Improvement of Ordinal Representation Scheme for Solving Optimal Component Arrangement Problem of Circular Consecutive-k-out-of-n: F System

Abstract

A circular consecutive-k-out-of-n: F system consists of n components arranged along a circular path. This system fails if k or more consecutive components fail. In order to obtain the optimal component arrangement, one needs to calculate n! system reliabilities. As n becomes large, however, the amount of calculation would be intolerably large. In order to ameliorate this problem, we propose two kinds of genetic algorithms to obtain the quasi optimal solution for this problem within a reasonable computing time. One employs Grefenstette’s ordinal representation scheme. The other employs special ordinal representation scheme we have developed to eliminate arrangements with the same system reliability produced by rotation and/or reversal of certain arrangements. In addition to that, we improved the scheme to produce only arrangements that allocate components with low failure probabilities at every k-th position. We compared their performances and demonstrated the advantage of the scheme we developed through numerical experiments.