Conditional residual lifetimes of coherent systems under double monitoring

In this paper, we obtain a mixture representation for the reliability function of the conditional residual lifetime of a coherent system with n independent and identically distributed (i.i.d.) components under double monitoring. We suppose that at time t1, j components have failed while at time t2 the system is still alive. Based on these mixture representation, we then study stochastic comparisons of the conditional residual lifetimes of two …