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Sankhya B

pp 1–39 | Cite as

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

  • Julian Górny
  • Erhard CramerEmail author
Article
  • 13 Downloads

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.

Keywords

Simple step-stress model Type-I censoring Cumulative exposure model Tampered failure rate model Exponential distribution Expected value approach Uniform distribution B-spline 

AMS (2000) subject classification

Primary 62E15, 62F10 Secondary 62F25, 62N05. 

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Notes

Acknowledgments

The authors are grateful to an anonymous referee for valuable comments and suggestions which led to this improved version of the manuscript.

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Copyright information

© Indian Statistical Institute 2019

Authors and Affiliations

  1. 1.Institute of StatisticsRWTH Aachen UniversityAachenGermany

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