Interval Estimation After Sequential Testing Based on the Total Time on Test

Industrial life testing experiments often select m items at random to put on test. The items operate independently and are not replaced upon failure. Assume that the lifetime of each item has a probability distribution depending on an unknown parameter , where lifetimes with parameter 1 tend to be smaller than lifetimes with parameter 2 whenever 1 is less than 2 . For example, the lifetime distribution can be exponential with mean . We develop a time truncated sequential procedure for testing the null hypothesis that is at least as large as a specified value 0 against the alternative hypothesis that is less than 0 . The procedure allows quick rejection of the null hypothesis when the alternative is true and provides an accurate confidence interval for when the null hypothesis is accepted at the conclusion of the test. After deriving this procedure, we discuss the exponential case and illustrate our results with an example.