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Optimum simple step‐stress accelerated life tests for weibull distribution and type I censoring

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  • Do Sun Bai
  • Myung Soo Kim

Abstract

This article presents an optimum simple step‐stress accelerated life test for the Weibull distribution under Type I censoring. It is assumed that a log‐linear relationship exists between the Weibull scale parameter and the (possibly transformed) stress and that a certain cumulative exposure model for the effect of changing stress holds. The optimum plan—low stress and stress change time—is obtained, which minimizes the asymptotic variance of the maximum likelihood estimator of a stated percentile at design stress. For selected values of the design parameters, nomographs useful for finding the optimum plan are given, and the effects of errors in preestimates of the parameters are investigated. As an alternative to the simple step‐stress test, a three‐level compromise plan is proposed, and its performance is studied and compared with that of the optimum simple step‐stress test. © 1993 John Wiley & Sons. Inc.

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  • 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.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:2:p:193-210
    DOI: 10.1002/1520-6750(199303)40:23.0.CO;2-J
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    References listed on IDEAS

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    1. Sun‐Keun Seo & Bong‐Jin Yum, 1991. "Accelerated life test plans under intermittent inspection and type‐I censoring: The case of weibull failure distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 1-22, February.
    2. Luis A. Escobar & William Q. Meeker, 1986. "Elements of the Fisher Information Matrix for the Smallest Extreme Value Distribution and Censored Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(1), pages 80-86, March.
    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.
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    Cited by:

    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. Sang-Jun Park & Bong-Jin Yum, 1998. "Optimal design of accelerated life tests under modified stress loading methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(1), pages 41-62.
    3. Haiming Ma & William Q. Meeker, 2008. "Optimum step‐stress accelerated life test plans for log‐location‐scale distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(6), pages 551-562, September.
    4. Cheng‐Hung Hu & Robert D. Plante & Jen Tang, 2013. "Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 19-30, February.
    5. A.D. Dharmadhikari & Md. Monsur Rahman, 2003. "A model for step‐stress accelerated life testing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(8), pages 841-868, December.
    6. Chien-Tai Lin & Cheng-Chieh Chou & N. Balakrishnan, 2020. "Planning step-stress test plans under Type-I hybrid censoring for the log-location-scale distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 265-288, June.
    7. L.C. Tang & T.N. Goh & Y.S. Sun & H.L. Ong, 1999. "Planning accelerated life tests for censored two‐parameter exponential distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(2), pages 169-186, March.
    8. Ling, Li & Xu, Wei & Li, Minghai, 2009. "Parametric inference for progressive Type-I hybrid censored data on a simple step-stress accelerated life test model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3110-3121.

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