From b2100d8d4db18abe56ec4825c60bc1616b8a874d Mon Sep 17 00:00:00 2001 From: 25efbdf864fd2ee93bfa85843f00803c <25efbdf864fd2ee93bfa85843f00803c@app-learninglab.inria.fr> Date: Sun, 2 Jun 2024 14:00:05 +0000 Subject: [PATCH] exo5 --- documents/notebooks/explanation.ipynb | 732 ++++++++++++++++++++++++++ 1 file changed, 732 insertions(+) create mode 100644 documents/notebooks/explanation.ipynb diff --git a/documents/notebooks/explanation.ipynb b/documents/notebooks/explanation.ipynb new file mode 100644 index 0000000..8d44d69 --- /dev/null +++ b/documents/notebooks/explanation.ipynb @@ -0,0 +1,732 @@ +{ + "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": { + "text/html": [ + "
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DateCountTemperaturePressureMalfunction
04/12/81666500
111/12/81670501
23/22/82669500
311/11/82668500
44/04/83667500
56/18/82672500
68/30/836731000
711/28/836701000
82/03/846572001
94/06/846632001
108/30/846702001
1110/05/846782000
1211/08/846672000
131/24/856532002
144/12/856672000
154/29/856752000
166/17/856702000
177/29/856812000
188/27/856762000
1910/03/856792000
2010/30/856752002
2111/26/856762000
221/12/866582001
\n", + "
" + ], + "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": [ + "
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DateCountTemperaturePressureMalfunction
111/12/81670501
82/03/846572001
94/06/846632001
108/30/846702001
131/24/856532002
2010/30/856752002
221/12/866582001
\n", + "
" + ], + "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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+ "text/plain": [ + "
" + ] + }, + "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": [ + "\n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "
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: 1.0000
Method: IRLS Log-Likelihood: -2.5250
Date: Sat, 13 Apr 2019 Deviance: 0.22231
Time: 19:11:24 Pearson chi2: 0.236
No. Iterations: 4 Covariance Type: nonrobust
\n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "\n", + " \n", + "\n", + "
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
" + ], + "text/plain": [ + "\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": [ + "
" + ] + }, + "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." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "EXPLICATION :\n", + "\n", + "Il y a un certain nombre d'erreurs \"grossières\" dans l'analyse que nous vous avons fournie. Nous vous invitons à la comparer avec celle-ci (et sur laquelle nous reviendrons dans le module 4).\n", + "Comme vous pouvez le constater, lorsque l'on effectue l'analyse sur l'ensemble des données, sans exclure les vols où aucune défaillance n'a été observée, il apparaît bien plus clairement que pour des températures moins froides, il y a bien moins de pannes. Après coup, l'exclusion de ces données parait une erreur énorme quand on cherche à déterminer l'origine des pannes mais elles ont pourtant été longuement discutées ce soir-là.\n", + "\n", + "On y perçoit également à quel point une extrapolation sur une zone aussi éloignée des observations dont l'on dispose semble hasardeux et ce d'autant plus que cette extrapolation fait l'hypothèse de linéarité dans la régression logistique. C'est une hypothèse classique en statistiques en l'absence d'information additionnelle mais qui ne se base sur aucune hypothèse \"physique\"... Une telle prédiction devrait être considérée avec beaucoup de suspicion. Au final, cette régression nous indique qu'on ne peut a priori pas éliminer l'hypothèse que la température ait un impact mais ne doit pas être utilisée pour faire une prédiction. À ce sujet, le dernier graphique qui indique l'incertitude associée à la régression logistique est particulièrement éloquent. On peut en gros y lire que la probabilité de panne à 30 Farenheit est comprise ... entre 0 et 1 ! Ça c'est de l'information.\n", + "\n", + "\n", + "En revanche, il n'y a a priori pas d'erreur de calcul dans l'analyse, les statistiques utilisées ne sont certainement pas trop élaborées, au contraire, et si vous comparez la pertinence d'un modèle avec et sans la pression, comme cela est fait dans l'article de Dalal et al. vous verrez que ce paramètre n'apporte effectivement rien.\n", + "\n", + "Cette étude de cas est très célèbre et en particulier le rôle de Richard Feynman dans [la Commission Rogers](https://fr.wikipedia.org/wiki/Commission_Rogers) chargée de l'enquête. Feynman fit une démonstration célèbre sur la manière dont les joints circulaires perdent de leur efficacité par températures glaciales en plongeant tout simplement un échantillon de joint dans un verre rempli d'eau glacée... Une telle expérience vaut bien plus que toutes les statistiques élaborées qu'on pourrait imaginer.\n", + "\n", + "Pour ceux qui souhaite en savoir plus, nous vous proposons de lire cet extrait de [\"Visual Explanations: Images and Quantities,Evidence and Narrative\" par Edward R. Tufte, ISBN-13 : 978-1930824157.](https://lms.fun-mooc.fr/asset-v1:inria+41016+self-paced+type@asset+block/Tufte_Visual_Explanations_Challenger.pdf)" + ] + } + ], + "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": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} -- 2.18.1