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Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring
Author(s) -
Ahmad Nesar,
Islam A.
Publication year - 1996
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/(sici)1520-6750(199612)43:8<1049::aid-nav2>3.0.co;2-e
Subject(s) - weibull distribution , mathematics , censoring (clinical trials) , estimator , statistics , shape parameter , accelerated life testing , optimal design , exponential function , test plan , exponential distribution , reliability (semiconductor) , delta method , sample size determination , scale parameter , mathematical analysis , power (physics) , physics , quantum mechanics
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.