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 l. Let Y1 denote the time at which the first failure 100(1 2 a)

Xi u

ˆ

u 5 1 3

(m1 1 m2 1 m3) 2 m4 mi 5 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 has a chi-squared distribution with 2r df.

Use this fact to develop a % CI formula for true average lifetime . Compute a 95% CI from the data in Example 6.8.