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Improving the Reliability of Parallel and Series–Parallel Systems by Reverse Engineering of Algebraic Inequalities

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  • Michael Todinov

    (School of Engineering, Computing and Mathematics, Oxford Brookes University, Oxford OX3 0BP, UK)

Abstract

This paper presents a novel, domain-independent method for enhancing system reliability based on reverse engineering of algebraic inequalities. Although system reliability has been extensively studied, existing approaches have not addressed the challenge of improving reliability without knowing the reliability of individual components. This work fills this gap by demonstrating that the reliability of both parallel and series–parallel systems can be improved without any information about component reliability values. Specifically, this study establishes that in parallel systems, a symmetric arrangement of interchangeable components of the same type across parallel branches consistently yields higher system reliability than an asymmetric arrangement—regardless of the individual component reliabilities. This finding is derived through the reverse engineering of a new general algebraic inequality, proposed and proved for the first time. Furthermore, applying the same approach to series–parallel systems reveals that asymmetric arrangements of interchangeable redundancies offer superior system reliability compared with symmetric configurations.

Suggested Citation

  • Michael Todinov, 2025. "Improving the Reliability of Parallel and Series–Parallel Systems by Reverse Engineering of Algebraic Inequalities," Mathematics, MDPI, vol. 13(9), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1381-:d:1641169
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    References listed on IDEAS

    as
    1. Chanchal Kundu & Amit Ghosh, 2017. "Inequalities involving expectations of selected functions in reliability theory to characterize distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8468-8478, September.
    2. Ding, Yi & Hu, Yishuang & Li, Daqing, 2021. "Redundancy Optimization for Multi-Performance Multi-State Series-Parallel Systems Considering Reliability Requirements," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    Full references (including those not matched with items on IDEAS)

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