Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints

Abstract

Modern systems are operating under dynamic environments and the components therein often exhibit positively correlated lifetimes. Moreover, due to various practical reasons such as the load sharing mechanism, it is not uncommon that lifetimes of some components dominate the others within the same system. In this study, we first propose a statistical model for system reliability evaluation by jointly considering the correlated component lifetimes and the lifetime ordering constraints. In specific, the effects of the dynamic environments are incorporated by modelling the cumulative hazard function as an exponential dispersion process and the lifetime ordering constraints are modelled by truncating the support of the joint lifetime distribution. We then discuss the statistical inference based on the proposed model. The point estimates of the model parameters as well as the lifetime quantiles are obtained by the maximum likelihood method, and the confidence intervals are constructed by using the generalized pivots. Extensive simulation show that the proposed interval estimation procedures can achieve accurate coverage even under small sample sizes. Two real examples are used to illustrate the proposed modelling and estimation framework.