In a 1996 article published in Technometrics, (Martz, Kvan, Abramson, 1996), the authors discuss the reliability of nuclear-power-plant emergency generators. To control the risk of damage to the nuclear core during accidents at nuclear plants, the reliability of emergency diesel generators (EDGs) to start on demand must be maintained at a very high level. At each nuclear power plant, there are a number of such generators. An overall measure of reliability is obtained by counting the number of times the EDGs successfully work when needed. The table here provides the number of successful demands for implementation of an EDG between each subsequent failure in an EDG for all the EDGs at each of seven nuclear power plants. A regulatory agency wants to determine if there is a difference in the reliabilities of the seven nuclear power plants.

a. Do the conditions necessary for conducting the AOV F test appear to be satisfied by these data?
b. Because the data are counts of the number of successes for the EDGs, the Poisson model may be an alternative to the normal-based analysis. Apply a ­transformation to the data, and then apply the AOV F test to the transformed data.
c. As a second alternative analysis that has fewer restrictions, answer the agency€™s question by applying the Kruskal€“Wallis test to the reliability data.
d. Compare your conclusions to parts (a)€“(c). Which of the three procedures provides the conclusion about which you feel most confident?

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Plant Number of Times EDG Works A 34 28 50 193 55 47 174 76 10 0 10 84 0 962 26 15 226 54 46 128 4 105 40 4 273 4 7 55 26 6 2 75 6 246 64 3 03 1 20 78 64 29 38 29 60 18 108 9 17 88 28 B 15 С 17 D 8 E 12 139 21 214 67 14 1 92 119 237 10 71 G 10 142 110 3273 54 32 3 40 23 30 17 7 12 6 12 7 5 0 6 016 1 58 13 36 3 19