{ "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": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 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\n", "Entre 6 et 6 joints ont été testés,\n", "entre 53°F et 81°F,\n", "à des pressions allant de 50psi à 200psi, \n", "ce qui a permis de déceler 9 dysfonctionnements. \n" ] } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "data = pd.read_csv(\"shuttle.csv\")\n", "print(data)\n", "\n", "print(\"Entre {} et {} joints ont été testés,\".format(np.min(data['Count']), np.max(data['Count'])))\n", "print(\"entre {}°F et {}°F,\".format(np.min(data['Temperature']), np.max(data['Temperature'])))\n", "print(\"à des pressions allant de {}psi à {}psi, \".format(np.min(data['Pressure']), np.max(data['Pressure'])))\n", "print(\"ce qui a permis de déceler {} dysfonctionnements. \".format(np.sum(data['Malfunction'])))" ] }, { "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": 50, "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
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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": 50, "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": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "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": 55, "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: Thu, 06 Jan 2022 Deviance: 0.22231
Time: 17:43:52 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: Thu, 06 Jan 2022 Deviance: 0.22231\n", "Time: 17:43:52 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": 55, "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": 56, "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": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probabilité de défaillance d'un joint = 0.06521739130434782\n", "Probabilité de défaillance de deux joints = 0.004253308128544423\n", "Probabilité de défaillance d'un lanceur = 0.01270572944054793\n" ] } ], "source": [ "data = pd.read_csv(\"shuttle.csv\")\n", "p = np.sum(data.Malfunction)/np.sum(data.Count)\n", "print(\"Probabilité de défaillance d'un joint = {}\".format(p))\n", "print(\"Probabilité de défaillance de deux joints = {}\".format(pow(p,2)))\n", "print(\"Probabilité de défaillance d'un lanceur = {}\".format(1-pow(1-pow(p,2),3)))" ] }, { "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": { "hideCode": true }, "source": [ "# Conserver la multiplicité des dysfonctionnements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Garder l'étude préliminaire" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "data = pd.read_csv(\"shuttle.csv\")\n", "\n", "%matplotlib inline\n", "pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\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": [ "## Vérifier les grandeurs statistiques\n", "\n", "Attention, Python fait des erreurs de calculs en stat..." ] }, { "cell_type": "code", "execution_count": 19, "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: 23
Model: GLM Df Residuals: 21
Model Family: Binomial Df Model: 1
Link Function: logit Scale: 1.0000
Method: IRLS Log-Likelihood: -3.9210
Date: Thu, 06 Jan 2022 Deviance: 3.0144
Time: 18:22:03 Pearson chi2: 5.00
No. Iterations: 6 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 5.0850 7.477 0.680 0.496 -9.570 19.740
Temperature -0.1156 0.115 -1.004 0.316 -0.341 0.110
" ], "text/plain": [ "\n", "\"\"\"\n", " Generalized Linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: Frequency No. Observations: 23\n", "Model: GLM Df Residuals: 21\n", "Model Family: Binomial Df Model: 1\n", "Link Function: logit Scale: 1.0000\n", "Method: IRLS Log-Likelihood: -3.9210\n", "Date: Thu, 06 Jan 2022 Deviance: 3.0144\n", "Time: 18:22:03 Pearson chi2: 5.00\n", "No. Iterations: 6 Covariance Type: nonrobust\n", "===============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "-------------------------------------------------------------------------------\n", "Intercept 5.0850 7.477 0.680 0.496 -9.570 19.740\n", "Temperature -0.1156 0.115 -1.004 0.316 -0.341 0.110\n", "===============================================================================\n", "\"\"\"" ] }, "execution_count": 19, "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", "logmodel.summary()" ] }, { "cell_type": "markdown", "metadata": { "hideOutput": true }, "source": [ "## Garder l'étude graphique mais avec toutes les valeurs !!" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\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", "\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": {}, "source": [ "## Afficher l'intervalle de confiance de la prédiction" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pred_res = logmodel.get_prediction(data_pred[['Intercept','Temperature']]).summary_frame(0.05)\n", "\n", "data_pred.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n", "plt.fill_between(x=data_pred['Temperature'], y1=pred_res['mean_ci_lower'], y2=pred_res['mean_ci_upper'], alpha=.5, label='Confidence interval')\n", "plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prendre en compte la multiplicité des joints\n", "\n", "Ce n'est pas normal que :\n", "1. la probabilité de dysfonctionnement à basse température soit minorée à 0 et majorée à 1\n", "2. cette probabilité augmente à hautes fréquences\n", "\n", "Donc formater les données pour dupliquer les résultats pour compter chaque joint" ] }, { "cell_type": "code", "execution_count": 15, "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: 138
Model: GLM Df Residuals: 136
Model Family: Binomial Df Model: 1
Link Function: logit Scale: 1.0000
Method: IRLS Log-Likelihood: -25.300
Date: Thu, 06 Jan 2022 Deviance: 50.600
Time: 18:20:28 Pearson chi2: 136.
No. Iterations: 6 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 4.6900 3.380 1.388 0.165 -1.934 11.314
Temperature -0.1138 0.052 -2.179 0.029 -0.216 -0.011
" ], "text/plain": [ "\n", "\"\"\"\n", " Generalized Linear Model Regression Results \n", "==============================================================================\n", "Dep. Variable: Frequency No. Observations: 138\n", "Model: GLM Df Residuals: 136\n", "Model Family: Binomial Df Model: 1\n", "Link Function: logit Scale: 1.0000\n", "Method: IRLS Log-Likelihood: -25.300\n", "Date: Thu, 06 Jan 2022 Deviance: 50.600\n", "Time: 18:20:28 Pearson chi2: 136.\n", "No. Iterations: 6 Covariance Type: nonrobust\n", "===============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "-------------------------------------------------------------------------------\n", "Intercept 4.6900 3.380 1.388 0.165 -1.934 11.314\n", "Temperature -0.1138 0.052 -2.179 0.029 -0.216 -0.011\n", "===============================================================================\n", "\"\"\"" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data_flat = pd.DataFrame({'Temperature':data.Temperature, 'Malfunction':data.Malfunction, 'Count':data.Count, 'Date':data.Date})\n", "\n", "count = 0\n", "for i in range(len(data.Count)):\n", " for j in range(data.at[i, 'Count']):\n", " data_flat.at[(i-1)*data.at[i, 'Count']+j,'Temperature']=data.at[i, 'Temperature']\n", " if (data.at[i, 'Malfunction']>0 and j==0):\n", " data_flat.at[(i-1)*data.at[i, 'Count']+j,'Malfunction']=1\n", " else:\n", " data_flat.at[(i-1)*data.at[i, 'Count']+j,'Malfunction']=0\n", " data_flat.at[(i-1)*data.at[i, 'Count']+j,'Count']=1\n", " data_flat.at[(i-1)*data.at[i, 'Count']+j,'Date']=data.at[i,'Date']\n", " count += 1\n", " \n", "data_flat[\"Frequency\"]=data_flat.Malfunction/data_flat.Count\n", "data_flat[\"Intercept\"]=1\n", "\n", "logmodel_flat = sm.GLM(data_flat['Frequency'], data_flat[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n", "logmodel_flat.summary()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data_pred_flat = pd.DataFrame({'Temperature': np.linspace(start=30, stop=90, num=121), 'Intercept': 1})\n", "data_pred_flat['Frequency'] = logmodel.predict(data_pred_flat[['Intercept','Temperature']])\n", "\n", "pred_res_flat = logmodel_flat.get_prediction(data_pred_flat[['Intercept','Temperature']]).summary_frame(0.05)\n", "\n", "data_pred_flat.plot(x=\"Temperature\",y=\"Frequency\",kind=\"line\",ylim=[0,1])\n", "plt.fill_between(x=data_pred_flat['Temperature'], y1=pred_res_flat['mean_ci_lower'], y2=pred_res_flat['mean_ci_upper'], alpha=.5, label='Confidence interval')\n", "plt.scatter(x=data_flat[\"Temperature\"],y=data_flat[\"Frequency\"])\n", "plt.scatter(x=data[\"Temperature\"],y=data[\"Frequency\"])\n", "plt.grid(True)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " mean mean_se mean_ci_lower mean_ci_upper\n", "0 0.781614 0.31284 0.089721 0.992364\n", "Probabilité de défaillance d'un joint à 30°F = 0.7816142740083805\n", "Probabilité de défaillance de deux joints à 30°F = 0.6109208733336476\n", "Probabilité de défaillance d'un lanceur à 30°F = 0.9411002031140461\n" ] } ], "source": [ "data_pred_flat_30 = pd.DataFrame({'Temperature': [30], 'Intercept': [1]})\n", "data_pred_flat_30['Frequency'] = logmodel_flat.predict(data_pred_flat_30[['Intercept','Temperature']])\n", "\n", "\n", "pred_res_flat_30 = logmodel_flat.get_prediction(data_pred_flat_30[['Intercept','Temperature']]).summary_frame(0.05)\n", "\n", "p = data_pred_flat_30.at[0,'Frequency']\n", "print(\"Probabilité de défaillance d'un joint à 30°F = {}\".format(p))\n", "print(\"Probabilité de défaillance de deux joints à 30°F = {}\".format(pow(p,2)))\n", "print(\"Probabilité de défaillance d'un lanceur à 30°F = {}\".format(1-pow(1-pow(p,2),3)))" ] } ], "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 }