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Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models

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  • Man-Ho Ling

    (Department of Mathematics and Information Technology, The Education University of Hong Kong, Tai Po, Hong Kong, China)

Abstract

Optimal designs of constant-stress accelerated life test plans is one of the important topics in reliability studies. Many devices produced have very high reliability under normal operating conditions. The question then arises of how to make the optimal decisions on life test plans to collect sufficient information about the corresponding lifetime distributions. Accelerated life testing has become a popular approach to tackling this problem in reliability studies, which attempts to extrapolate from the information obtained from accelerated testing conditions to normal operating conditions. In this paper, we develop a general framework to obtain optimal constant-stress accelerated life test plans for one-shot devices with dependent components, subject to time and budget constraints. The optimal accelerated test plan considers an economical approach to determine the inspection time and the sample size of each accelerating testing condition so that the asymptotic variance of the maximum likelihood estimator for the mean lifetime under normal operating conditions is minimized. This study also investigates the impact of the dependence between components on the optimal designs and provides practical recommendations on constant-stress accelerated life test plans for one-shot devices with dependent components.

Suggested Citation

  • Man-Ho Ling, 2022. "Optimal Constant-Stress Accelerated Life Test Plans for One-Shot Devices with Components Having Exponential Lifetimes under Gamma Frailty Models," Mathematics, MDPI, vol. 10(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:840-:d:765611
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    References listed on IDEAS

    as
    1. Ling, M.H. & Hu, X.W., 2020. "Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    2. G. Asha & A. Vincent Raja & Nalini Ravishanker, 2018. "Reliability modelling incorporating load share and frailty," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(2), pages 206-223, March.
    3. Wu, Shuo-Jye & Huang, Syuan-Rong, 2017. "Planning two or more level constant-stress accelerated life tests with competing risks," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 1-8.
    4. Li, Yao & Coolen, Frank P.A. & Zhu, Caichao & Tan, Jianjun, 2020. "Reliability assessment of the hydraulic system of wind turbines based on load-sharing using survival signature," Renewable Energy, Elsevier, vol. 153(C), pages 766-776.
    5. David Han & H.K.T. Ng, 2013. "Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 541-556, October.
    6. Zhu, Xiaojun & Balakrishnan, N., 2022. "One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    7. Balakrishnan, N. & So, H.Y. & Ling, M.H., 2015. "EM algorithm for one-shot device testing with competing risks under exponential distribution," Reliability Engineering and System Safety, Elsevier, vol. 137(C), pages 129-140.
    8. Zhu, Xiaojun & Liu, Kai & He, Mu & Balakrishnan, N., 2021. "Reliability estimation for one-shot devices under cyclic accelerated life-testing," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    9. M. H. Ling & P. S. Chan & H. K. T. Ng & N. Balakrishnan, 2021. "Copula models for one-shot device testing data with correlated failure modes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(16), pages 3875-3888, August.
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    Cited by:

    1. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.

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