Reliability allocation through cost minimization

This paper considers the allocation of reliability and redundancy to parallel-series systems, while minimizing the cost of the system. It is proven that under usual conditions satisfied by cost functions, a necessary condition for optimal reliability allocation of parallel-series systems is that the reliability of the redundant components of a given subsystem are identical. An optimal algorithm is proposed to solve this optimization problem. This paper proves that the components in each stage of a parallel-series system must have identical reliability, under some nonrestrictive condition on the component's reliability cost functions. This demonstration provides a firm grounding for what many authors have hitherto taken as a working hypothesis. Using this result, an algorithm, ECAY, is proposed for the design of systems with parallel-series architecture, which allows the allocation of both reliability and redundancy to each subsystem for a target reliability for minimizing the system cost. ECAY has the added advantage of allowing the optimal reliability allocation in a very short time. A benchmark is used to compare the ECAY performance to LM-based algorithms. For a given reliability target, ECAY produced the lowest reliability costs and the optimum redundancy levels in the successive reliability allocation for all cases studied, viz, systems of 4,5, 6,7, 8, 9 stages or subsystems. Thus ECAY, as compared with LM-based algorithms, yields a less costly reliability allocation within a reasonable computing time on large systems, and optimizes the weight and space-obstruction in system design throughout an optimal redundancy allocation.