A Markov chain-based genetic algorithm for solving a redundancy allocation problem for a system with repairable warm standby components

Abstract

Many studies have been conducted on designing systems based on the redundancy allocation problem (RAP). However, considering repairable warm-standby components (which are subject to failure even in an idle state) is somewhat neglected by researchers due to the complex mathematical models. One of the crucial aspects of these systems is considering the probability of failure when switching to a standby component or subsystem. This study tries to highlight these imperfect switching and switch selection strategies in the redundancy allocation designs. In this regard, this article is dedicated to developing two RAP models (a single objective and a bi-objective) with warm standby repairable components by proposing a solving approach based on the genetic algorithm (GA) and Markov chains. Since the model’s objective functions minimize the system’s mean time to failure (MTTF) and cost, we discussed how imperfect switches affect the total system’s cost and mean time to failure for the proposed RAPs. Finally, we adopted a GA and a non-dominated sorting genetic algorithm (NSGA-II) to solve the proposed models due to the models’ complexity. Solving these models clearly indicates the critical role of selecting an appropriate switching strategy on the system’s costs and reliability.