On the optimal allocation of components within coherent systems

This paper addresses the problem of identifying optimal allocation(s) of independent components with varying individual reliabilities to specific locations within a given coherent system. Using the notion of criticality introduced by Boland et al. [Boland, P., Proschan, F., Tong, Y., 1989. Optimal arrangement of components via pairwise rearrangements. Naval Research Logistics 36, 807-815], sufficient conditions on the system design are given for ensuring that the highest possible system reliability is achieved. It is then noted that this theorem may be adapted to apply to any partial ordering of component criticalities, thereby yielding a result that may be used in tandem with algebraic arguments to identify the optimal allocation of component reliabilities in systems which fail to satisfy the sufficient conditions for overall optimality given in the main result. The latter program is illustrated in the identification of optimal allocations for systems considered by El-Neweihi et al. [El-Neweihi, E., Proschan, F., Sethuraman, J., 1986. Optimal allocation of components in parallel-series and series-parallel systems. Journal of Applied Probability 23, 770-777] and by Boland et al. [Boland, P., Proschan, F., Tong, Y., 1989. Optimal arrangement of components via pairwise rearrangements. Naval Research Logistics 36, 807-815].