A novel approach for optimal cost-effective design of complex repairable systems

Almost every engineering and manufacturing system consists of several, subsystems, which are in general nonidentical and are subjected to stochastic failures and repairs. The system success logic can be represented using a combinatorial reliability model in terms of the states of subsystems, where as the success logic of each subsystem can be represented using a k-out-of-n structure. The long run cost associated with the downtime can be lowered by adding additional spares in each subsystem, which in turn can increase the operational and maintenance costs. Thus, it is desirable to find the optimal number of components in each subsystem that minimizes the overall cost associated with the system. The main contributions of this paper are the following: 1) formulation of an average cost function of complex. repairable systems and 2) development of a new method to obtain tighter bounds for the optimal number of spares for each subsystem. The tighter bounds are extremely useful to reduce the search space and hence improve the efficiency of the optimization algorithm. With the proposed bounds, for a series system consisting of m parallel subsystems, the computational complexity to find the near optimal solution, which is the optimal solution in most cases, is 0 (m).