From 3975cde1b1d1702b08630eccf890148d73f822d3 Mon Sep 17 00:00:00 2001 From: Mingming GUO Date: Fri, 13 Jun 2025 14:18:22 +0000 Subject: [PATCH] Upload New File --- module2/exo5/exo_02_5.ipynb | 714 ++++++++++++++++++++++++++++++++++++ 1 file changed, 714 insertions(+) create mode 100644 module2/exo5/exo_02_5.ipynb diff --git a/module2/exo5/exo_02_5.ipynb b/module2/exo5/exo_02_5.ipynb new file mode 100644 index 0000000..8aa5a29 --- /dev/null +++ b/module2/exo5/exo_02_5.ipynb @@ -0,0 +1,714 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Analysis of the risk of failure of the O-rings on the Challenger shuttle" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On January 27, 1986, the day before the takeoff of the shuttle _Challenger_, had\n", + "a three-hour teleconference was held between \n", + "Morton Thiokol (the manufacturer of one of the engines) and NASA. The\n", + "discussion focused on the consequences of the\n", + "temperature at take-off of 31°F (just below\n", + "0°C) for the success of the flight and in particular on the performance of the\n", + "O-rings used in the engines. Indeed, no test\n", + "had been performed at this temperature.\n", + "\n", + "The following study takes up some of the analyses carried out that\n", + "night with the objective of assessing the potential influence of\n", + "the temperature and pressure to which the O-rings are subjected\n", + "on their probability of malfunction. Our starting point is \n", + "the results of the experiments carried out by NASA engineers\n", + "during the six years preceding the launch of the shuttle\n", + "Challenger." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loading the data\n", + "We start by loading this data:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "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": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "data = pd.read_csv(\"shuttle.csv\")\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The data set shows us the date of each test, the number of O-rings (there are 6 on the main launcher), the temperature (in Fahrenheit) and pressure (in psi), and finally the number of identified malfunctions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Graphical inspection\n", + "Flights without incidents do not provide any information\n", + "on the influence of temperature or pressure on malfunction.\n", + "We thus focus on the experiments in which at least one O-ring\n", + "was defective." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "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": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = data[data.Malfunction>0]\n", + "data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have a high temperature variability but\n", + "the pressure is almost always 200, which should\n", + "simplify the analysis.\n", + "\n", + "How does the frequency of failure vary with temperature?" + ] + }, + { + "cell_type": "code", + "execution_count": 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", + "pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n", + "import matplotlib.pyplot as plt\n", + "\n", + "data[\"Frequency\"]=data.Malfunction/data.Count\n", + "data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n", + "plt.grid(True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At first glance, the dependence does not look very important, but let's try to\n", + "estimate the impact of temperature $t$ on the probability of O-ring malfunction." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Estimation of the temperature influence\n", + "\n", + "Suppose that each of the six O-rings is damaged with the same\n", + "probability and independently of the others and that this probability\n", + "depends only on the temperature. If $p(t)$ is this probability, the\n", + "number $D$ of malfunctioning O-rings during a flight at\n", + "temperature $t$ follows a binomial law with parameters $n=6$ and\n", + "$p=p(t)$. To link $p(t)$ to $t$, we will therefore perform a\n", + "logistic regression." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "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: Fri, 13 Jun 2025 Deviance: 0.22231
Time: 14:15:51 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: Fri, 13 Jun 2025 Deviance: 0.22231\n", + "Time: 14:15:51 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": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import statsmodels.api as sm\n", + "\n", + "data[\"Success\"]=data.Count-data.Malfunction\n", + "data[\"Intercept\"]=1\n", + "\n", + "logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()\n", + "\n", + "logmodel.summary()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most likely estimator of the temperature parameter is 0.0014\n", + "and the standard error of this estimator is 0.122, in other words we\n", + "cannot distinguish any particular impact and we must take our\n", + "estimates with caution." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Estimation of the probability of O-ring malfunction\n", + "\n", + "The expected temperature on the take-off day is 31°F. Let's try to\n", + "estimate the probability of O-ring malfunction at\n", + "this temperature from the model we just built:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "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": [ + "As expected from the initial data, the\n", + "temperature has no significant impact on the probability of failure of the\n", + "O-rings. It will be about 0.2, as in the tests\n", + "where we had a failure of at least one joint. Let's get back\n", + "to the initial dataset to estimate the probability of failure:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.06521739130434782\n" + ] + } + ], + "source": [ + "data = pd.read_csv(\"shuttle.csv\")\n", + "print(np.sum(data.Malfunction)/np.sum(data.Count))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This probability is thus about $p=0.065$. Knowing that there is\n", + "a primary and a secondary O-ring on each of the three parts of the\n", + "launcher, the probability of failure of both joints of a launcher\n", + "is $p^2 \\approx 0.00425$. The probability of failure of any one of the\n", + "launchers is $1-(1-p^2)^3 \\approx 1.2%$. That would really be\n", + "bad luck.... Everything is under control, so the takeoff can happen\n", + "tomorrow as planned.\n", + "\n", + "But the next day, the Challenger shuttle exploded and took away\n", + "with her the seven crew members. The public was shocked and in\n", + "the subsequent investigation, the reliability of the\n", + "O-rings was questioned. Beyond the internal communication problems\n", + "of NASA, which have a lot to do with this fiasco, the previous analysis\n", + "includes (at least) a small problem.... Can you find it?\n", + "You are free to modify this analysis and to look at this dataset\n", + "from all angles in order to to explain what's wrong." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "celltoolbar": "Hide code", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.4" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} -- 2.18.1