On the choice of precedence tests

Abstract

The best precedence test (BPT) is derived for testing the hypothesis that the lifetimes of two types of items on test have the same distribution. The test has maximum power in the class of the Lehmann type of alternatives F - 1 - (1-G) , A > 1, where F and G are probability distributions of the lifetimes of two types of items on test. This class includes exponential distributions, the Weibull distribution differing only in scale and distributions with proportional hazard rates. Exact power of the BPT is compared with other nonparametrie and parametric tests. The test may terminate before all the lifetimes of the items on test are recorded. In comparing with competing tests of equal size, the power functions are similar but a considerable number of items can be saved and the time on test can be reduced by using the BPT

Keywords:

• Lehmann alternatives
• Mann-Whitney-Wilcoxon test
• average number of failures