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Multi‐sample simple step‐stress experiment under time constraints

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  • M. Kateri
  • U. Kamps
  • N. Balakrishnan

Abstract

In the context of accelerated life testing, a step‐stress model allows for testing under different conditions at various intermediate stages of the experiment. The goal is to develop inference for the mean lifetime at each stress level. The maximum likelihood estimates (MLEs) exist only when some (at least one) failures are observed at each stress level. This limitation can be tackled by a multi‐sample step‐stress model, which imposes a weaker condition for the existence of the MLEs, i.e. at each stress level, some failures (at least one) must be observed in at least one of the samples. The step‐stress experiment with multiple samples at the same stress levels was introduced by Kateri et al. (Journal of Statistical Planning and Inference, 139, 2009a). In this article, we focus on the likelihood inference under such a multi‐sample set‐up for the case of a simple step‐stress experiment under exponentially distributed lifetimes when time constraints are in place in the experimentation.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:1:p:77-96
    DOI: 10.1111/j.1467-9574.2009.00444.x
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    References listed on IDEAS

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    1. 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.
    2. Shuo‐Jye Wu & Ying‐Po Lin & Yi‐Ju Chen, 2006. "Planning step‐stress life test with progressively type I group‐censored exponential data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 60(1), pages 46-56, February.
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    Cited by:

    1. Maria Kateri & Udo Kamps, 2015. "Inference in step-stress models based on failure rates," Statistical Papers, Springer, vol. 56(3), pages 639-660, August.
    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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