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.
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.
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The authors are grateful to the reviewers for their thorough and constructive comments, which have significantly improved the quality of the manuscript.
This work has been partially supported by the Ministry of Higher Education of Algeria, GEANLAB Laboratory of the University of Oran 1 Ahmed Ben Bella, and the LMSA Laboratory of the University of Science and Technology of Oran Mohamed Boudiaf (USTOMB).
Author notes
Zohra Benkamra, Benchikh Lehocine Ghanem and Mounir Tlemcani contributed equally to this work.
Department of Mathematics, University of Sciences and Technology of Oran Mohamed Boudiaf, Oran, 31000, Algeria
Zohra Benkamra, Benchikh Lehocine Ghanem & Mounir Tlemcani
Authors
Correspondence to Mounir Tlemcani.
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Benkamra, Z., Ghanem, B.L. & Tlemcani, M. Best Fixed and Sequential Design for Bayesian Estimation of a Sum of Two Failure Rates of Exponential Distributions. J Stat Theory Pract 20, 99 (2026). https://doi.org/10.1007/s42519-026-00622-y
Received: 25 December 2025
Accepted: 07 July 2026
Published: 20 July 2026
Version of record: 20 July 2026
DOI: https://doi.org/10.1007/s42519-026-00622-y