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<p>This study introduces a novel fuzzy reliability analysis framework for dynamic discrete-state, continuous-time multi-state systems that operate under a shared performance-based common-bus mechanism. In the proposed structure, each subsystem works at multiple performance levels, and any excess performance is dynamically redistributed via a shared bus to prevent degradation or failure. To effectively handle the system uncertainties, the present work introduces a hybrid method integrating the triangular intuitionistic fuzzy framework with an <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_z\)</EquationSource> </InlineEquation>-transform technique. This methodology enables the computation of fuzzy reliability metrics such as fuzzy reliability, fuzzy availability, fuzzy sensitivity and fuzzy mean time to failure under varying operational conditions. A detailed power-grid system taken as a case study demonstrates the applicability of the proposed framework. The numerical results indicate a steady decline in TI fuzzy reliability and availability from <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(t=0\)</EquationSource> </InlineEquation> to 5, where reliability drops from 0.7945 to 0.1207 and availability from 0.8772 to 0.5866. The system is less sensitive to the failure rate <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\tilde{\lambda }^{(1)}_{(3,1)}\)</EquationSource> </InlineEquation> and stable TI fuzzy MTTF membership values between 2.0562 to 2.2298, and non-membership values span from 2.0104 to 2.3269. These results illustrate the model’s precision and computational efficiency in time-varying degradation and improve the overall reliability assessment of the complex multi-state system.</p>

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Dynamic reliability measures from triangular intuitionistic fuzzy \(L_z\)-transform with common bus performance sharing mechanism

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Manpreet Kaur,
  • Soni Bisht

摘要

This study introduces a novel fuzzy reliability analysis framework for dynamic discrete-state, continuous-time multi-state systems that operate under a shared performance-based common-bus mechanism. In the proposed structure, each subsystem works at multiple performance levels, and any excess performance is dynamically redistributed via a shared bus to prevent degradation or failure. To effectively handle the system uncertainties, the present work introduces a hybrid method integrating the triangular intuitionistic fuzzy framework with an \(L_z\) -transform technique. This methodology enables the computation of fuzzy reliability metrics such as fuzzy reliability, fuzzy availability, fuzzy sensitivity and fuzzy mean time to failure under varying operational conditions. A detailed power-grid system taken as a case study demonstrates the applicability of the proposed framework. The numerical results indicate a steady decline in TI fuzzy reliability and availability from \(t=0\) to 5, where reliability drops from 0.7945 to 0.1207 and availability from 0.8772 to 0.5866. The system is less sensitive to the failure rate \(\tilde{\lambda }^{(1)}_{(3,1)}\) and stable TI fuzzy MTTF membership values between 2.0562 to 2.2298, and non-membership values span from 2.0104 to 2.3269. These results illustrate the model’s precision and computational efficiency in time-varying degradation and improve the overall reliability assessment of the complex multi-state system.