Cost minimization of maintained multi-state system using optimal load distribution

This paper presents a method for determining a minimal cost of a multi-state system subject to a corrective maintenance. The minimal cost is achieved by finding an optimal load distribution from a sequence of possible combinations. The cost considered is a combination of downtime cost (loss of productivity) and repair cost. The former is affected by a penalty value. The element failure rate depends on its current load. The universal generating function is used to evaluate the performance distribution of the entire system. Then, the unavailability and the repair time are estimated in order to obtain the objective function. The objective function is minimized using genetic algorithm. An illustrative example is presented. The effect of penalty value is studied.