Conditional Residual Lifetimes of (n-k+1)-out-of n Systems with Mixed Erlang Components

Abstract

We consider an (n−k+1)-out-of-n system with component lifetimes being correlated. The main objective of this paper is to study the conditional residual lifetime of an (n−k+1)-out-of-n system, given that at a fixed time a certain number of components have failed, assuming that the component lifetimes follow a multivariate Erlang mixture. Comparison studies of the stochastic ordering of the (n−k+1)-out-ofn system are presented. Several examples are presented to illustrate and confirm our results.