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 θ, where lifetimes with parameter θ₁ tend to be smaller than lifetimes with parameter θ₂ whenever θ₁ is less than θ₂. For example, the lifetime distribution can be exponential with mean θ. We develop a time truncated sequential procedure for testing the null hypothesis that θ is at least as large as a specified value θ₀ against the alternative hypothesis that θ is less than θ₀. The procedure allows quick rejection of the null hypothesis when the alternative is true and provides an accurate confidence interval for θ 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.