Abstract:

In system reliability engineering, systems are made up of different components, and these systems can be complex. For various purposes, engineers and researchers are often interested in the lifetime distribution of the system as well as the lifetime distribution of the components that make up the system. In many cases, the lifetimes of an n-component coherent system can be observed, but not the lifetimes of the components. In recent years, parametric and nonparametric inference for the lifetime distribution of components based on system lifetime lifetimes has been developed. In this talk, the recent development of statistical inference of the reliability characteristics of the components in the system based on the lifetimes of systems with the same structure will be discussed. First, we discuss the problem of testing the homogeneity of component lifetime distributions based on system lifetime data with known system signatures. Several nonparametric testing statistics based on the empirical likelihood method are proposed for testing the homogeneity of two or more component lifetime distributions. Both complete and Type-II censored system lifetime data will be considered. The performance of the proposed empirical likelihood ratio tests is compared with other parametric and nonparametric tests in the literature. Then, we study the optimal design of constant-stress life-testing experiments with n-component systems. Since experimental schemes with shorter experimental time and accurate statistical inference are desired, we consider putting the experimental units as n-component systems and propose schemes based on those n-component systems. Different experimental schemes based on n-component systems are considered, and the performances of these experimental schemes are compared via mathematical analysis and Monte Carlo simulation. The merits of the proposed experimental schemes based on n-component systems are discussed, and future research directions are provided.