| Abstract: | In this paper, we consider a coherent system with n independent and identically distributed components under the condition that the system is monitored at time instances t1 and t2 (t1 < t2). First, various mixture representations for reliability function of the conditional residual lifetime of the coherent system are derived under different scenarios at times t1 and t2 (t1 < t2). Several stochastic comparisons between two systems are also made based on the proposed conditional random variables. Then, we consider the conditional residual lifetime of the functioning components of the system given that j components have failed at time t1 and the system has failed at time t2. Some stochastic comparisons on the proposed conditional residual lifetimes are investigated. Several illustrative graphs and examples are also provided. |
