Hon Keung Tony Ng
In system reliability, practitioners may be interested in testing the homogeneity of the component lifetime distributions based on system lifetimes from multiple data sources for various reasons, such as identifying the component supplier that provides the most reliable components.
In the first part of the dissertation, we develop distribution-free hypothesis testing procedures for the homogeneity of the component lifetime distributions based on system lifetime data when the system structures are known. Several nonparametric testing statistics based on the empirical likelihood method are proposed for testing the homogeneity of two or more component lifetime distributions. The computational approaches to obtain the critical values of the proposed test procedures are provided. The performances of the proposed empirical likelihood ratio test procedures are evaluated and compared to the nonparametric Mann-Whitney $U$ test and some parametric test procedures. The simulation results show that the proposed test procedures provide comparable power performance under different sample sizes and underlying component lifetime distributions, and they are powerful in detecting changes in the shape of the distributions.
In collecting system lifetime data, censoring is often adopted due to time and budget constraints. In the second part of the dissertation, we consider the situation where the system lifetime data from two different kinds of systems are subjected to Type-II censoring, and we are interested in testing the homogeneity of distributions of component lifetimes from Type-II censored system lifetime data with known system structures. Based on the Mann-Whitney $U$ test and empirical likelihood ratio tests developed for testing the homogeneity of distributions of component lifetimes with complete system lifetime data, we propose different non-parametric test procedures using the idea of permutation of the censored system lifetimes. We consider a restricted assumption on the equality of 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 performances of the proposed test procedures are evaluated and compared using a Monte Carlo simulation study. The simulation results show that the proposed test procedures provide good power performance for Type-II censored system lifetime data under different scenarios.
Finally, summaries of the major contributions of the thesis and concluding remarks are provided. Some possible future research directions are also discussed.
Hon Keung Tony Ng
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Qu, Jingjing, "Empirical Likelihood Ratio Tests for Homogeneity of Distributions of Component Lifetimes from System Lifetime Data with Known System Structures" (2023). Statistical Science Theses and Dissertations. 38.