Estimating Jointly System and Component Reliabilities Using a Mutual Censorship Approach

Abstract

Let $F$ denote the life distribution of a coherent structure of independent components. Suppose that we have a sample of independent systems, all having the same structure. Each system is continuously observed until it fails. For every component in each system, either a failure time or a censoring time is recorded. A failure time is recorded if the component fails before or at the time of system failure; otherwise a censoring time is recorded. We introduce a method for finding estimates for $F(t)$, quantiles and other functionals of $F$, based on the censorship of the component lives by system failure. We use the theory of counting processes and stochastic integrals to obtain limit theorems that enable the construction of confidence intervals for large samples. Our approach extends and gives a novel application of censoring methodology.