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<p>The introduction of copula distribution by the Gumbel-Hougaard family sparked a new line of research in multi-state complex engineering systems, and it is now extensively used in numerous series–parallel complex engineering systems. In light of this, we study various reliability metrics for a complex system that consists of two subsystems: subsystem-1, which has five identical units in a parallel configuration working under the 2-out-of-5: G policy, and subsystem-2, which has three identical units in a parallel configuration working under the 1-out-of-3: G policy. The controllers regulate the units of both subsystems to prevent implications of failure. Both the controllers and subsystems have distinct exponentially distributed failure rates. A human operator controls the entire system, and when the system fails because of the human operator, it fails completely. The purpose of this study was to assess the system’s availability, reliability, MTTF, and expected profit using a Markovian process by taking arbitrary parameter values. Copula repair, Laplace transformation, and supplementary variable techniques were used to model the problem at hand and results were obtained using MAPLE and demonstrated with the help of tables and graphs. We emphasize the use of copula repair while highlighting areas for development and potential future research directions.</p>

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Reliability analysis of a series–parallel system under different failures using Gumbel-Hougaard copula repair

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Praveen Kumar Poonia,
  • Meghna Tyagi

摘要

The introduction of copula distribution by the Gumbel-Hougaard family sparked a new line of research in multi-state complex engineering systems, and it is now extensively used in numerous series–parallel complex engineering systems. In light of this, we study various reliability metrics for a complex system that consists of two subsystems: subsystem-1, which has five identical units in a parallel configuration working under the 2-out-of-5: G policy, and subsystem-2, which has three identical units in a parallel configuration working under the 1-out-of-3: G policy. The controllers regulate the units of both subsystems to prevent implications of failure. Both the controllers and subsystems have distinct exponentially distributed failure rates. A human operator controls the entire system, and when the system fails because of the human operator, it fails completely. The purpose of this study was to assess the system’s availability, reliability, MTTF, and expected profit using a Markovian process by taking arbitrary parameter values. Copula repair, Laplace transformation, and supplementary variable techniques were used to model the problem at hand and results were obtained using MAPLE and demonstrated with the help of tables and graphs. We emphasize the use of copula repair while highlighting areas for development and potential future research directions.