The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections

Abstract

In this manuscript, we gain a mixture representation for reliability function of the residual lifetime of unfailed components in a coherent system under periodical inspections, given that the number of failed components before time t1 is r(≥0), but the system is still operating at time t1, and the system eventually failed at time t2(>t1). Some aging properties and stochastic orders of the residual lifetime on survival components are also established. Finally, some numerical examples and graphs are given in order to confirm the theoretical results.