To control the risk of severe core damage during a commercial nuclear power station blackout accident, the reliability of the emergency diesel generators in starting on demand must be maintained at a high level. The paper “Empirical Bayes Estimation of the Reliability of Nuclear-Power Emergency Diesel Generators”[Technometrics (1996) 38: 11–23] contains data on the failure history of seven nuclear power plants. The following data are the number of successful demands between failures for the diesel generators at one of these plants from 1982 to 1988.

a. Calculate the mean and median of the successful demands between failures.

b. Which measure appears to best represent the center of the data?

c. Calculate the range and standard deviation, s.

d. Use the range approximation to estimate s. How close is the approximation to the true value?

e. Construct the intervals

y-bar ± s y-bar ± 2s y-bar ± 3s

Count the number of demands between failures falling in each of the three intervals. Convert these numbers to percentages and compare your results to the Empirical Rule.

f. Why do you think the Empirical Rule and your percentages do not match well?

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28 50 193 55 4 7 147 76 10 0 10 84 0 9 1 0 62 26 15 226 54 46 128 4 105 40 4 273 164 7 55 41 26 6