Number of Working Components in Consecutive K-Out System While It Is Working

Abstract

In this article we study the distribution and expected value of the number of working components at time t in a consecutive k-out-of-n system under the condition that it is working at time t. We provide the exact distribution of the corresponding conditional random variable and compute its expected value for the system consisting of exchangeable dependent components. The results are also extended to any coherent system by the aid of system signature. Finally, we present illustrative and computational results for some systems having Lomax components.