Statistica Sinica 5(1995), 251-260

ON TIME-SEQUENTIAL TEST FOR A CLASS

OF DISTRIBUTIONS

Jeng-Fu Liu

Fu Jen Catholic University

Abstract: This paper studies the sequential life testing problem in which the underlying distribution of the length of life can be transformed to an exponential distribution in a certain way. We obtain some asymptotic optimum properties of time-sequential probability ratio tests (TSPRT), and give approximate formulas for the error probabilities and for the expected number of failures of these tests, which improve some of the results in Epstein and Sobel (1955).

Key words and phrases: Asymptotic optimality, intensity, on-test time, time-sequent- ial test, time-sequential probability ratio test.