Optimization Problems in k-out-of-n Systems

A k-out-of-n:G system is an important complex system and is used for mass transit and computer systems. This paper does not discuss the availability, but considers what is the most economical k-out-of-n system when the failure rate of each element is constant. We solve two problems to minimize the mean cost-rate; i) the optimal number of elements and ii) the optimal replacement time before system failure. A numerical example is given.