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

Julian Górny and Erhard Cramer ()
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Julian Górny: RWTH Aachen University
Erhard Cramer: RWTH Aachen University

Sankhya B: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 1, 239 pages

Abstract: 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; Primary 62E15; 62F10; Secondary 62F25; 62N05. (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13571-019-00188-9

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Handle: RePEc:spr:sankhb:v:82:y:2020:i:2:d:10.1007_s13571-019-00188-9