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Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

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  • H. K. T. Ng
  • N. Balakrishnan
  • P. S. Chan

Abstract

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

Suggested Citation

  • H. K. T. Ng & N. Balakrishnan & P. S. Chan, 2007. "Optimal sample size allocation for tests with multiple levels of stress with extreme value regression," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(3), pages 237-249, April.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:3:p:237-249
    DOI: 10.1002/nav.20207
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    References listed on IDEAS

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    1. Paula, Gilberto A. & Rojas, Oscar V., 1997. "On restricted hypotheses in extreme value regression models," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 143-157, July.
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    Cited by:

    1. Fode Zhang & Hon Keung Tony Ng & Yimin Shi & Ruibing Wang, 2019. "Amari–Chentsov structure on the statistical manifold of models for accelerated life tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 77-105, March.
    2. 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.
    3. Chien‐Yu Peng, 2012. "A note on optimal allocations for the second elementary symmetric function with applications for optimal reliability design," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 278-284, April.
    4. David Han & H.K.T. Ng, 2013. "Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 541-556, October.
    5. Mohamed Sief & Xinsheng Liu & Abd El-Raheem Mohamed Abd El-Raheem, 2024. "Inference for a constant-stress model under progressive type-II censored data from the truncated normal distribution," Computational Statistics, Springer, vol. 39(5), pages 2791-2820, July.

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