Tests for homogeneity of distributions of component lifetimes from Type‐II censored system lifetime data with known system structures

In system reliability analysis, researchers are interested in evaluating the characteristics of the lifetime distribution of components in a system based on system lifetime data. In collecting system lifetime data, a censoring scheme is often adopted due to time and budget constraints. In this article, we consider the situation where the system lifetime data from two different coherent systems are subjected to Type‐II right‐censoring, and we are interested in testing the homogeneity of component lifetime distributions based on Type‐II censored system lifetime data with known system structures. Based on the Mann‐Whitney test and empirical likelihood ratio tests developed for testing the homogeneity of component lifetime distributions with complete system lifetime data, we propose different non‐parametric test procedures using the permutation of the unobserved censored system lifetimes. We consider a restricted assumption on the censored lifetimes to reduce the permutations required in the computation. The computational approaches to obtain the critical values of the proposed test procedures are provided using the Monte Carlo method. A practical example is used to illustrate the proposed test procedures. Then, the power performance of the proposed test procedures is evaluated and compared through a Monte Carlo simulation study. The simulation results show that the proposed test procedures provide comparable power performance for Type‐II censored system lifetime data in contrast to the complete sample case under different scenarios. Finally, recommendations based on the simulation results and concluding remarks are provided.