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Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application

Author

Listed:
  • Hassan S. Bakouch

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia)

  • Fernando A. Moala

    (Department of Statistics, State University of Sao Paulo, Sao Paulo 19060-900, Brazil)

  • Shuhrah Alghamdi

    (Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11564, Saudi Arabia)

  • Olayan Albalawi

    (Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia)

Abstract

This paper presents a multiple step-stress accelerated life test using type II censoring. Assuming that the lifetimes of the test item follow the gamma distribution, the maximum likelihood estimation and Bayesian approaches are used to estimate the distribution parameters. In the Bayesian approach, new parametrizations can lead to new prior distributions and can be a useful technique to improve the efficiency and effectiveness of Bayesian modeling, particularly when dealing with complex or high-dimensional models. Therefore, in this paper, we present two sets of prior distributions for the parameters of the accelerated test where one of them is based on the reparametrization of the other. The performance of the proposed prior distributions and maximum likelihood approach are investigated and compared by examining the summaries and frequentist coverage probabilities of intervals. We introduce the Markov Chain Monte Carlo (MCMC) algorithms to generate samples from the posterior distributions in order to evaluate the estimators and intervals. Numerical simulations are conducted to examine the approach’s performance and one-sample lifetime data are presented to illustrate the proposed methodology.

Suggested Citation

  • Hassan S. Bakouch & Fernando A. Moala & Shuhrah Alghamdi & Olayan Albalawi, 2024. "Bayesian Methods for Step-Stress Accelerated Test under Gamma Distribution with a Useful Reparametrization and an Industrial Data Application," Mathematics, MDPI, vol. 12(17), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2747-:d:1471395
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    References listed on IDEAS

    as
    1. Gelman A., 2004. "Parameterization and Bayesian Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 537-545, January.
    2. Abdalla Rabie & Abd EL-Baset A. Ahmad & Mohamad A. Fawzy & Tahani A. Aloafi & Ali Sajid, 2022. "Bayesian Prediction Intervals Based on Type-I Hybrid Censored Data from the Lomax Distribution under Step-Stress Model," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, December.
    3. Kangwon Seo & Rong Pan, 2017. "Data analysis of step-stress accelerated life tests with heterogeneous group effects," IISE Transactions, Taylor & Francis Journals, vol. 49(9), pages 885-898, September.
    4. Varghese A. Sharon & V. S. Vaidyanathan, 2016. "Analysis of simple step-stress accelerated life test data from Lindley distribution under type-I censoring," Statistica, Department of Statistics, University of Bologna, vol. 76(3), pages 233-248.
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