{
 "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>7/29/85</td>\n",
       "      <td>6</td>\n",
       "      <td>81</td>\n",
       "      <td>200</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>8/27/85</td>\n",
       "      <td>6</td>\n",
       "      <td>76</td>\n",
       "      <td>200</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>10/03/85</td>\n",
       "      <td>6</td>\n",
       "      <td>79</td>\n",
       "      <td>200</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>10/30/85</td>\n",
       "      <td>6</td>\n",
       "      <td>75</td>\n",
       "      <td>200</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>11/26/85</td>\n",
       "      <td>6</td>\n",
       "      <td>76</td>\n",
       "      <td>200</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1/12/86</td>\n",
       "      <td>6</td>\n",
       "      <td>58</td>\n",
       "      <td>200</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date  Count  Temperature  Pressure  Malfunction\n",
       "0    4/12/81      6           66        50            0\n",
       "1   11/12/81      6           70        50            1\n",
       "2    3/22/82      6           69        50            0\n",
       "3   11/11/82      6           68        50            0\n",
       "4    4/04/83      6           67        50            0\n",
       "5    6/18/82      6           72        50            0\n",
       "6    8/30/83      6           73       100            0\n",
       "7   11/28/83      6           70       100            0\n",
       "8    2/03/84      6           57       200            1\n",
       "9    4/06/84      6           63       200            1\n",
       "10   8/30/84      6           70       200            1\n",
       "11  10/05/84      6           78       200            0\n",
       "12  11/08/84      6           67       200            0\n",
       "13   1/24/85      6           53       200            2\n",
       "14   4/12/85      6           67       200            0\n",
       "15   4/29/85      6           75       200            0\n",
       "16   6/17/85      6           70       200            0\n",
       "17   7/29/85      6           81       200            0\n",
       "18   8/27/85      6           76       200            0\n",
       "19  10/03/85      6           79       200            0\n",
       "20  10/30/85      6           75       200            2\n",
       "21  11/26/85      6           76       200            0\n",
       "22   1/12/86      6           58       200            1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "data = pd.read_csv(\"shuttle.csv\")\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OWN ANALYSIS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     False\n",
       "1      True\n",
       "2     False\n",
       "3     False\n",
       "4     False\n",
       "5     False\n",
       "6     False\n",
       "7     False\n",
       "8      True\n",
       "9      True\n",
       "10     True\n",
       "11    False\n",
       "12    False\n",
       "13     True\n",
       "14    False\n",
       "15    False\n",
       "16    False\n",
       "17    False\n",
       "18    False\n",
       "19    False\n",
       "20     True\n",
       "21    False\n",
       "22     True\n",
       "Name: malfunction_binary, dtype: bool"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['malfunction_binary'] = data['Malfunction'] > 0\n",
    "data['malfunction_binary']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f55904844e0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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",
    "import seaborn as sns\n",
    "sns.regplot(x='Temperature', y='malfunction_binary', data=data, logistic=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f55903c5198>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.regplot(x='Pressure', y='malfunction_binary', data=data, logistic=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# /OWN ANALYSIS"
   ]
  },
  {
   "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": [
    "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"
   ]
  },
  {
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     "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."
   ]
  }
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