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On Exact Inferential Results for a Simple Step-Stress Model Under a Time Constraint

Author

Listed:
  • Julian Górny

    (RWTH Aachen University)

  • Erhard Cramer

    (RWTH Aachen University)

Abstract

In simple step-stress models based on exponential distributions, the distributions of the MLEs are commonly obtained using the moment generating function. In this paper, we propose an alternative method, the so-called expected value approach, introduced in Górny (2017) to derive the exact distribution of the MLEs. Moreover, we discuss the benefits of this technique. Further, assuming uniformly distributed lifetimes, we show that the MLEs are also explicitly available and that their distributions are discrete for both the cumulative exposure and the tampered failure rate model. Additionally, we illustrate that confidence regions as well as confidence intervals can be established utilizing a connection to the multinomial distribution. The results are illustrated by an illustrative example as well as simulation results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankhb:v:82:y:2020:i:2:d:10.1007_s13571-019-00188-9
    DOI: 10.1007/s13571-019-00188-9
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    References listed on IDEAS

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