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Inference in step-stress models based on failure rates

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  • Maria Kateri
  • Udo Kamps

Abstract

In step-stress modeling with the cumulative exposure model it is well known that, for underlying exponential distributions, explicit expressions can be obtained for maximum likelihood estimators of parameters as well as for their conditional density functions or conditional moment generation functions, given their existence. Applying a failure rate based approach instead, similar results can be also obtained for underlying lifetime distributions out of a general scale family of distributions, which allows for a flexible modeling. Exemplarily, respective results are presented for Type-I and Type-II censored experiments. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Maria Kateri & Udo Kamps, 2015. "Inference in step-stress models based on failure rates," Statistical Papers, Springer, vol. 56(3), pages 639-660, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:639-660
    DOI: 10.1007/s00362-014-0601-y
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    References listed on IDEAS

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    1. Ronghua Wang & Heliang Fei, 2004. "Conditions for the coincidence of the TFR, TRV and CE models," Statistical Papers, Springer, vol. 45(3), pages 393-412, July.
    2. N. Balakrishnan & G. Iliopoulos, 2010. "Stochastic monotonicity of the MLEs of parameters in exponential simple step-stress models under Type-I and Type-II censoring," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 89-109, July.
    3. N. Balakrishnan & Qihao Xie & D. Kundu, 2009. "Exact inference for a simple step-stress model from the exponential distribution under time constraint," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 251-274, March.
    4. René Van Dorp, J. & Mazzuchi, Thomas A., 2005. "A general Bayes weibull inference model for accelerated life testing," Reliability Engineering and System Safety, Elsevier, vol. 90(2), pages 140-147.
    5. M. Kateri & U. Kamps & N. Balakrishnan, 2010. "Multi‐sample simple step‐stress experiment under time constraints," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 77-96, February.
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    Cited by:

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    2. Julian Górny & Erhard Cramer, 2020. "On Exact Inferential Results for a Simple Step-Stress Model Under a Time Constraint," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 201-239, November.

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