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Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions

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  • Ling, M.H.
  • Hu, X.W.

Abstract

One-shot devices, such as rockets, airbags of automobiles, and electro-explosive devices, can be used only once and will be extensively destroyed. The actual lifetimes of the devices cannot be observed, no matter whether the outcomes are successful or not. Step-stress accelerated life tests, which are useful for shortening the lifetimes of devices and quickly collecting lifetime data in a limited time, are widely adopted in engineering reliability studies. However, optimal designs of step-stress accelerated life tests for one-shot devices have not been well studied. This paper provides a procedure of determining optimal designs of simple step-stress accelerated life tests for one-shot devices by minimizing the asymptotic variance of the maximum likelihood estimate of reliability at normal operating conditions under Weibull distributions, with respect to inspection times and sample allocations. Comprehensive simulation studies are carried out to study the optimal designs under Weibull distributions with various hazard rates, showing that the optimal designs can maintain the simulated standard deviations at the nominal level of standard error. Besides, sensitivity analysis is conducted to evaluate the robustness of determined designs when mis-specification on planning values of model parameters exists. Finally, an application in grease-based magnetorheological fluids is presented to illustrate the optimal designs.

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  • 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).
    • Handle: RePEc:eee:reensy:v:193:y:2020:i:c:s0951832019306064
    DOI: 10.1016/j.ress.2019.106630
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    References listed on IDEAS

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    1. Cheng, Yao & Elsayed, Elsayed A., 2017. "Reliability modeling of mixtures of one-shot units under thermal cyclic stresses," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 58-66.
    2. Naijun Sha & Rong Pan, 2014. "Bayesian analysis for step-stress accelerated life testing using weibull proportional hazard model," Statistical Papers, Springer, vol. 55(3), pages 715-726, August.
    3. Balakrishnan, N. & Ling, M.H., 2014. "Gamma lifetimes and one-shot device testing analysis," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 54-64.
    4. 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.
    5. Cheng, Yao & Elsayed, Elsayed A., 2018. "Reliability modeling and optimization of operational use of one-shot units," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 27-36.
    6. Muhammad Aslam & Chi-Hyuck Jun, 2009. "A group acceptance sampling plan for truncated life test having Weibull distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(9), pages 1021-1027.
    7. Do Sun Bai & Myung Soo Kim, 1993. "Optimum simple step‐stress accelerated life tests for weibull distribution and type I censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(2), pages 193-210, March.
    8. Yao Zhang & William Q. Meeker, 2005. "Bayesian life test planning for the Weibull distribution with given shape parameter," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 237-249, June.
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    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).

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