A note on the conditional residual lifetime of a coherent system under double monitoring

摘要

In this note, we derive some 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 time t(1) the jth failures has occurred and at time t(2) the kth failures (j k) have not occurred yet. Based on the mixture representations, we then discuss the stochastic comparisons of the conditional residual lifetimes of two coherent systems with i.i.d. components.