Tests for homogeneity of distributions of component lifetimes from system lifetime data with known system signatures

In this article, we discuss the problem of testing the homogeneity of distributions of component lifetimes based on system lifetime data when the system signatures are known. Both parametric and nonparametric procedures are developed for this problem. For nonparametric testing, the Mann–Whitney‐type statistic is used, and its performance and limitations are discussed. Next, we assume the component lifetimes to follow exponential distributions and then develop different parametric tests. Exact and asymptotic methods are developed based on the method of moments estimators. A Monte Carlo simulation study is used to compare the performance of different parametric procedures with that of the nonparametric procedure. Based on the results of the simulation study, discussions and practical recommendations are made and finally some concluding remarks are provided.