Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 7, Problem 57SE
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 Tr = Y1 + ⋯ + Yr + (n − r)Yr is the total accumulated lifetime at termination. Then it can be shown that 2λTr 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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Chapter 7 Solutions
Probability and Statistics for Engineering and the Sciences
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