Bayesian D-optimal design for regression-based stopping time of a system under the δ-shock model

Document Type : Original Scientific Paper

Authors

Department of Statistics‎, ‎Razi University‎, ‎Kermanshah‎, ‎Iran

Abstract

‎According to the δ-shock model, the system fails when the inter-arrival time between two successive shocks falls below a given critical threshold, δ. Therefore, the system's failure depends on both the probabilistic behavior of the inter-arrival times and the threshold δ. As a result, the factors affecting these two variables also influence the system's stopping time. In this paper, we consider a regression model with an explanatory factor for the system's stopping time and then apply the Bayesian D-optimal criterion to obtain optimal designs. Assuming a uniform prior, the obtained Bayesian optimal designs all have a general form corresponding to the design space.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 5, Issue 2
July 2024
Pages 165-174

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History

  • Receive Date: 05 April 2025
  • Revise Date: 26 July 2025
  • Accept Date: 01 August 2025

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