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<p>Reliability is a key ingredient of a supply chain—a complex network of suppliers, manufacturer and distributors whose ultimate objective is to provide goods and services to the client in a timely manner. The reliability of this supply chain depends on all the people in the network and also the equipment involved including transportation vehicles, sophisticated machines and computer-based information systems. The reliability of this equipment depends very much on their design, maintenance, and subsequent repairs. Reliability testing&#xa0;ensures that the quality and durability of a given product is consistent with its specifications throughout the product's intended lifecycle. This&#xa0;testing&#xa0;can be done at both the design and production levels. Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components lasting for several years. Life test under accelerated environmental conditions may be fully accelerated or partially accelerated. In fully accelerated life testing all the test units are run at accelerated condition, while in partially accelerated life testing, they are both run at normal and accelerated conditions. The products can fail due to one of the several possible causes of failure which need not be independent. This paper deals with the design of step-stress PALT using tampered failure rate model with dependent competing causes of failure. Gumbel-Hougaard Copula is used to model and measure the dependence between the life times of competing causes of failure. The optimal plan consists in finding out stress rate change point by maximizing the log to the base 10 of the determinant of Fisher Information Matrix. The method develop has been explained using a numerical example. Probability plots have been drawn and it has been found that exponential models used for failure modes are a good fit to the given data. Cumulative hazard plots are drawn to examine change in the relative dominance of failure modes with change in stress. Confidence Interval for the estimated values of the design parameters has been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.</p>

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Copula based step-stress PALT using tampered failure rate model with dependent competing risks

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Preeti Wanti Srivastava,
  • Tanu Gupta

摘要

Reliability is a key ingredient of a supply chain—a complex network of suppliers, manufacturer and distributors whose ultimate objective is to provide goods and services to the client in a timely manner. The reliability of this supply chain depends on all the people in the network and also the equipment involved including transportation vehicles, sophisticated machines and computer-based information systems. The reliability of this equipment depends very much on their design, maintenance, and subsequent repairs. Reliability testing ensures that the quality and durability of a given product is consistent with its specifications throughout the product's intended lifecycle. This testing can be done at both the design and production levels. Accelerated life tests (ALTs) are used to make timely assessments of the life time distribution of highly reliable materials and components lasting for several years. Life test under accelerated environmental conditions may be fully accelerated or partially accelerated. In fully accelerated life testing all the test units are run at accelerated condition, while in partially accelerated life testing, they are both run at normal and accelerated conditions. The products can fail due to one of the several possible causes of failure which need not be independent. This paper deals with the design of step-stress PALT using tampered failure rate model with dependent competing causes of failure. Gumbel-Hougaard Copula is used to model and measure the dependence between the life times of competing causes of failure. The optimal plan consists in finding out stress rate change point by maximizing the log to the base 10 of the determinant of Fisher Information Matrix. The method develop has been explained using a numerical example. Probability plots have been drawn and it has been found that exponential models used for failure modes are a good fit to the given data. Cumulative hazard plots are drawn to examine change in the relative dominance of failure modes with change in stress. Confidence Interval for the estimated values of the design parameters has been obtained and sensitivity analysis carried out. The results of sensitivity analysis show that the plan is robust to small deviations from the true values of baseline parameters.