Question

Asked Nov 21, 2019

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In a 1996 article published in Technometrics, 38, pp. 11–22, 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 (EDG) 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 reliability of the seven nuclear power plants. (Use Data _8).

Run an ANOVA (Regardless of the assumptions) and Kruskal–Wallis test.

Step 1

**Introduction:**

The null and alternative hypotheses for both the tests are:

H_{0}: There is no significant difference between the groups.

H_{1}: At lest one of the groups has different effect than the others.

Step 2

**ANOVA:**

Enter the data in an Excel sheet, as given.

Choose Data > Data Analysis > Anova: Single Factor > OK.

Enter Input Range as $A$1:$G$35, choose Columns under Grouped by, tick on Labels and click OK.

The output is:

Step 3

**Kruskal-Wallis test:**

In cell I2, enter the formula =RANK.AVG(A2,$A$2:$G$35,1).

Drag it along the column, as well as along the rows, to ensure that the rank of each observation is obtained.

Find the value of *R*, that is total group rank for each group.

Denote *N* as the total number of observations, *n* as the observation for a particular group.

The test statistic is obtained below:

*H* = [12/{*N* (*N* + 1)} Σ (*R*2/*n*)] – 3 (*N* + 1)

= 12/{(103) (104)} (289,694) – 3 (104) [Refer to the calculation shown below in the screenshot of the...

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