Weighted precedence and maximal precedence tests and an extension to progressive censoring

In this paper, we introduce weighted precedence and maximal precedence tests for testing the hypothesis that two distribution functions are equal, which is an extension of the precedence life-test first proposed by Nelson [Technometrics 5 (1963) 491–499] and the maximal precedence test proposed by Balakrishnan and Ng [In: Hayakawa et al. (Eds.), System and Bayesian Reliability—Essays in Honor of Prof. Richard E. Barlow on his 70th Birthday. World Scientific, Singapore, pp. 105–122]. The null distributions of these test statistics are derived. Then, we present the exact power functions under the Lehmann alternative, and compare the exact power as well as simulated power (under location-shift) of the weighted precedence and maximal precedence tests with those of the original precedence and maximal precedence tests. Next, we extend these test procedures to Type-II progressive censoring. Critical values for some combination of sample sizes and censoring schemes for r=2(1)5 are presented. We then examine the power properties of the weighted precedence and maximal precedence tests under a location-shift alternative through Monte Carlo simulations. Two examples are presented to illustrate all the test procedures discussed here. Finally, we make some concluding remarks.