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mooc-rr-ressources
Commit ff757645 authored by Arnaud Legrand's avatar Arnaud Legrand
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Demo CI. 

Some polish is still required though but we should talk about it. I
need some feedback.
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{
"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": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" 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",
" </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>7/2903/85</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 7/2903/85 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",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" 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",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>11/12/81</td>\n",
" <td>6</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",
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" <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",
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" <td>6</td>\n",
" <td>58</td>\n",
" <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": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:6: DeprecationWarning: Calling Family(..) with a link class as argument is deprecated.\n",
"Use an instance of a link class instead.\n",
" \n"
]
},
{
"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>Tue, 20 Aug 2019</td> <th> Deviance: </th> <td> 0.22231</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>09:05:05</td> <th> Pearson chi2: </th> <td> 0.236</td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Iterations:</th> <td>4</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </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: Tue, 20 Aug 2019 Deviance: 0.22231\n",
"Time: 09:05:05 Pearson chi2: 0.236\n",
"No. Iterations: 4 \n",
"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",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module4/ressources/moocrr_notebook/correct_output/notebook_orig.ipynb 0 → 100644
View file @ ff757645
{
"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": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" 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",
" </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>7/2903/85</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 7/2903/85 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",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" 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",
" </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",
" <td>50</td>\n",
" <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",
" <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",
"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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"version": "3.7.3"
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module4/ressources/moocrr_notebook/notebook.ipynb 0 → 100644
View file @ ff757645
{
"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": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
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"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" 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",
" </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>7/2903/85</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 7/2903/85 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",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
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" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" 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",
" </tr>\n",
" </thead>\n",
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" <td>11/12/81</td>\n",
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" </tr>\n",
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" <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",
" <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",
"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",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
module4/ressources/moocrr_notebook/notebook_test.sh 0 → 100644
View file @ ff757645
jupyter-nbconvert --to notebook --execute notebook.ipynb --output notebook.nbconvert.ipynb
compare_notebooks() {
OLD=$1
NEW=$2
mkdir -p `dirname sed/$1`
mkdir -p `dirname sed/$2`
echo "======= Comparing to $OLD ======="
sed -e "s/Date:.*Deviance:/Deviance/" -e "s/Time:.*Pearson/Pearson/" $1 > sed/$1
sed -e "s/Date:.*Deviance:/Deviance/" -e "s/Time:.*Pearson/Pearson/" $2 > sed/$2
# Test #1 (--ignore-matching-lines="image/png" )
diff -w --ignore-matching-lines="nbformat_minor" \
--ignore-matching-lines="hidePrompt" \
--ignore-matching-lines="scrolled" \
--ignore-matching-lines="No. Iterations:" \
--ignore-matching-lines="Covariance Type:" \
sed/$1 sed/$2 # | sed 's/^/>/'
CMP_RES=$?
echo "======= End of Comparison ======="
rm sed/$1 sed/$2
return $CMP_RES
}
compare_notebooks correct_output/notebook_orig.ipynb notebook.nbconvert.ipynb
CMP1=$?
compare_notebooks correct_output/notebook_844815ed865e.ipynb notebook.nbconvert.ipynb
CMP2=$?
if [ $CMP1 -eq "0" -o $CMP2 -eq "0" ] ; then
echo "Test succeeded";
return 0;
else
echo "Test failed";
return 1;
fi
module4/ressources/moocrr_notebook/shuttle.csv 0 → 100644
View file @ ff757645
Date,Count,Temperature,Pressure,Malfunction
4/12/81,6,66,50,0
11/12/81,6,70,50,1
3/22/82,6,69,50,0
11/11/82,6,68,50,0
4/04/83,6,67,50,0
6/18/82,6,72,50,0
8/30/83,6,73,100,0
11/28/83,6,70,100,0
2/03/84,6,57,200,1
4/06/84,6,63,200,1
8/30/84,6,70,200,1
10/05/84,6,78,200,0
11/08/84,6,67,200,0
1/24/85,6,53,200,2
4/12/85,6,67,200,0
4/29/85,6,75,200,0
6/17/85,6,70,200,0
7/2903/85,6,81,200,0
8/27/85,6,76,200,0
10/03/85,6,79,200,0
10/30/85,6,75,200,2
11/26/85,6,76,200,0
1/12/86,6,58,200,1
module4/ressources/test_jupyter/.gitlab-ci.yml.basic 0 → 100644
View file @ ff757645
image: "debian:stable"
before_script:
- perl -v
- which perl
perl_addition:
script:
- perl -e "print(3+2);"
perl_multiplication:
script:
- perl -e "print(3*2);"
module4/ressources/test_jupyter/.gitlab-ci.yml.full 0 → 100644
View file @ ff757645
jupyter_debian_frozen:
image: "alegrand38/moocrr_jupyter"
before_script:
- python3 --version
- jupyter-nbconvert --version
script:
- sh notebook_test.sh
jupyter_scipy_uptodate:
image: "jupyter/scipy-notebook"
before_script:
- python3 --version
- jupyter-nbconvert --version
script:
- sh notebook_test.sh
jupyter_debian_uptodate:
image: "debian:stable"
before_script:
- apt-get update && apt-get install -y python3 jupyter-nbconvert python3-ipykernel python3-matplotlib python3-pandas python3-numpy python3-statsmodels
- python3 --version
- jupyter-nbconvert --version
script:
- sh notebook_test.sh
module4/ressources/test_jupyter/.gitlab-ci.yml.scipy 0 → 100644
View file @ ff757645
image: "jupyter/scipy-notebook"
before_script:
- python3 --version
- jupyter-nbconvert --version
jupyter:
script:
- sh notebook_test.sh
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