Reliability allocation through cost minimization

• Published in: IEEE transactions on reliability Vol. 52; no. 1; pp. 106 - 111
• Main Authors: Elegbede, A.O.C., Chengbin Chu, Adjallah, K.H., Yalaoui, F.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithm design and analysis; Algorithms; Allocations; Computational efficiency; Computer Science; Constraint optimization; Cost engineering; Cost function; Design optimization; Grounding; Minimization methods; Optimization; Optimization methods; Performance evaluation; Redundancy; Redundant components; Reliability; Studies; Performance evaluation; Algorithm design and analysis; Constraint optimization; Minimization methods; Grounding; Redundancy; Optimization methods; Cost function; Reliability; Design optimization
• ISSN: 0018-9529; 1558-1721
• DOI: 10.1109/TR.2002.807242

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.