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Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan

Author

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  • Abdalla Abdel-Ghaly

    (Cairo University)

  • Hanan Aly

    (Cairo University)

  • Elham Abdel-Rahman

    (Cairo University)

Abstract

In this paper, the implementations of No-U-Turn Sampler (NUTS), an extension of Hamiltonian Monte Carlo (HMC) method, via Stan software is considered for the first time under ramp stress accelerated life testing (RS-ALT). Assuming an extended Weibul (EW) distribution in the presence of adaptive type-II progressive censoring (A-II-PC) scheme, NUTS is adopted to obtain point and interval Bayesian estimation for the unknown parameters and acceleration factors when the scale parameter is related to stress through inverse power law relationship. One-sample and two-sample prediction problems are also studied under the same framework using two different approaches. To asses the performance of the suggested methods, a Monte Carlo simulation study is conducted. Finally, a real data example is provided to illustrate the application of the proposed methods in reality.

Suggested Citation

  • Abdalla Abdel-Ghaly & Hanan Aly & Elham Abdel-Rahman, 2023. "Bayesian Inference Under Ramp Stress Accelerated Life Testing Using Stan," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 132-174, May.
    • Handle: RePEc:spr:sankhb:v:85:y:2023:i:1:d:10.1007_s13571-022-00300-6
    DOI: 10.1007/s13571-022-00300-6
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    References listed on IDEAS

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    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
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