Tests for the mean residual life

TLDR

The study aims to develop statistical tests for decreasing mean residual life and the “new better than used in expectation” property. The authors construct V* and K* test statistics to evaluate these alternatives, providing critical values and large‑sample approximations. They show that V* is a new test for decreasing mean residual life, K* equals the total time on test, and both tests are consistent with asymptotic relative efficiency, thereby reinterpreting the total time on test as a test for a broader class of alternatives including NBU.

Abstract

In this paper we develop tests for alternatives representing decreasing mean residual life and the property 'new better than used in expectation'. The decreasing mean residual life test statistic, V*, is new, and critical constants and a large-sample approximation are obtained to make the test readily applicable. The new better than used in expectation statistic, K*, is shown to be equivalent to the total time on test statistic; the latter is ordinarily viewed as a test statistic for alternatives of increasing failure rate. Consistency and asymptotic relative efficiency results are obtained for the tests based on V* and K*. These results lead to a reinterpretation of the total time on test statistic as a test statistic for classes of alternatives larger than the increasing failure rate class and including the 'new better than used in expectation' class.