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<p>This paper presents a comprehensive framework for reliability and availability analysis of multi-state <i>k</i>-out-of-<i>n</i>:G systems in star topology, with application to weather monitoring infrastructure. The proposed model integrates performance sharing and copula-based repair strategies to capture dependencies between component failures and repairs. A Markov process formulation, solved using the Sumudu transform, evaluates time-dependent reliability and availability metrics. To address uncertainty in failure parameters, the model incorporates Fermatean fuzzy set theory via Triangular Fermatean Fuzzy Numbers (TFFNs) and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\alpha ,\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-cuts, enabling robust fuzzy reliability and sensitivity analyses. A comparative study demonstrates that the copula-based approach yields more accurate long-run reliability forecasts than traditional Markov models by considering repair dependencies. The framework also includes a cost analysis module for evaluating maintenance strategies under uncertainty, supported by a structured failure–repair flowchart for intuitive system representation. The results reveal that while inherent reliability declines over time, proper maintenance sustains high system availability, with Fermatean fuzzy modeling providing realistic performance bounds. This study offers a novel integration of copula theory and Fermatean fuzzy sets for analyzing complex multi-state systems, providing a vital decision-support tool for long-run infrastructure planning and maintenance optimization.</p>

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Performance Analysis of Multi-state k-out-of-n:G Star Configuration System with Fermatean Fuzzy Set

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • G. Hemalatha,
  • G. Vijayalakshmi

摘要

This paper presents a comprehensive framework for reliability and availability analysis of multi-state k-out-of-n:G systems in star topology, with application to weather monitoring infrastructure. The proposed model integrates performance sharing and copula-based repair strategies to capture dependencies between component failures and repairs. A Markov process formulation, solved using the Sumudu transform, evaluates time-dependent reliability and availability metrics. To address uncertainty in failure parameters, the model incorporates Fermatean fuzzy set theory via Triangular Fermatean Fuzzy Numbers (TFFNs) and \((\alpha ,\beta )\) ( α , β ) -cuts, enabling robust fuzzy reliability and sensitivity analyses. A comparative study demonstrates that the copula-based approach yields more accurate long-run reliability forecasts than traditional Markov models by considering repair dependencies. The framework also includes a cost analysis module for evaluating maintenance strategies under uncertainty, supported by a structured failure–repair flowchart for intuitive system representation. The results reveal that while inherent reliability declines over time, proper maintenance sustains high system availability, with Fermatean fuzzy modeling providing realistic performance bounds. This study offers a novel integration of copula theory and Fermatean fuzzy sets for analyzing complex multi-state systems, providing a vital decision-support tool for long-run infrastructure planning and maintenance optimization.