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<p>Engineering systems often rely on linear consecutive (LC) <i>k</i>-out-of-<i>r</i>-from-<i>n</i> systems, which fail when at least <i>k</i> consecutive components break down within a sequence of <i>r</i> components among <i>n</i> elements. Reliability assessment is essential for any system to operate effectively over a specified time period. However, Traditional reliability analysis techniques struggle to effectively handle the real-world uncertainty and imprecision that arise in complex engineering systems. To address this limitation, this study proposes an intuitionistic fuzzy reliability framework that employs intuitionistic fuzzy sets (IFS) for LC <i>k</i>-out-of-<i>r</i>-from-<i>n</i> systems. The approach uses IFS to model uncertainty by considering membership and non-membership degrees. In this framework, triangular intuitionistic fuzzy numbers (TIFNs) are used to represent uncertain component lifetimes. The reliability function and related indices, such as sensitivity, fuzzy mean time to failure, and cost analysis, are evaluated using the context of the universal generating function (UGF) algorithm under the Weibull distribution. Moreover, an arithmetic average operator with equal weights is applied to combine the TIFNs to maintain balanced parameter representation. The effectiveness of the proposed method is demonstrated through numerical examples, and the obtained results are presented in both tabular and graphical formats for greater clarity. The results indicate that the proposed intuitionistic fuzzy UGF framework provides a systematic and flexible approach for reliability evaluation of LC systems under uncertainty.</p>

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Linear consecutive k-out-of-r-from-n systems reliability measures with intuitionistic fuzzy weighted aggregation operator

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Vidhi Tiwari,
  • Akshay Kumar,
  • Mangey Ram

摘要

Engineering systems often rely on linear consecutive (LC) k-out-of-r-from-n systems, which fail when at least k consecutive components break down within a sequence of r components among n elements. Reliability assessment is essential for any system to operate effectively over a specified time period. However, Traditional reliability analysis techniques struggle to effectively handle the real-world uncertainty and imprecision that arise in complex engineering systems. To address this limitation, this study proposes an intuitionistic fuzzy reliability framework that employs intuitionistic fuzzy sets (IFS) for LC k-out-of-r-from-n systems. The approach uses IFS to model uncertainty by considering membership and non-membership degrees. In this framework, triangular intuitionistic fuzzy numbers (TIFNs) are used to represent uncertain component lifetimes. The reliability function and related indices, such as sensitivity, fuzzy mean time to failure, and cost analysis, are evaluated using the context of the universal generating function (UGF) algorithm under the Weibull distribution. Moreover, an arithmetic average operator with equal weights is applied to combine the TIFNs to maintain balanced parameter representation. The effectiveness of the proposed method is demonstrated through numerical examples, and the obtained results are presented in both tabular and graphical formats for greater clarity. The results indicate that the proposed intuitionistic fuzzy UGF framework provides a systematic and flexible approach for reliability evaluation of LC systems under uncertainty.