Solved: In Example 6.8, we introduced the concept of a

Chapter 7, Problem 57E

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Problem 57E

In Example 6.8, we introduced the concept of a censored experiment in which n components are put on test and the experiment terminates as soon as r of the components have failed. Suppose component lifetimes are independent, each having an exponential distribution with parameter λ. Let Y1 denote the time at which the first failure occurs, Y2 the time at which the second failure occurs, and so on, so that  is the total accumulated lifetime at termination. Then it can be shown that 2 λTr has a chi-squared distribution with 2r df. Use this fact to develop a 100(1–α) CI formula for

true average lifetime 1/ λ. Compute a 95% CI from the data in Example 6.8.

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