The number of failed components in series–parallel system and its application to optimal design. (December 2020) - Eryilmaz, Serkan; Özkurt, Fatma Yerlikaya; Erkan, T. Erman
Abstract: The number of components that are failed at the time of system failure is a useful quantity since it gives an idea of how many spares should be available to replace all failed components upon the system failure. In this paper, the number of failed components is considered at subsystem and system levels for the series–parallel system that consists of K subsystems. In particular, the joint behavior of the number of failed components in each subsystem is studied when each subsystem has identical components and different subsystems have different types of components. The results are then used to find the optimal number of components in each subsystem by minimizing an expected cost per unit of time upon the system failure. Highlights: The number of failed component at the when the system fails. series–parallel system consists of K subsystems. Probabilistic derivations on the number of failed components. Optimal number of components that minimize mean cost rate.