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Tampered Random Variable Analysis in Step-Stress Testing: Modeling, Inference, and Applications

Author

Listed:
  • Hanan Haj Ahmad

    (Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia
    Department of Mathematics and Statistics, College of Science, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia)

  • Dina A. Ramadan

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt)

  • Ehab M. Almetwally

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Riyadh, Saudi Arabia
    Faculty of Business Administration, Delta University of Science and Technology, Gamasa 11152, Egypt)

Abstract

This study explores a new dimension of accelerated life testing by analyzing competing risk data through Tampered Random Variable (TRV) modeling, a method that has not been extensively studied. This method is applied to simple step-stress life testing (SSLT), and it considers multiple causes of failure. The lifetime of test units under changeable stress levels is modeled using Power Rayleigh distribution with distinct scale parameters and a constant shape parameter. The research introduces unique tampering coefficients for different failure causes in step-stress data modeling through TRV. Using SSLT data, we calculate maximum likelihood estimates for the parameters of our model along with the tampering coefficients and establish three types of confidence intervals under the Type-II censoring scheme. Additionally, we delve into Bayesian inference for these parameters, supported by suitable prior distributions. Our method’s validity is demonstrated through extensive simulations and real data application in the medical and electrical engineering fields. We also propose an optimal stress change time criterion and conduct a thorough sensitivity analysis.

Suggested Citation

  • Hanan Haj Ahmad & Dina A. Ramadan & Ehab M. Almetwally, 2024. "Tampered Random Variable Analysis in Step-Stress Testing: Modeling, Inference, and Applications," Mathematics, MDPI, vol. 12(8), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1248-:d:1379450
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    References listed on IDEAS

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    1. Yuri A. Iriarte & F. Vilca & Héctor Varela & Héctor W. Gómez, 2017. "Slashed generalized Rayleigh distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4686-4699, May.
    2. Debashis Samanta & Debasis Kundu & Ayon Ganguly, 2018. "Order Restricted Bayesian Analysis of a Simple Step Stress Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-221, November.
    3. Morris H. Degroot & Prem K. Goel, 1979. "Bayesian estimation and optimal designs in partially accelerated life testing," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(2), pages 223-235, June.
    4. Dina A. Ramadan & Ehab M. Almetwally & Ahlam H. Tolba, 2023. "Statistical Inference to the Parameter of the Akshaya Distribution under Competing Risks Data with Application HIV Infection to AIDS," Annals of Data Science, Springer, vol. 10(6), pages 1499-1525, December.
    5. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
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