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Reliability of Automobile Models

A study is performed to compare the reliability of several models of automobiles. Three different automobile models ( Model ) from each of four domestic automobile manufacturers ( Make ) are tested . Three different cars of each make and model are subjected to a reliability test and given a score between 1 and 100 ( Score ), where higher scores indicate greater reliability.

The following statements create the SAS data set auto .

  title 'Reliability of Automobile Models';   data auto;   input Make $ Model Score @@;   datalines;   a 1 62  a 2 77  a 3 59   a 1 67  a 2 73  a 3 64   a 1 60  a 2 79  a 3 60   b 1 72  b 2 58  b 3 80   b 1 75  b 2 63  b 3 84   b 1 69  b 2 57  b 3 89   c 1 94  c 2 76  c 3 81   c 1 90  c 2 75  c 3 85   c 1 88  c 2 78  c 3 85   d 1 69  d 2 73  d 3 90   d 1 72  d 2 88  d 3 87   d 1 76  d 2 87  d 3 92   ;  

The Make variable contains the make of the automobile, represented here by ˜a , ˜b , ˜c , or ˜d , while the Model variable represents the automobile model with a ˜1 , ˜2 , or ˜3 . The Score variable contains the reliability scores given to the three sampled cars from each Make - Model group . Since the automobile models are nested within their makes, the NESTED procedure is used to analyze this data. The NESTED procedure requires the data to be sorted by Make and, within Make , by Model , so the following statements execute a PROC SORT before completing the analysis.

  proc sort;   by Make Model;   proc nested;   class Make Model;   var Score;   run;  

The Model variable appears after the Make variable in the CLASS statement because it is nested within Make . The VAR statement specifies the response variable. The output is displayed in Figure 49.1.

  Reliability of Automobile Models   The NESTED Procedure   Coefficients of Expected Mean Squares   Source      Make      Model      Error   Make           9          3          1   Model          0          3          1   Error          0          0          1   Nested Random Effects Analysis of Variance for Variable Score   Variance                Sum of                   Error                    Variance   Percent   Source        DF       Squares  F Value  Pr > F  Term    Mean Square     Component  of Total   Total         35   4177.888889                            119.368254    131.876543  100.0000   Make           3   1709.000000     2.15  0.1719   Model   569.666667     33.867284   25.6811   Model          8   2118.888889    18.16  <.0001   Error   264.861111     83.425926   63.2606   Error         24    350.000000                             14.583333     14.583333   11.0583   Score Mean                         75.94444444   Standard Error of Score Mean        3.97794848  

Figure 49.1: Output from PROC NESTED

Figure 49.1 first displays the coefficients of the variance components that make up each of the expected mean squares, then the ANOVA table is displayed. The results do not indicate significant variation between the different automobile makes ( F = 2.15 , p = 0.1719). However, they do suggest that there is significant variation between the different models within the makes ( F = 18.16 , p < 0.0001). This is evident in the fact that the make of car accounts for only 25.7% of the total variation in the data, while the car model accounts for 63.3% (as shown in the Percent of Total column). The estimated variance components are shown in the Variance Component column.