Testing whether failure rate changes its trend with unknown change points

The problem of testing the trend change of failure rate is of great interest in the reliability and survival analysis. In this paper, we develop a new test procedure for testing whether or not the failure rate changes its trend. One big advantage of this test is that neither the change points nor the proportions at which the trend changes occur need to be known. We establish the asymptotic null distribution of the proposed test statistic to obtain the asymptotic null critical values for the test to be applied. To study the performance of the new test procedure, we conduct Monte Carlo simulations to compute the powers of the test against the lognormal alternatives and the Hjorth alternatives and to compare these powers with those of other existing tests. An example is presented to illustrate the application of the test.