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Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring

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  • Nesar Ahmad
  • A. Islam

Abstract

This article develops optimal accelerated life test designs for Burr Type XII distributions under periodic inspection and Type I censoring. It is assumed that the mean lifetime (the Burr XII scale parameter) is a log‐linear function of stress and that the shape parameters are independent of stress. For given shape parameters, design stress and high test stress, the test design is optimized with respect to the low test stress and the proportion of test units allocated to the low stress. The optimality criterion is the asymptotic variance of the maximum‐likelihood estimator of log mean life at the design stress with the use of equally spaced inspection times. Computational results for various values of the shape parameters show that this criterion is insensitive to the number of inspection times and to misspecification of imputed failure probabilities at the design and high test stresses. Procedures for planning an accelerated life test, including selection of sample size, are also discussed. It is shown that optimal designs previously obtained for exponential and Weibull distributions are similar to those obtained here for the appropriate special cases of the Burr XII distribution. Thus the Burr XII distribution is a useful and widely applicable family of reliability models for ALT design. © 1996 John Wiley & Sons, Inc.

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  • Nesar Ahmad & A. Islam, 1996. "Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1049-1077, December.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:8:p:1049-1077
    DOI: 10.1002/(SICI)1520-6750(199612)43:83.0.CO;2-E
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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. Bong‐Jin Yum & Seung‐Cheol Choi, 1989. "Optimal design of accelerated life tests under periodic inspection," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(6), pages 779-795, December.
    4. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
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    1. Hua Xin & Zhifang Liu & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution," Mathematics, MDPI, vol. 8(2), pages 1-23, January.

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