Conditional residual lifetimes of coherent systems

Abstract

In this paper, we derive mixture representations for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under the condition that at least j and at most k - 1 (. j < k) components have failed by time t. Based on these mixture representations, we then discuss stochastic comparisons of the conditional residual lifetimes of two coherent systems with independent and identical components. © 2013 Elsevier B.V.