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<p>This paper investigates the sequential Bayesian estimation of the sum of two failure rates in a series system, where the component lifetimes follow exponential distributions. Traditional fixed sampling allocations, based on prior engineering judgment, are often suboptimal under limited testing budgets or poor prior knowledge. We develop a fully adaptive two-stage sequential procedure that dynamically allocates tests between components to recover from prior mismatch. Theoretical analysis establishes the first-order asymptotic optimality of the sequential scheme. Extensive simulations demonstrate that sequential allocation consistently reduces mean squared error compared to best fixed allocation, while remaining robust across a variety of priors and budget constraints. The results offer a practical and theoretically grounded strategy for resource-efficient reliability testing and risk assessment in engineering systems.</p>

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Best Fixed and Sequential Design for Bayesian Estimation of a Sum of Two Failure Rates of Exponential Distributions

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Zohra Benkamra,
  • Benchikh Lehocine Ghanem,
  • Mounir Tlemcani

摘要

This paper investigates the sequential Bayesian estimation of the sum of two failure rates in a series system, where the component lifetimes follow exponential distributions. Traditional fixed sampling allocations, based on prior engineering judgment, are often suboptimal under limited testing budgets or poor prior knowledge. We develop a fully adaptive two-stage sequential procedure that dynamically allocates tests between components to recover from prior mismatch. Theoretical analysis establishes the first-order asymptotic optimality of the sequential scheme. Extensive simulations demonstrate that sequential allocation consistently reduces mean squared error compared to best fixed allocation, while remaining robust across a variety of priors and budget constraints. The results offer a practical and theoretically grounded strategy for resource-efficient reliability testing and risk assessment in engineering systems.