Cost optimal, parallel reliability systems with fixed repair sanction

Optimisation methods under varied criteria for different parameters in stochastic reliability systems are being increasingly developed and have been reported in recent literature. The large interest evinced in this fascinating area is primarily due to its applicational value and operational role in the decision making process. Recently a parallel system has been considered and the optimal number of units discussed, as well as optimal replacement times for the system based on acquisition and replacement costs.In this paper we consider an improved version of the model formulation, by bringing in additionally the maintenance and per unit repair time costs, and develop a procedure to obtain the optimal number of components in the system with the condition that the system is allowed to undergo a prefixed maximum number of repairs, after which the system is to be replaced.The applicational use of the results is illustrated through numerical work, specialising to some known laws governing the system parameters and corresponding to different fixed number of repair sanctions.