Optimal cost effective design of a class of noncoherent systems

A k-to-l-out-of-n system is a noncoherent system which no fewer than k and no more than l out of n units are to function for the successful operation of the system. Examples of noncoherent systems are found in communication, multiprocessor and transportation systems. Assume that the cost of units and the cost of system failure are given. In the paper, the optimization problems are formulated and solved for the minimum expected total cost of k-to-l-out-of-n systems. For fixed values of k and l, the author determines the optimal number of units minimizing the expected total system cost. Several numerical examples are given to illustrate the results