R version of the notebook

module2/exo5/exo5_R_en.ipynb

+{
+ "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": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<caption>A data.frame: 23 × 5</caption>\n",
+       "<thead>\n",
+       "\t<tr><th scope=col>Date</th><th scope=col>Count</th><th scope=col>Temperature</th><th scope=col>Pressure</th><th scope=col>Malfunction</th></tr>\n",
+       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
+       "</thead>\n",
+       "<tbody>\n",
+       "\t<tr><td>4/12/81  </td><td>6</td><td>66</td><td> 50</td><td>0</td></tr>\n",
+       "\t<tr><td>11/12/81 </td><td>6</td><td>70</td><td> 50</td><td>1</td></tr>\n",
+       "\t<tr><td>3/22/82  </td><td>6</td><td>69</td><td> 50</td><td>0</td></tr>\n",
+       "\t<tr><td>11/11/82 </td><td>6</td><td>68</td><td> 50</td><td>0</td></tr>\n",
+       "\t<tr><td>4/04/83  </td><td>6</td><td>67</td><td> 50</td><td>0</td></tr>\n",
+       "\t<tr><td>6/18/82  </td><td>6</td><td>72</td><td> 50</td><td>0</td></tr>\n",
+       "\t<tr><td>8/30/83  </td><td>6</td><td>73</td><td>100</td><td>0</td></tr>\n",
+       "\t<tr><td>11/28/83 </td><td>6</td><td>70</td><td>100</td><td>0</td></tr>\n",
+       "\t<tr><td>2/03/84  </td><td>6</td><td>57</td><td>200</td><td>1</td></tr>\n",
+       "\t<tr><td>4/06/84  </td><td>6</td><td>63</td><td>200</td><td>1</td></tr>\n",
+       "\t<tr><td>8/30/84  </td><td>6</td><td>70</td><td>200</td><td>1</td></tr>\n",
+       "\t<tr><td>10/05/84 </td><td>6</td><td>78</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>11/08/84 </td><td>6</td><td>67</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>1/24/85  </td><td>6</td><td>53</td><td>200</td><td>2</td></tr>\n",
+       "\t<tr><td>4/12/85  </td><td>6</td><td>67</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>4/29/85  </td><td>6</td><td>75</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>6/17/85  </td><td>6</td><td>70</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>7/2903/85</td><td>6</td><td>81</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>8/27/85  </td><td>6</td><td>76</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>10/03/85 </td><td>6</td><td>79</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>10/30/85 </td><td>6</td><td>75</td><td>200</td><td>2</td></tr>\n",
+       "\t<tr><td>11/26/85 </td><td>6</td><td>76</td><td>200</td><td>0</td></tr>\n",
+       "\t<tr><td>1/12/86  </td><td>6</td><td>58</td><td>200</td><td>1</td></tr>\n",
+       "</tbody>\n",
+       "</table>\n"
+      ],
+      "text/latex": [
+       "A data.frame: 23 × 5\n",
+       "\\begin{tabular}{r|lllll}\n",
+       " Date & Count & Temperature & Pressure & Malfunction\\\\\n",
+       " <fct> & <int> & <int> & <int> & <int>\\\\\n",
+       "\\hline\n",
+       "\t 4/12/81   & 6 & 66 &  50 & 0\\\\\n",
+       "\t 11/12/81  & 6 & 70 &  50 & 1\\\\\n",
+       "\t 3/22/82   & 6 & 69 &  50 & 0\\\\\n",
+       "\t 11/11/82  & 6 & 68 &  50 & 0\\\\\n",
+       "\t 4/04/83   & 6 & 67 &  50 & 0\\\\\n",
+       "\t 6/18/82   & 6 & 72 &  50 & 0\\\\\n",
+       "\t 8/30/83   & 6 & 73 & 100 & 0\\\\\n",
+       "\t 11/28/83  & 6 & 70 & 100 & 0\\\\\n",
+       "\t 2/03/84   & 6 & 57 & 200 & 1\\\\\n",
+       "\t 4/06/84   & 6 & 63 & 200 & 1\\\\\n",
+       "\t 8/30/84   & 6 & 70 & 200 & 1\\\\\n",
+       "\t 10/05/84  & 6 & 78 & 200 & 0\\\\\n",
+       "\t 11/08/84  & 6 & 67 & 200 & 0\\\\\n",
+       "\t 1/24/85   & 6 & 53 & 200 & 2\\\\\n",
+       "\t 4/12/85   & 6 & 67 & 200 & 0\\\\\n",
+       "\t 4/29/85   & 6 & 75 & 200 & 0\\\\\n",
+       "\t 6/17/85   & 6 & 70 & 200 & 0\\\\\n",
+       "\t 7/2903/85 & 6 & 81 & 200 & 0\\\\\n",
+       "\t 8/27/85   & 6 & 76 & 200 & 0\\\\\n",
+       "\t 10/03/85  & 6 & 79 & 200 & 0\\\\\n",
+       "\t 10/30/85  & 6 & 75 & 200 & 2\\\\\n",
+       "\t 11/26/85  & 6 & 76 & 200 & 0\\\\\n",
+       "\t 1/12/86   & 6 & 58 & 200 & 1\\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/markdown": [
+       "\n",
+       "A data.frame: 23 × 5\n",
+       "\n",
+       "| Date &lt;fct&gt; | Count &lt;int&gt; | Temperature &lt;int&gt; | Pressure &lt;int&gt; | Malfunction &lt;int&gt; |\n",
+       "|---|---|---|---|---|\n",
+       "| 4/12/81   | 6 | 66 |  50 | 0 |\n",
+       "| 11/12/81  | 6 | 70 |  50 | 1 |\n",
+       "| 3/22/82   | 6 | 69 |  50 | 0 |\n",
+       "| 11/11/82  | 6 | 68 |  50 | 0 |\n",
+       "| 4/04/83   | 6 | 67 |  50 | 0 |\n",
+       "| 6/18/82   | 6 | 72 |  50 | 0 |\n",
+       "| 8/30/83   | 6 | 73 | 100 | 0 |\n",
+       "| 11/28/83  | 6 | 70 | 100 | 0 |\n",
+       "| 2/03/84   | 6 | 57 | 200 | 1 |\n",
+       "| 4/06/84   | 6 | 63 | 200 | 1 |\n",
+       "| 8/30/84   | 6 | 70 | 200 | 1 |\n",
+       "| 10/05/84  | 6 | 78 | 200 | 0 |\n",
+       "| 11/08/84  | 6 | 67 | 200 | 0 |\n",
+       "| 1/24/85   | 6 | 53 | 200 | 2 |\n",
+       "| 4/12/85   | 6 | 67 | 200 | 0 |\n",
+       "| 4/29/85   | 6 | 75 | 200 | 0 |\n",
+       "| 6/17/85   | 6 | 70 | 200 | 0 |\n",
+       "| 7/2903/85 | 6 | 81 | 200 | 0 |\n",
+       "| 8/27/85   | 6 | 76 | 200 | 0 |\n",
+       "| 10/03/85  | 6 | 79 | 200 | 0 |\n",
+       "| 10/30/85  | 6 | 75 | 200 | 2 |\n",
+       "| 11/26/85  | 6 | 76 | 200 | 0 |\n",
+       "| 1/12/86   | 6 | 58 | 200 | 1 |\n",
+       "\n"
+      ],
+      "text/plain": [
+       "   Date      Count Temperature Pressure Malfunction\n",
+       "1  4/12/81   6     66           50      0          \n",
+       "2  11/12/81  6     70           50      1          \n",
+       "3  3/22/82   6     69           50      0          \n",
+       "4  11/11/82  6     68           50      0          \n",
+       "5  4/04/83   6     67           50      0          \n",
+       "6  6/18/82   6     72           50      0          \n",
+       "7  8/30/83   6     73          100      0          \n",
+       "8  11/28/83  6     70          100      0          \n",
+       "9  2/03/84   6     57          200      1          \n",
+       "10 4/06/84   6     63          200      1          \n",
+       "11 8/30/84   6     70          200      1          \n",
+       "12 10/05/84  6     78          200      0          \n",
+       "13 11/08/84  6     67          200      0          \n",
+       "14 1/24/85   6     53          200      2          \n",
+       "15 4/12/85   6     67          200      0          \n",
+       "16 4/29/85   6     75          200      0          \n",
+       "17 6/17/85   6     70          200      0          \n",
+       "18 7/2903/85 6     81          200      0          \n",
+       "19 8/27/85   6     76          200      0          \n",
+       "20 10/03/85  6     79          200      0          \n",
+       "21 10/30/85  6     75          200      2          \n",
+       "22 11/26/85  6     76          200      0          \n",
+       "23 1/12/86   6     58          200      1          "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "data = read.csv(\"shuttle.csv\",header=T)\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": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<table>\n",
+       "<caption>A data.frame: 7 × 5</caption>\n",
+       "<thead>\n",
+       "\t<tr><th></th><th scope=col>Date</th><th scope=col>Count</th><th scope=col>Temperature</th><th scope=col>Pressure</th><th scope=col>Malfunction</th></tr>\n",
+       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
+       "</thead>\n",
+       "<tbody>\n",
+       "\t<tr><th scope=row>2</th><td>11/12/81</td><td>6</td><td>70</td><td> 50</td><td>1</td></tr>\n",
+       "\t<tr><th scope=row>9</th><td>2/03/84 </td><td>6</td><td>57</td><td>200</td><td>1</td></tr>\n",
+       "\t<tr><th scope=row>10</th><td>4/06/84 </td><td>6</td><td>63</td><td>200</td><td>1</td></tr>\n",
+       "\t<tr><th scope=row>11</th><td>8/30/84 </td><td>6</td><td>70</td><td>200</td><td>1</td></tr>\n",
+       "\t<tr><th scope=row>14</th><td>1/24/85 </td><td>6</td><td>53</td><td>200</td><td>2</td></tr>\n",
+       "\t<tr><th scope=row>21</th><td>10/30/85</td><td>6</td><td>75</td><td>200</td><td>2</td></tr>\n",
+       "\t<tr><th scope=row>23</th><td>1/12/86 </td><td>6</td><td>58</td><td>200</td><td>1</td></tr>\n",
+       "</tbody>\n",
+       "</table>\n"
+      ],
+      "text/latex": [
+       "A data.frame: 7 × 5\n",
+       "\\begin{tabular}{r|lllll}\n",
+       "  & Date & Count & Temperature & Pressure & Malfunction\\\\\n",
+       "  & <fct> & <int> & <int> & <int> & <int>\\\\\n",
+       "\\hline\n",
+       "\t2 & 11/12/81 & 6 & 70 &  50 & 1\\\\\n",
+       "\t9 & 2/03/84  & 6 & 57 & 200 & 1\\\\\n",
+       "\t10 & 4/06/84  & 6 & 63 & 200 & 1\\\\\n",
+       "\t11 & 8/30/84  & 6 & 70 & 200 & 1\\\\\n",
+       "\t14 & 1/24/85  & 6 & 53 & 200 & 2\\\\\n",
+       "\t21 & 10/30/85 & 6 & 75 & 200 & 2\\\\\n",
+       "\t23 & 1/12/86  & 6 & 58 & 200 & 1\\\\\n",
+       "\\end{tabular}\n"
+      ],
+      "text/markdown": [
+       "\n",
+       "A data.frame: 7 × 5\n",
+       "\n",
+       "| <!--/--> | Date &lt;fct&gt; | Count &lt;int&gt; | Temperature &lt;int&gt; | Pressure &lt;int&gt; | Malfunction &lt;int&gt; |\n",
+       "|---|---|---|---|---|---|\n",
+       "| 2 | 11/12/81 | 6 | 70 |  50 | 1 |\n",
+       "| 9 | 2/03/84  | 6 | 57 | 200 | 1 |\n",
+       "| 10 | 4/06/84  | 6 | 63 | 200 | 1 |\n",
+       "| 11 | 8/30/84  | 6 | 70 | 200 | 1 |\n",
+       "| 14 | 1/24/85  | 6 | 53 | 200 | 2 |\n",
+       "| 21 | 10/30/85 | 6 | 75 | 200 | 2 |\n",
+       "| 23 | 1/12/86  | 6 | 58 | 200 | 1 |\n",
+       "\n"
+      ],
+      "text/plain": [
+       "   Date     Count Temperature Pressure Malfunction\n",
+       "2  11/12/81 6     70           50      1          \n",
+       "9  2/03/84  6     57          200      1          \n",
+       "10 4/06/84  6     63          200      1          \n",
+       "11 8/30/84  6     70          200      1          \n",
+       "14 1/24/85  6     53          200      2          \n",
+       "21 10/30/85 6     75          200      2          \n",
+       "23 1/12/86  6     58          200      1          "
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "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": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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9cvK3J/KJoojpBgGU8hPWUuPpxcfTnU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\nRTZ+AAAAAElFTkSuQmCC",
+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot(data=data, Malfunction/Count ~ Temperature, ylim=c(0,1))"
+   ]
+  },
+  {
+   "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": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "Call:\n",
+       "glm(formula = Malfunction/Count ~ Temperature, family = binomial(link = \"logit\"), \n",
+       "    data = data, weights = Count)\n",
+       "\n",
+       "Deviance Residuals: \n",
+       "      2        9       10       11       14       21       23  \n",
+       "-0.3015  -0.2836  -0.2919  -0.3015   0.6891   0.6560  -0.2850  \n",
+       "\n",
+       "Coefficients:\n",
+       "             Estimate Std. Error z value Pr(>|z|)\n",
+       "(Intercept) -1.389528   3.195752  -0.435    0.664\n",
+       "Temperature  0.001416   0.049773   0.028    0.977\n",
+       "\n",
+       "(Dispersion parameter for binomial family taken to be 1)\n",
+       "\n",
+       "    Null deviance: 1.3347  on 6  degrees of freedom\n",
+       "Residual deviance: 1.3339  on 5  degrees of freedom\n",
+       "AIC: 18.894\n",
+       "\n",
+       "Number of Fisher Scoring iterations: 4\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "logistic_reg = glm(data=data, Malfunction/Count ~ Temperature, weights=Count, \n",
+    "                   family=binomial(link='logit'))\n",
+    "summary(logistic_reg)"
+   ]
+  },
+  {
+   "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": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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DSkUReP4+VvgJe/AQFCAgQICRAgJECA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\n/416p0vO+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+      "text/plain": [
+       "plot without title"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "tempv = seq(from=30, to=90, by = .5)\n",
+    "rmv <- predict(logistic_reg,list(Temperature=tempv),type=\"response\")\n",
+    "plot(tempv,rmv,type=\"l\",ylim=c(0,1))\n",
+    "points(data=data, Malfunction/Count ~ Temperature)"
+   ]
+  },
+  {
+   "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": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "0.0652173913043478"
+      ],
+      "text/latex": [
+       "0.0652173913043478"
+      ],
+      "text/markdown": [
+       "0.0652173913043478"
+      ],
+      "text/plain": [
+       "[1] 0.06521739"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "data_full = read.csv(\"shuttle.csv\",header=T)\n",
+    "sum(data_full$Malfunction)/sum(data_full$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": "R",
+   "language": "R",
+   "name": "ir"
+  },
+  "language_info": {
+   "codemirror_mode": "r",
+   "file_extension": ".r",
+   "mimetype": "text/x-r-source",
+   "name": "R",
+   "pygments_lexer": "r",
+   "version": "3.6.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}