Component reliability analysis of k-out-of- n systems with censored data

Abstract

It is well-known that k-out-of- n systems are of great use for improving system reliability by introducing component redundancy. In this article, we develop a method for analyzing component reliability as well as system reliability of k-out-of- n systems with independent and identically distributed components based on system lifetime data. We consider both complete and censored data. In the censored case, we distinguish situations where lifetimes are censored with and without observations on the number of failed components. The estimator of the component lifetime distribution with complete data is obtained by an appropriate functional transformation of the empirical distribution of the observed system lifetimes. The estimator is then adapted for the censored case without observation on the number of failed components by using Kaplan–Meier estimators. A data completion procedure is developed for the situation where observations on the number of failed components are available for censored units. The consistency and asymptotic distribution of the estimators are established. Simulation studies on the effect of the data completion procedure are reported.