mirror of
https://app-learninglab.inria.fr/moocrr/gitlab/da84ababf0696af51bddad556af86353/mooc-rr.git
synced 2026-06-17 09:35:24 +02:00
717 lines
40 KiB
Text
717 lines
40 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Analyse du risque de défaillance des joints toriques de la navette Challenger"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Le 27 Janvier 1986, veille du décollage de la navette *Challenger*, eu\n",
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"lieu une télé-conférence de trois heures entre les ingénieurs de la\n",
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"Morton Thiokol (constructeur d'un des moteurs) et de la NASA. La\n",
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"discussion portait principalement sur les conséquences de la\n",
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"température prévue au moment du décollage de 31°F (juste en dessous de\n",
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"0°C) sur le succès du vol et en particulier sur la performance des\n",
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"joints toriques utilisés dans les moteurs. En effet, aucun test\n",
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"n'avait été effectué à cette température.\n",
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"\n",
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"L'étude qui suit reprend donc une partie des analyses effectuées cette\n",
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"nuit là et dont l'objectif était d'évaluer l'influence potentielle de\n",
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"la température et de la pression à laquelle sont soumis les joints\n",
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"toriques sur leur probabilité de dysfonctionnement. Pour cela, nous\n",
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"disposons des résultats des expériences réalisées par les ingénieurs\n",
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"de la NASA durant les 6 années précédant le lancement de la navette\n",
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"Challenger.\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Chargement des données\n",
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"Nous commençons donc par charger ces données:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" .dataframe thead th {\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>Date</th>\n",
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" <th>Count</th>\n",
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" <th>Temperature</th>\n",
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" <th>Pressure</th>\n",
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" <th>Malfunction</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>0</th>\n",
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" <td>4/12/81</td>\n",
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" <td>6</td>\n",
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" <td>66</td>\n",
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" <td>50</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1</th>\n",
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" <td>11/12/81</td>\n",
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" <td>6</td>\n",
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" <td>70</td>\n",
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" <td>50</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2</th>\n",
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" <td>3/22/82</td>\n",
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" <td>6</td>\n",
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" <td>69</td>\n",
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" <td>50</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>3</th>\n",
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" <td>11/11/82</td>\n",
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" <td>6</td>\n",
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" <td>68</td>\n",
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" <td>50</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>4</th>\n",
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" <td>4/04/83</td>\n",
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" <td>6</td>\n",
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" <td>67</td>\n",
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" <td>50</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>5</th>\n",
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" <td>6/18/82</td>\n",
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" <td>6</td>\n",
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" <td>72</td>\n",
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" <td>50</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>6</th>\n",
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" <td>8/30/83</td>\n",
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" <td>6</td>\n",
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" <td>73</td>\n",
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" <td>100</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>7</th>\n",
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" <td>11/28/83</td>\n",
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" <td>6</td>\n",
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" <td>70</td>\n",
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" <td>100</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>8</th>\n",
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" <td>2/03/84</td>\n",
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" <td>6</td>\n",
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" <td>57</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>9</th>\n",
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" <td>4/06/84</td>\n",
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" <td>6</td>\n",
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" <td>63</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>10</th>\n",
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" <td>8/30/84</td>\n",
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" <td>6</td>\n",
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" <td>70</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>11</th>\n",
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" <td>10/05/84</td>\n",
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" <td>6</td>\n",
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" <td>78</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>12</th>\n",
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" <td>11/08/84</td>\n",
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" <td>6</td>\n",
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" <td>67</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>13</th>\n",
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" <td>1/24/85</td>\n",
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" <td>6</td>\n",
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" <td>53</td>\n",
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" <td>200</td>\n",
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" <td>2</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>14</th>\n",
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" <td>4/12/85</td>\n",
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" <td>6</td>\n",
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" <td>67</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>15</th>\n",
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" <td>4/29/85</td>\n",
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" <td>6</td>\n",
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" <td>75</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>16</th>\n",
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" <td>6/17/85</td>\n",
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" <td>6</td>\n",
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" <td>70</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>17</th>\n",
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" <td>7/2903/85</td>\n",
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" <td>6</td>\n",
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" <td>81</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>18</th>\n",
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" <td>8/27/85</td>\n",
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" <td>6</td>\n",
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" <td>76</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>19</th>\n",
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" <td>10/03/85</td>\n",
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" <td>6</td>\n",
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" <td>79</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>20</th>\n",
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" <td>10/30/85</td>\n",
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" <td>6</td>\n",
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" <td>75</td>\n",
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" <td>200</td>\n",
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" <td>2</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>21</th>\n",
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" <td>11/26/85</td>\n",
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" <td>6</td>\n",
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" <td>76</td>\n",
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" <td>200</td>\n",
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" <td>0</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>22</th>\n",
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" <td>1/12/86</td>\n",
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" <td>6</td>\n",
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" <td>58</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" Date Count Temperature Pressure Malfunction\n",
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"0 4/12/81 6 66 50 0\n",
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"1 11/12/81 6 70 50 1\n",
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"2 3/22/82 6 69 50 0\n",
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"3 11/11/82 6 68 50 0\n",
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"4 4/04/83 6 67 50 0\n",
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"5 6/18/82 6 72 50 0\n",
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"6 8/30/83 6 73 100 0\n",
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"7 11/28/83 6 70 100 0\n",
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"8 2/03/84 6 57 200 1\n",
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"9 4/06/84 6 63 200 1\n",
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"10 8/30/84 6 70 200 1\n",
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"11 10/05/84 6 78 200 0\n",
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"12 11/08/84 6 67 200 0\n",
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"13 1/24/85 6 53 200 2\n",
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"14 4/12/85 6 67 200 0\n",
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"15 4/29/85 6 75 200 0\n",
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"16 6/17/85 6 70 200 0\n",
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"17 7/2903/85 6 81 200 0\n",
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"18 8/27/85 6 76 200 0\n",
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"19 10/03/85 6 79 200 0\n",
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"20 10/30/85 6 75 200 2\n",
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"21 11/26/85 6 76 200 0\n",
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"22 1/12/86 6 58 200 1"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"data = pd.read_csv(\"shuttle.csv\")\n",
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"data"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Le jeu de données nous indique la date de l'essai, le nombre de joints\n",
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"toriques mesurés (il y en a 6 sur le lançeur principal), la\n",
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"température (en Farenheit) et la pression (en psi), et enfin le\n",
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"nombre de dysfonctionnements relevés. "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Inspection graphique des données\n",
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"Les vols où aucun incident n'est relevé n'apportant aucun information\n",
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"sur l'influence de la température ou de la pression sur les\n",
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"dysfonctionnements, nous nous concentrons sur les expériences où au\n",
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"moins un joint a été défectueux.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" vertical-align: middle;\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" .dataframe thead th {\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>Date</th>\n",
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" <th>Count</th>\n",
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" <th>Temperature</th>\n",
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" <th>Pressure</th>\n",
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" <th>Malfunction</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>1</th>\n",
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" <td>11/12/81</td>\n",
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" <td>6</td>\n",
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" <td>70</td>\n",
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" <td>50</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>8</th>\n",
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" <td>2/03/84</td>\n",
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" <td>6</td>\n",
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" <td>57</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>9</th>\n",
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" <td>4/06/84</td>\n",
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" <td>6</td>\n",
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" <td>63</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>10</th>\n",
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" <td>8/30/84</td>\n",
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" <td>6</td>\n",
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" <td>70</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>13</th>\n",
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" <td>1/24/85</td>\n",
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" <td>6</td>\n",
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" <td>53</td>\n",
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" <td>200</td>\n",
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" <td>2</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>20</th>\n",
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" <td>10/30/85</td>\n",
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" <td>6</td>\n",
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" <td>75</td>\n",
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" <td>200</td>\n",
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" <td>2</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>22</th>\n",
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" <td>1/12/86</td>\n",
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" <td>6</td>\n",
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" <td>58</td>\n",
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" <td>200</td>\n",
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" <td>1</td>\n",
|
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" </tr>\n",
|
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" </tbody>\n",
|
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"</table>\n",
|
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"</div>"
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],
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"text/plain": [
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" Date Count Temperature Pressure Malfunction\n",
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"1 11/12/81 6 70 50 1\n",
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"8 2/03/84 6 57 200 1\n",
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"9 4/06/84 6 63 200 1\n",
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"10 8/30/84 6 70 200 1\n",
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"13 1/24/85 6 53 200 2\n",
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"20 10/30/85 6 75 200 2\n",
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"22 1/12/86 6 58 200 1"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"data = data[data.Malfunction>0]\n",
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"data"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Très bien, nous avons une variabilité de température importante mais\n",
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"la pression est quasiment toujours égale à 200, ce qui devrait\n",
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"simplifier l'analyse.\n",
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"\n",
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"Comment la fréquence d'échecs varie-t-elle avec la température ?\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"data": {
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|
"image/png": "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\n",
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"text/plain": [
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"<matplotlib.figure.Figure at 0x7f98e29d9dd8>"
|
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]
|
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},
|
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"metadata": {},
|
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"output_type": "display_data"
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}
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],
|
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"source": [
|
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"%matplotlib inline\n",
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"pd.set_option('mode.chained_assignment',None) # this removes a useless warning from pandas\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
|
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"data[\"Frequency\"]=data.Malfunction/data.Count\n",
|
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"data.plot(x=\"Temperature\",y=\"Frequency\",kind=\"scatter\",ylim=[0,1])\n",
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"plt.grid(True)"
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]
|
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},
|
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{
|
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"cell_type": "markdown",
|
|
"metadata": {},
|
|
"source": [
|
|
"À première vue, ce n'est pas flagrant mais bon, essayons quand même\n",
|
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"d'estimer l'impact de la température $t$ sur la probabilité de\n",
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"dysfonctionnements d'un joint. \n"
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]
|
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},
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{
|
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"cell_type": "markdown",
|
|
"metadata": {},
|
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"source": [
|
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"## Estimation de l'influence de la température\n",
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"\n",
|
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"Supposons que chacun des 6 joints toriques est endommagé avec la même\n",
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|
"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": [
|
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"/usr/lib/python3/dist-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
|
|
" from pandas.core import datetools\n"
|
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]
|
|
},
|
|
{
|
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"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>1.0</td> \n",
|
|
"</tr>\n",
|
|
"<tr>\n",
|
|
" <th>Method:</th> <td>IRLS</td> <th> Log-Likelihood: </th> <td> -3.6370</td>\n",
|
|
"</tr>\n",
|
|
"<tr>\n",
|
|
" <th>Date:</th> <td>Fri, 20 Jul 2018</td> <th> Deviance: </th> <td> 3.3763</td>\n",
|
|
"</tr>\n",
|
|
"<tr>\n",
|
|
" <th>Time:</th> <td>17:09:09</td> <th> Pearson chi2: </th> <td> 0.236</td> \n",
|
|
"</tr>\n",
|
|
"<tr>\n",
|
|
" <th>No. Iterations:</th> <td>5</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: 1.0\n",
|
|
"Method: IRLS Log-Likelihood: -3.6370\n",
|
|
"Date: Fri, 20 Jul 2018 Deviance: 3.3763\n",
|
|
"Time: 17:09:09 Pearson chi2: 0.236\n",
|
|
"No. Iterations: 5 \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",
|
|
"\"\"\""
|
|
]
|
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},
|
|
"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": [
|
|
"<matplotlib.figure.Figure at 0x7f98d595b8d0>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"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)\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": "3.6.5rc1"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 2
|
|
}
|