Cost—Optimal replacement policy (N∗, n∗) for a parallel system with common cause failure

Abstract The purpose of this article is to present an improved replacement model for a parallel system of N identical units, by taking common failure and repair and maintenance costs into consideration, and to develop the methods for obtaining the (1) optimal redundant units N ∗ for a fixed n , (2) optimal number of repairs n ∗ for a fixed N , and (3) optimal pair ( N ∗ , n ∗ ) simultaneously, respectively, under the condition that the system is allowed to undergo at most a prefixed number of repairs before being replaced. The results are illustrated by numerical examples.