Tests for the mean residual life

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.