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Optimal sample size allocation for tests with multiple levels of stress with extreme value regression
Author(s) -
Ng H. K. T.,
Balakrishnan N.,
Chan P. S.
Publication year - 2007
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/nav.20207
Subject(s) - estimator , statistics , mathematics , fisher information , sample size determination , covariance matrix , extreme value theory , monte carlo method , regression analysis , covariance , sample (material) , optimal allocation , variance (accounting) , maximum likelihood , econometrics , mathematical optimization , economics , accounting , chromatography , chemistry
In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k ‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007