Redundancy optimization of k-out-of-n systems with common-cause failures

The problem of determining the optimal number of redundant units in k-out-of-n systems with common-cause failures (CCFs) is discussed. The mean cost rate is obtained, its behavior is examined considering both CCFs and random failures of the units, and the number of redundant units minimizing the mean cost rate is shown to be finite and unique. For the problem of determining the optimal number of redundant units and inspection period, the mean cost rate is obtained and a solution procedure is presented. Numerical studies are given which indicate that CCFs tend to reduce the optimal number of redundant units