module2 exo5

module2/exo5/exo5_python_en.org

@@ -14,12 +14,12 @@
 
 # #+PROPERTY: header-args  :session  :exports both
 
-On January 27, 1986, the day before the takeoff of the shuttle /Challenger/, had
+On January 27, 1986, the day before the takeoff of the shuttle /Challenger/,
 a three-hour teleconference was held between
 Morton Thiokol (the manufacturer of one of the engines) and NASA. The
-discussion focused on the consequences of the
-temperature at take-off of 31°F (just below
-0°C) for the success of the flight and in particular on the performance of the
+discussion focused on the consequences of a 31°F (just below
+0°C) temperature, at take-off, in the success of the flight and in particular
+on the performance of the
 O-rings used in the engines. Indeed, no test
 had been performed at this temperature.
 
@@ -79,19 +79,37 @@ on the influence of temperature or pressure on malfunction.
 We thus focus on the experiments in which at least one O-ring was defective.
 
 #+begin_src python :results value :session *python* :exports both
-data = data[data.Malfunction>0]
+#data = data[data.Malfunction>0]
 data
 #+end_src
 
 #+RESULTS:
-:         Date  Count  Temperature  Pressure  Malfunction
-: 1   11/12/81      6           70        50            1
-: 8    2/03/84      6           57       200            1
-: 9    4/06/84      6           63       200            1
-: 10   8/30/84      6           70       200            1
-: 13   1/24/85      6           53       200            2
-: 20  10/30/85      6           75       200            2
-: 22   1/12/86      6           58       200            1
+#+begin_example
+        Date  Count  Temperature  Pressure  Malfunction
+0    4/12/81      6           66        50            0
+1   11/12/81      6           70        50            1
+2    3/22/82      6           69        50            0
+3   11/11/82      6           68        50            0
+4    4/04/83      6           67        50            0
+5    6/18/82      6           72        50            0
+6    8/30/83      6           73       100            0
+7   11/28/83      6           70       100            0
+8    2/03/84      6           57       200            1
+9    4/06/84      6           63       200            1
+10   8/30/84      6           70       200            1
+11  10/05/84      6           78       200            0
+12  11/08/84      6           67       200            0
+13   1/24/85      6           53       200            2
+14   4/12/85      6           67       200            0
+15   4/29/85      6           75       200            0
+16   6/17/85      6           70       200            0
+17   7/29/85      6           81       200            0
+18   8/27/85      6           76       200            0
+19  10/03/85      6           79       200            0
+20  10/30/85      6           75       200            2
+21  11/26/85      6           76       200            0
+22   1/12/86      6           58       200            1
+#+end_example
 
 We have a high temperature variability but
 the pressure is almost always 200, which should
@@ -133,29 +151,31 @@ data["Success"]=data.Count-data.Malfunction
 data["Intercept"]=1
 
 
-# logit_model=sm.Logit(data["Frequency"],data[["Intercept","Temperature"]]).fit() 
+#logit_model=sm.Logit(data['Frequency'],data[['Intercept','Temperature']]).fit()
 logmodel=sm.GLM(data['Frequency'], data[['Intercept','Temperature']], family=sm.families.Binomial(sm.families.links.logit)).fit()
 
 logmodel.summary()
+#logit_model.summary()
 #+end_src
 
 #+RESULTS:
 #+begin_example
                   Generalized Linear Model Regression Results
-==============================================================================
-Dep. Variable:              Frequency   No. Observations:                    7
-Model:                            GLM   Df Residuals:                        5
+===============================================================================
+Dep. Variable:               Frequency   No. Observations:                   23
+Model:                             GLM   Df Residuals:                       21
 Model Family:                 Binomial   Df Model:                            1
-Link Function:                  logit   Scale:                             1.0
-Method:                          IRLS   Log-Likelihood:                -3.6370
-Date:                Fri, 20 Jul 2018   Deviance:                       3.3763
-Time:                        16:56:08   Pearson chi2:                    0.236
-No. Iterations:                     5                                         
+Link Function:                   logit   Scale:                          1.0000
+Method:                           IRLS   Log-Likelihood:                -3.9210
+Date:              mer., 29 avril 2020   Deviance:                       3.0144
+Time:                         20:57:18   Pearson chi2:                     5.00
+No. Iterations:                      6
+Covariance Type:             nonrobust
 ===============================================================================
                   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
+Intercept       5.0850      7.477      0.680      0.496      -9.570      19.740
+Temperature    -0.1156      0.115     -1.004      0.316      -0.341       0.110
 ===============================================================================
 #+end_example
 
@@ -185,6 +205,7 @@ print(matplot_lib_filename)
 #+RESULTS:
 [[file:proba_estimate_python.png]]
 
+
 As expected from the initial data, the
 temperature has no significant impact on the probability of failure of the
 O-rings. It will be about 0.2, as in the tests
@@ -193,10 +214,18 @@ where we had a failure of at least one joint. Let's get back to the initial data
 #+begin_src python :results output :session *python* :exports both
 data = pd.read_csv("shuttle.csv")
 print(np.sum(data.Malfunction)/np.sum(data.Count))
+print(np.sum(data.Count))
+pfailure = np.sum(data.Malfunction)/23
+print(1-(1-0.39**2)**3)
 #+end_src
 
 #+RESULTS:
 : 0.06521739130434782
+: 138
+: Probability of failure 0.391304347826087
+: Probability failure both joints: 0.15311909262759926
+: 0.010869565217391304
+: 0.39041551376100003
 
 This probability is thus about $p=0.065$. Knowing that there is
 a primary and a secondary O-ring on each of the three parts of the
@@ -213,5 +242,4 @@ O-rings was questioned. Beyond the internal communication problems
 of NASA, which have a lot to do with this fiasco, the previous analysis
 includes (at least) a small problem.... Can you find it?
 You are free to modify this analysis and to look at this dataset
-from all angles in order to to explain what's wrong.
-
+from all angles in order to explain what's wrong.