A cost minimisation model for system reliability allocation
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 28 May 2019
Issue publication date: 23 September 2019
Abstract
Purpose
The purpose of this paper is to consider a nonlinear problem of minimizing the cost of providing reliable systems. The authors assume that the system consists of several components in series, and for each such component, the cost of the component increases exponentially with its reliability.
Design/methodology/approach
In order to solve this nonlinear optimization problem, the authors propose two approaches. The first approach is based on the concept of adjusting the reliability of a pair of components to minimize the cost of the system. The authors call this procedure as reliability adjustment routine (RAR). Proofs of optimality and convergence for the proposed model are also provided. The second approach solves the problem by using a Lagrangian multiplier. A procedure is developed to obtain the maximum step size to achieve the desired optimal solution in minimum iterations. Proposed approaches are efficient and give exact solutions.
Findings
Proposed methods enable a decision maker to allocate reliability to the components in series while minimizing the total cost of the system. The developed procedures are illustrated using a numerical example. Although an exponential relationship between the component cost and reliability is assumed, this can be extended to various other nonlinear distributions.
Originality/value
This cost optimization problem, subject to system component reliability values, assumes the near practical nonlinear pattern of cost vs reliability. Such problems are complex to solve. The authors provide a unique approach called RAR to solve such convoluted problems. The authors also provide an approach to solve such problems by using a Lagrangian multiplier method. Various proofs have been worked out to substantiate the work.
Keywords
Acknowledgements
The authors thank the Editor-in Chief Professor Ton van der Wiele and the three unknown reviewers for their useful suggestions which has resulted in substantial improvements over the earlier submission. The authors gratefully acknowledge the help provided by Professor K. Nilakanthan for his contributions in deriving the proofs of convexity and global optimality. The authors also thank Professor Sachin Kamble for going through the revised manuscript meticulously and suggesting changes.
Citation
Vaidya, O.S., Ganapathy, L. and Kumar, S. (2019), "A cost minimisation model for system reliability allocation", International Journal of Quality & Reliability Management, Vol. 36 No. 9, pp. 1620-1643. https://doi.org/10.1108/IJQRM-07-2018-0199
Publisher
:Emerald Publishing Limited
Copyright © 2019, Emerald Publishing Limited