Optimization problems in systems with minimal repair

Abstract

Abstract The k- out-of -n system is a system with n independent components such that the system operates if and only if at least k of these n components operate succesfully. Such a system is an important complex system and is used for mass transit, safety systems and computer systems. This paper considers what is the most economical k- out-of -n system with minimal repair. We solve two problems to minimise the long term expected cost rate per unit time; (i) the optimal number of elements, and (ii) the optimal replacement time before system failure. Finally, a numerical example is given.