navette Challenger explosera et emportera\n",
"avec elle ses sept membres d'équipages. L'opinion publique est\n",
"fortement touchée et lors de l'enquête qui suivra, la fiabilité des\n",
"joints toriques sera directement mise en cause. Au delà des problèmes\n",
"de communication interne à la NASA qui sont pour beaucoup dans ce\n",
"fiasco, l'analyse précédente comporte (au moins) un petit\n",
"problème... Saurez-vous le trouver ? Vous êtes libre de modifier cette\n",
"analyse et de regarder ce jeu de données sous tous les angles afin\n",
"d'expliquer ce qui ne va pas."
]
}
],
"metadata": {
"celltoolbar": "Hide code",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
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#+TITLE: Analysis of the risk of failure of the O-rings on the Challenger shuttle
#+AUTHOR: Arnaud Legrand
#+LANGUAGE: en
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
#+LATEX_HEADER: \usepackage{a4}
#+LATEX_HEADER: \usepackage[french]{babel}
# #+PROPERTY: header-args :session :exports both
On January 27, 1986, the day before the takeoff of the shuttle /Challenger/, had
a three-hour teleconference was held between
Morton Thiokol (the manufacturer of one of the engines) and NASA. The
discussion focused on the consequences of the
temperature at take-off of 31°F (just below
0°C) for the success of the flight and in particular on the performance of the
O-rings used in the engines. Indeed, no test
had been performed at this temperature.
The following study takes up some of the analyses carried out that
night with the objective of assessing the potential influence of
the temperature and pressure to which the O-rings are subjected
on their probability of malfunction. Our starting point is
the results of the experiments carried out by NASA engineers
during the six years preceding the launch of the shuttle
Challenger.
* Loading the data
We start by loading this data:
#+begin_src python :results value :session *python* :exports both
import numpy as np
import pandas as pd
data = pd.read_csv("shuttle.csv")
data
#+end_src
#+RESULTS:
#+begin_example
Date Count Temperature Pressure Malfunction
0 4/12/81 6 66 50 0
1 11/12/81 6 70 50 1
2 3/22/82 6 69 50 0
3 11/11/82 6 68 50 0
4 4/04/83 6 67 50 0
5 6/18/82 6 72 50 0
6 8/30/83 6 73 100 0
7 11/28/83 6 70 100 0
8 2/03/84 6 57 200 1
9 4/06/84 6 63 200 1
10 8/30/84 6 70 200 1
11 10/05/84 6 78 200 0
12 11/08/84 6 67 200 0
13 1/24/85 6 53 200 2
14 4/12/85 6 67 200 0
15 4/29/85 6 75 200 0
16 6/17/85 6 70 200 0
17 7/29/85 6 81 200 0
18 8/27/85 6 76 200 0
19 10/03/85 6 79 200 0
20 10/30/85 6 75 200 2
21 11/26/85 6 76 200 0
22 1/12/86 6 58 200 1
#+end_example
The data set shows us the date of each test, the number of O-rings
(there are 6 on the main launcher), the
temperature (in Fahrenheit) and pressure (in psi), and finally the
number of identified malfunctions.
* Graphical inspection
Flights without incidents do not provide any information
on the influence of temperature or pressure on malfunction.
We thus focus on the experiments in which at least one O-ring was defective.
#+begin_src python :results value :session *python* :exports both
data = data[data.Malfunction>0]
data
#+end_src
#+RESULTS:
: Date Count Temperature Pressure Malfunction
: 1 11/12/81 6 70 50 1
: 8 2/03/84 6 57 200 1
: 9 4/06/84 6 63 200 1
: 10 8/30/84 6 70 200 1
: 13 1/24/85 6 53 200 2
: 20 10/30/85 6 75 200 2
: 22 1/12/86 6 58 200 1
We have a high temperature variability but
the pressure is almost always 200, which should
simplify the analysis.
How does the frequency of failure vary with temperature?
#+begin_src python :results output file :var matplot_lib_filename="freq_temp_python.png" :exports both :session *python*
import matplotlib.pyplot as plt
plt.clf()
data["Frequency"]=data.Malfunction/data.Count
data.plot(x="Temperature",y="Frequency",kind="scatter",ylim=[0,1])
plt.grid(True)
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:freq_temp_python.png]]
At first glance, the dependence does not look very important, but let's try to
estimate the impact of temperature $t$ on the probability of O-ring malfunction.
* Estimation of the temperature influence
Suppose that each of the six O-rings is damaged with the same
probability and independently of the others and that this probability
depends only on the temperature. If $p(t)$ is this probability, the
number $D$ of malfunctioning O-rings during a flight at
temperature $t$ follows a binomial law with parameters $n=6$ and
$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a
logistic regression.
#+begin_src python :results value :session *python* :exports both
import statsmodels.api as sm
data["Success"]=data.Count-data.Malfunction
data["Intercept"]=1
# logit_model=sm.Logit(data["Frequency"],data[["Intercept","Temperature"]]).fit()
logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()
logmodel.summary()
#+end_src
#+RESULTS:
#+begin_example
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable: Frequency No. Observations: 7
Model: GLM Df Residuals: 5
Model Family: Binomial Df Model: 1
Link Function: logit Scale: 1.0
Method: IRLS Log-Likelihood: -3.6370
Date: Fri, 20 Jul 2018 Deviance: 3.3763
Time: 16:56:08 Pearson chi2: 0.236
No. Iterations: 5
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
Intercept -1.3895 7.828 -0.178 0.859 -16.732 13.953
Temperature 0.0014 0.122 0.012 0.991 -0.238 0.240
===============================================================================
#+end_example
The most likely estimator of the temperature parameter is 0.0014
and the standard error of this estimator is 0.122, in other words we
cannot distinguish any particular impact and we must take our
estimates with caution.
* Estimation of the probability of O-ring malfunction
The expected temperature on the take-off day is 31°F. Let's try to
estimate the probability of O-ring malfunction at
this temperature from the model we just built:
#+begin_src python :results output file :var matplot_lib_filename="proba_estimate_python.png" :exports both :session *python*
import matplotlib.pyplot as plt
data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})
data_pred['Frequency'] = logmodel.predict(data_pred[['Intercept','Temperature']])
data_pred.plot(x="Temperature",y="Frequency",kind="line",ylim=[0,1])
plt.scatter(x=data["Temperature"],y=data["Frequency"])
plt.grid(True)
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:proba_estimate_python.png]]
As expected from the initial data, the
temperature has no significant impact on the probability of failure of the
O-rings. It will be about 0.2, as in the tests
where we had a failure of at least one joint. Let's get back to the initial dataset to estimate the probability of failure:
#+begin_src python :results output :session *python* :exports both
data = pd.read_csv("shuttle.csv")
print(np.sum(data.Malfunction)/np.sum(data.Count))
#+end_src
#+RESULTS:
: 0.06521739130434782
This probability is thus about $p=0.065$. Knowing that there is
a primary and a secondary O-ring on each of the three parts of the
launcher, the probability of failure of both joints of a launcher
is $p^2 \approx 0.00425$. The probability of failure of any one of the
launchers is $1-(1-p^2)^3 \approx 1.2%$. That would really be
bad luck.... Everything is under control, so the takeoff can happen
tomorrow as planned.
But the next day, the Challenger shuttle exploded and took away
with her the seven crew members. The public was shocked and in
the subsequent investigation, the reliability of the
O-rings was questioned. Beyond the internal communication problems
of NASA, which have a lot to do with this fiasco, the previous analysis
includes (at least) a small problem.... Can you find it?
You are free to modify this analysis and to look at this dataset
from all angles in order to to explain what's wrong.
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#+TITLE: Analyse du risque de défaillance des joints toriques de la navette Challenger
#+AUTHOR: Arnaud Legrand
#+LANGUAGE: fr
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
#+LATEX_HEADER: \usepackage{a4}
#+LATEX_HEADER: \usepackage[french]{babel}
# #+PROPERTY: header-args :session :exports both
Le 27 Janvier 1986, veille du décollage de la navette /Challenger/, eu
lieu une télé-conférence de trois heures entre les ingénieurs de la
Morton Thiokol (constructeur d'un des moteurs) et de la NASA. La
discussion portait principalement sur les conséquences de la
température prévue au moment du décollage de 31°F (juste en dessous de
0°C) sur le succès du vol et en particulier sur la performance des
joints toriques utilisés dans les moteurs. En effet, aucun test
n'avait été effectué à cette température.
L'étude qui suit reprend donc une partie des analyses effectuées cette
nuit là et dont l'objectif était d'évaluer l'influence potentielle de
la température et de la pression à laquelle sont soumis les joints
toriques sur leur probabilité de dysfonctionnement. Pour cela, nous
disposons des résultats des expériences réalisées par les ingénieurs
de la NASA durant les 6 années précédant le lancement de la navette
Challenger.
* Chargement des données
Nous commençons donc par charger ces données:
#+begin_src python :results value :session *python* :exports both
import numpy as np
import pandas as pd
data = pd.read_csv("shuttle.csv")
data
#+end_src
#+RESULTS:
#+begin_example
Date Count Temperature Pressure Malfunction
0 4/12/81 6 66 50 0
1 11/12/81 6 70 50 1
2 3/22/82 6 69 50 0
3 11/11/82 6 68 50 0
4 4/04/83 6 67 50 0
5 6/18/82 6 72 50 0
6 8/30/83 6 73 100 0
7 11/28/83 6 70 100 0
8 2/03/84 6 57 200 1
9 4/06/84 6 63 200 1
10 8/30/84 6 70 200 1
11 10/05/84 6 78 200 0
12 11/08/84 6 67 200 0
13 1/24/85 6 53 200 2
14 4/12/85 6 67 200 0
15 4/29/85 6 75 200 0
16 6/17/85 6 70 200 0
17 7/29/85 6 81 200 0
18 8/27/85 6 76 200 0
19 10/03/85 6 79 200 0
20 10/30/85 6 75 200 2
21 11/26/85 6 76 200 0
22 1/12/86 6 58 200 1
#+end_example
Le jeu de données nous indique la date de l'essai, le nombre de joints
toriques mesurés (il y en a 6 sur le lançeur principal), la
température (en Fahrenheit) et la pression (en psi), et enfin le
nombre de dysfonctionnements relevés.
* Inspection graphique des données
Les vols où aucun incident n'est relevé n'apportant aucune information
sur l'influence de la température ou de la pression sur les
dysfonctionnements, nous nous concentrons sur les expériences où au
moins un joint a été défectueux.
#+begin_src python :results value :session *python* :exports both
data = data[data.Malfunction>0]
data
#+end_src
#+RESULTS:
: Date Count Temperature Pressure Malfunction
: 1 11/12/81 6 70 50 1
: 8 2/03/84 6 57 200 1
: 9 4/06/84 6 63 200 1
: 10 8/30/84 6 70 200 1
: 13 1/24/85 6 53 200 2
: 20 10/30/85 6 75 200 2
: 22 1/12/86 6 58 200 1
Très bien, nous avons une variabilité de température importante mais
la pression est quasiment toujours égale à 200, ce qui devrait
simplifier l'analyse.
Comment la fréquence d'échecs varie-t-elle avec la température ?
#+begin_src python :results output file :var matplot_lib_filename="freq_temp_python.png" :exports both :session *python*
import matplotlib.pyplot as plt
plt.clf()
data["Frequency"]=data.Malfunction/data.Count
data.plot(x="Temperature",y="Frequency",kind="scatter",ylim=[0,1])
plt.grid(True)
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:freq_temp_python.png]]
À première vue, ce n'est pas flagrant mais bon, essayons quand même
d'estimer l'impact de la température $t$ sur la probabilité de
dysfonctionnements d'un joint.
* Estimation de l'influence de la température
Supposons que chacun des 6 joints toriques est endommagé avec la même
probabilité et indépendamment des autres et que cette probabilité ne
dépend que de la température. Si on note $p(t)$ cette probabilité, le
nombre de joints $D$ dysfonctionnant lorsque l'on effectue le vol à
température $t$ suit une loi binomiale de paramètre $n=6$ et
$p=p(t)$. Pour relier $p(t)$ à $t$, on va donc effectuer une
régression logistique.
#+begin_src python :results value :session *python* :exports both
import statsmodels.api as sm
data["Success"]=data.Count-data.Malfunction
data["Intercept"]=1
# logit_model=sm.Logit(data["Frequency"],data[["Intercept","Temperature"]]).fit()
logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()
logmodel.summary()
#+end_src
#+RESULTS:
#+begin_example
Generalized Linear Model Regression Results
==============================================================================
Dep. Variable: Frequency No. Observations: 7
Model: GLM Df Residuals: 5
Model Family: Binomial Df Model: 1
Link Function: logit Scale: 1.0
Method: IRLS Log-Likelihood: -3.6370
Date: Fri, 20 Jul 2018 Deviance: 3.3763
Time: 16:56:08 Pearson chi2: 0.236
No. Iterations: 5
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
Intercept -1.3895 7.828 -0.178 0.859 -16.732 13.953
Temperature 0.0014 0.122 0.012 0.991 -0.238 0.240
===============================================================================
#+end_example
L'estimateur le plus probable du paramètre de température est 0.0014
et l'erreur standard de cet estimateur est de 0.122, autrement dit on
ne peut pas distinguer d'impact particulier et il faut prendre nos
estimations avec des pincettes.
* Estimation de la probabilité de dysfonctionnant des joints toriques
La température prévue le jour du décollage est de 31°F. Essayons
d'estimer la probabilité de dysfonctionnement des joints toriques à
cette température à partir du modèle que nous venons de construire:
#+begin_src python :results output file :var matplot_lib_filename="proba_estimate_python.png" :exports both :session *python*
import matplotlib.pyplot as plt
data_pred = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})
data_pred['Frequency'] = logmodel.predict(data_pred[['Intercept','Temperature']])
data_pred.plot(x="Temperature",y="Frequency",kind="line",ylim=[0,1])
plt.scatter(x=data["Temperature"],y=data["Frequency"])
plt.grid(True)
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:proba_estimate_python.png]]
Comme on pouvait s'attendre au vu des données initiales, la
température n'a pas d'impact notable sur la probabilité d'échec des
joints toriques. Elle sera d'environ 0.2, comme dans les essais
précédents où nous il y a eu défaillance d'au moins un joint. Revenons
à l'ensemble des données initiales pour estimer la probabilité de
défaillance d'un joint:
#+begin_src python :results output :session *python* :exports both
data = pd.read_csv("shuttle.csv")
print(np.sum(data.Malfunction)/np.sum(data.Count))
#+end_src
#+RESULTS:
: 0.06521739130434782
Cette probabilité est donc d'environ $p=0.065$, sachant qu'il existe
un joint primaire un joint secondaire sur chacune des trois parties du
lançeur, la probabilité de défaillance des deux joints d'un lançeur
est de $p^2 \approx 0.00425$. La probabilité de défaillance d'un des
lançeur est donc de $1-(1-p^2)^3 \approx 1.2%$. Ça serait vraiment
pas de chance... Tout est sous contrôle, le décollage peut donc avoir
lieu demain comme prévu.
Seulement, le lendemain, la navette Challenger explosera et emportera
avec elle ses sept membres d'équipages. L'opinion publique est
fortement touchée et lors de l'enquête qui suivra, la fiabilité des
joints toriques sera directement mise en cause. Au delà des problèmes
de communication interne à la NASA qui sont pour beaucoup dans ce
fiasco, l'analyse précédente comporte (au moins) un petit
problème... Saurez-vous le trouver ? Vous êtes libre de modifier cette
analyse et de regarder ce jeu de données sous tous les angles afin
d'expliquer ce qui ne va pas.
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"display_name": "Python 3",
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"name": "python3"
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"version": 3
},
"file_extension": ".py",
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#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, R code is included as follows (and is
exxecuted by typing ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
And now the same but in an R session. This is the most frequent
situation, because R is really an interactive language. With a
session, R's state, i.e. the values of all the variables, remains
persistent from one code block to the next. The code is still executed
using ~C-c C-c~.
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Finally, an example for graphical output:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cars.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in R by typing ~<r~ or ~<R~ followed by
~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
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#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
R. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclut du code
R de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src R :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: [1] "Hello world!"
Voici la même chose, mais avec une session R (c'est le cas le
plus courant, R étant vraiment un langage interactif), donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src R :results output :session *R* :exports both
summary(cars)
#+end_src
#+RESULTS:
: speed dist
: Min. : 4.0 Min. : 2.00
: 1st Qu.:12.0 1st Qu.: 26.00
: Median :15.0 Median : 36.00
: Mean :15.4 Mean : 42.98
: 3rd Qu.:19.0 3rd Qu.: 56.00
: Max. :25.0 Max. :120.00
Et enfin, voici un exemple de sortie graphique:
#+begin_src R :results output graphics :file "./cars.png" :exports results :width 600 :height 400 :session *R*
plot(cars)
#+end_src
#+RESULTS:
[[file:./cars.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cars.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, pour les prochains exercices, nous ne vous fournirons pas
forcément de fichier de départ, ça sera à vous de le créer, par
exemple en repartant de ce document et de le commiter vers
gitlab. N'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code R (en
faisant ~<r~ ou ~<R~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
module3/exo3/exercice_en.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module3/exo3/exercice_fr.ipynb deleted 100644 → 0
View file @ ecd554d7
{
"cells": [],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module3/exo3/exercice_python_en.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Your title
#+AUTHOR: Your name
#+DATE: Today's date
#+LANGUAGE: en
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Some explanations
This is an org-mode document with code examples in R. Once opened in
Emacs, this document can easily be exported to HTML, PDF, and Office
formats. For more information on org-mode, see
https://orgmode.org/guide/.
When you type the shortcut =C-c C-e h o=, this document will be
exported as HTML. All the code in it will be re-executed, and the
results will be retrieved and included into the exported document. If
you do not want to re-execute all code each time, you can delete the #
and the space before ~#+PROPERTY:~ in the header of this document.
Like we showed in the video, Python code is included as follows (and
is exxecuted by typing ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
And now the same but in an Python session. With a session, Python's
state, i.e. the values of all the variables, remains persistent from
one code block to the next. The code is still executed using ~C-c
C-c~.
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Finally, an example for graphical output:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Note the parameter ~:exports results~, which indicates that the code
will not appear in the exported document. We recommend that in the
context of this MOOC, you always leave this parameter setting as
~:exports both~, because we want your analyses to be perfectly
transparent and reproducible.
Watch out: the figure generated by the code block is /not/ stored in
the org document. It's a plain file, here named ~cosxsx.png~. You have
to commit it explicitly if you want your analysis to be legible and
understandable on GitLab.
Finally, don't forget that we provide in the resource section of this
MOOC a configuration with a few keyboard shortcuts that allow you to
quickly create code blocks in Python by typing ~<p~, ~<P~ or ~<PP~
followed by ~Tab~.
Now it's your turn! You can delete all this information and replace it
by your computational document.
module3/exo3/exercice_python_fr.org deleted 100644 → 0
View file @ ecd554d7
#+TITLE: Votre titre
#+AUTHOR: Votre nom
#+DATE: La date du jour
#+LANGUAGE: fr
# #+PROPERTY: header-args :eval never-export
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/htmlize.css"/>
#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="http://www.pirilampo.org/styles/readtheorg/css/readtheorg.css"/>
#+HTML_HEAD: <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.3/jquery.min.js"></script>
#+HTML_HEAD: <script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/lib/js/jquery.stickytableheaders.js"></script>
#+HTML_HEAD: <script type="text/javascript" src="http://www.pirilampo.org/styles/readtheorg/js/readtheorg.js"></script>
* Quelques explications
Ceci est un document org-mode avec quelques exemples de code
python. Une fois ouvert dans emacs, ce document peut aisément être
exporté au format HTML, PDF, et Office. Pour plus de détails sur
org-mode vous pouvez consulter https://orgmode.org/guide/.
Lorsque vous utiliserez le raccourci =C-c C-e h o=, ce document sera
compilé en html. Tout le code contenu sera ré-exécuté, les résultats
récupérés et inclus dans un document final. Si vous ne souhaitez pas
ré-exécuter tout le code à chaque fois, il vous suffit de supprimer
le # et l'espace qui sont devant le ~#+PROPERTY:~ au début de ce
document.
Comme nous vous l'avons montré dans la vidéo, on inclue du code
python de la façon suivante (et on l'exécute en faisant ~C-c C-c~):
#+begin_src python :results output :exports both
print("Hello world!")
#+end_src
#+RESULTS:
: Hello world!
Voici la même chose, mais avec une session python, donc une
persistance d'un bloc à l'autre (et on l'exécute toujours en faisant
~C-c C-c~).
#+begin_src python :results output :session :exports both
import numpy
x=numpy.linspace(-15,15)
print(x)
#+end_src
#+RESULTS:
#+begin_example
[-15. -14.3877551 -13.7755102 -13.16326531 -12.55102041
-11.93877551 -11.32653061 -10.71428571 -10.10204082 -9.48979592
-8.87755102 -8.26530612 -7.65306122 -7.04081633 -6.42857143
-5.81632653 -5.20408163 -4.59183673 -3.97959184 -3.36734694
-2.75510204 -2.14285714 -1.53061224 -0.91836735 -0.30612245
0.30612245 0.91836735 1.53061224 2.14285714 2.75510204
3.36734694 3.97959184 4.59183673 5.20408163 5.81632653
6.42857143 7.04081633 7.65306122 8.26530612 8.87755102
9.48979592 10.10204082 10.71428571 11.32653061 11.93877551
12.55102041 13.16326531 13.7755102 14.3877551 15. ]
#+end_example
Et enfin, voici un exemple de sortie graphique:
#+begin_src python :results output file :session :var matplot_lib_filename="./cosxsx.png" :exports results
import matplotlib.pyplot as plt
plt.figure(figsize=(10,5))
plt.plot(x,numpy.cos(x)/x)
plt.tight_layout()
plt.savefig(matplot_lib_filename)
print(matplot_lib_filename)
#+end_src
#+RESULTS:
[[file:./cosxsx.png]]
Vous remarquerez le paramètre ~:exports results~ qui indique que le code
ne doit pas apparaître dans la version finale du document. Nous vous
recommandons dans le cadre de ce MOOC de ne pas changer ce paramètre
(indiquer ~both~) car l'objectif est que vos analyses de données soient
parfaitement transparentes pour être reproductibles.
Attention, la figure ainsi générée n'est pas stockée dans le document
org. C'est un fichier ordinaire, ici nommé ~cosxsx.png~. N'oubliez pas
de le committer si vous voulez que votre analyse soit lisible et
compréhensible sur GitLab.
Enfin, n'oubliez pas que nous vous fournissons dans les ressources de
ce MOOC une configuration avec un certain nombre de raccourcis
claviers permettant de créer rapidement les blocs de code python (en
faisant ~<p~, ~<P~ ou ~<PP~ suivi de ~Tab~).
Maintenant, à vous de jouer! Vous pouvez effacer toutes ces
informations et les remplacer par votre document computationnel.
mooc-rr @ c82e5ab6
Subproject commit c82e5ab6c52e46b2529759495edefeed27fcae27
mooc-rr.Rproj 0 → 100644
View file @ 79b24318
Version: 1.0
RestoreWorkspace: Default
SaveWorkspace: Default
AlwaysSaveHistory: Default
EnableCodeIndexing: Yes
UseSpacesForTab: Yes
NumSpacesForTab: 2
Encoding: UTF-8
RnwWeave: Sweave
LaTeX: pdfLaTeX
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