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Testing the Validity of a Link Function Assumption in Repeated Type-II Censored General Step-Stress Experiments

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  • Stefan Bedbur

    (Institute of Statistics)

  • Thomas Seiche

    (Institute of Statistics)

Abstract

In step-stress experiments, test units are successively exposed to higher usually increasing levels of stress to cause earlier failures and to shorten the duration of the experiment. When parameters are associated with the stress levels, one problem is to estimate the parameter corresponding to normal operating conditions based on failure data obtained under higher stress levels. For this purpose, a link function connecting parameters and stress levels is usually assumed, the validity of which is often at the discretion of the experimenter. In a general step-stress model based on multiple samples of sequential order statistics, we provide exact statistical tests to decide whether the assumption of some link function is adequate. The null hypothesis of a proportional, linear, power or log-linear link function is considered in detail, and associated inferential results are stated. In any case, except for the linear link function, the test statistics derived are shown to have only one distribution under the null hypothesis, which simplifies the computation of (exact) critical values. Asymptotic results are addressed, and a power study is performed for testing on a log-linear link function. Some improvements of the tests in terms of power are discussed.

Suggested Citation

  • Stefan Bedbur & Thomas Seiche, 2022. "Testing the Validity of a Link Function Assumption in Repeated Type-II Censored General Step-Stress Experiments," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 106-129, May.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:1:d:10.1007_s13571-021-00250-5
    DOI: 10.1007/s13571-021-00250-5
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    References listed on IDEAS

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    1. N. Balakrishnan & U. Kamps & M. Kateri, 2012. "A sequential order statistics approach to step-stress testing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 303-318, April.
    2. Bing Wang & Keming Yu, 2009. "Optimum plan for step-stress model with progressive type-II censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 115-135, May.
    3. Bedbur, S. & Kamps, U., 2019. "Confidence regions in step–stress experiments with multiple samples under repeated type-II censoring," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 181-186.
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