Results on the past lifetime of (n - k + 1)-out-of-n structures with nonidentical components

Abstract

We consider a (n - k + 1)-out-of-n system with independent and nonidentical components. Under the condition that at time t the system has failed we study the past lifetime of the components of the system. The mean past lifetime of the components is defined and some of its properties are investigated. Stochastic comparisons are also made between the past lifetime of different systems. © 2010 Springer-Verlag.