k-out-of-m system availability with minimum-cost allocation spares

An optimization method for determining the number of spare units that should be allocated to a k-out-of-m system to minimize the system-spares cost yet attain the specified system availability is presented. The objective function for optimization is a nonlinear integer type. The optimization method is a variation of the simplex search technique used for continuous functions. The optimization problem is cast in a form that minimizes the system-spares cost, with the required system availability as an inequality constraint. Results obtained by using the proposed optimization technique, as well as the computation time required for optimization, are compared to those for methods developed specifically for dealing with nonlinear integer problems. The method is simple, easy to implement, and yet very effective in dealing with the spare allocation problem for k-out-of-m:F systems