Single change-point detection methods for small lifetime samples

In this paper, we address the problem of deciding if either n consecutive independent failure times have the same failure rate or if there exists some k∈{1,…,n}$$k\in \{1,\ldots ,n\}$$ such that the common failure rate of the first k failure times is different from the common failure rate of the last n-k$$n-k$$ failure times, based on an exponential lifetime distribution. The statistical test we propose is based on the empirical average ratio under the assumption of exponentiality. The proposed test is compared to the one based on the Mann–Whitney statistic for which no parametric assumption on the underlying distribution is necessary. The proposed statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the n failure times which enables the determination of critical values of the proposed tests by Monte Carlo methods for small sample sizes.