Qualitative Properties of Profit-Maximizing K-Out-of-N Systems Subject to Two Kinds of Failures

Abstract

This paper derives several properties of the optimal k-out-of-n: G systems where: (i) the i.i.d. components can be, with a pre-specified frequency, in one of two possible modes, (ii) components are subject to failures in each of the two modes, and (iii) the costs of two kinds of system's failures are not necessarily the same. A characterization of the optimal k which maximizes the system's expected profit is obtained (a special case of this optimization criterion is the maximization of the system's reliability). We show how one can predict, based directly on the parameters of the system, whether the optimal k is smaller or larger than one-half of n. Also, the directions of change in the optimal k resulting from changes in the system's parameters are ascertained.