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<p>This paper presents a procedure for constructing the membership functions of system characteristics for a repairable system with two primary units, where the coverage factor for an operating unit failure remains constant and includes detection delay. The times to failure and repair of the operating units are assumed to follow fuzzified exponential distributions. The <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41872_2025_298_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-cut method is employed to derive a set of regular crisp intervals from the fuzzy repairable system, based on the desired system characteristics. These intervals are established through a combination of parametric non-linear programmes that utilise their membership functions. A numerical example is provided to demonstrate the effectiveness of the proposed approach. The system characteristics, defined by the membership functions, offer enhanced information for decision-making. Extending the repairable system into a fuzzy environment allows for a more accurate representation of standard repairable systems. The analytical results are valuable for both developers and practitioners.</p>

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Parametric optimization of repairable systems in IoT: addressing detection delays, imperfect coverage, and fuzzy parameters

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • Amit Kumar

摘要

This paper presents a procedure for constructing the membership functions of system characteristics for a repairable system with two primary units, where the coverage factor for an operating unit failure remains constant and includes detection delay. The times to failure and repair of the operating units are assumed to follow fuzzified exponential distributions. The \(\alpha\) α -cut method is employed to derive a set of regular crisp intervals from the fuzzy repairable system, based on the desired system characteristics. These intervals are established through a combination of parametric non-linear programmes that utilise their membership functions. A numerical example is provided to demonstrate the effectiveness of the proposed approach. The system characteristics, defined by the membership functions, offer enhanced information for decision-making. Extending the repairable system into a fuzzy environment allows for a more accurate representation of standard repairable systems. The analytical results are valuable for both developers and practitioners.