Qualitative properties of profit-making
k-out-of-n systems subject to two kinds of
Raaj Kumar Sah and Joseph E. Stiglitz
IEEE Transactions on Reliability, Volume 37, Number 5, December 1988, pages 515-520.
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This paper derives several properties of the optimal k-out-of-n systems where: 1) the i.i.d. components can be, with a pre-specified frequency, in one of two possible modes, 2) components are subject to failures in each of the two modes, and 3) the costs of two kinds of system failures are not necessarily the same. A characterization of the optimal k which maximizes the mean system-profit is obtained (a special case of this optimization criterion is the maximization of system reliability). We show how one can predict, based directly on the parameters of the system, whether the optimal k is smaller or larger than ½ n. Also, the directions of change in the optimal k resulting from changes in system parameters are ascertained. A sub-class of our formulation and results corresponds to the case examined in the literature in which the optimal k is chosen to maximize the system’s reliability.