Optimal replacement policy (N∗, n∗) for a parallel system with common cause failure and geometric repair time

Abstract The purpose of this article is to present an improved replacement model for a parallel system of N identical units, by bringing in common cause failure (CCF), maintenance cost and repair cost per unit time additionally, and to develop a procedure to obtain the optimal redundant units N∗ and optimal number of repairs n∗ with the conditions that the system is allowed to undergo at most a prefixed number of repairs before to be replaced and the successive reapir times after failures constitute a non-decreasing Geometric process. Several conditions for the existence of the optimal N∗ and n∗ is stated and the results are illustrated by a numerical example.