On Exact Inferential Results for a Simple Step-Stress Model Under a Time Constraint
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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.
KeywordsSimple 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 classificationPrimary 62E15, 62F10 Secondary 62F25, 62N05.
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The authors are grateful to an anonymous referee for valuable comments and suggestions which led to this improved version of the manuscript.
- Barlevy, G. and Nagaraja, H. N. (2015). Ordered data analysis, modeling and health research methods. In: honor of H. N. Nagaraja’s 60th birthday. (Chap. Properties of the vacancy statistic in the discrete circle covering problem, pp 121–146).Google Scholar
- Górny, J. and Cramer, E. (2017a). A volume based approach to establish B-spline based expressions for density functions and its application to progressive hybrid censoring. submitted.Google Scholar
- Górny, J. and Cramer, E (2017b). From B-spline representations to gamma representations in hybrid censoring. Stat. Pap., to appear.Google Scholar
- Górny, J. and Cramer, E (2017c). Type-I hybrid censoring of uniformly distributed lifetimes. Commun. Stat. - Theory Methods, to appear.Google Scholar
- Koley, A. and Kundu, D (2017). Step stress modeling with random stress changing time point submitted.Google Scholar
- Koley, A. (2018). Some contributions to exponential failure data modeling (Doctoral dissertation, Department of Mathematics and Statistics Indian Institute of Technology Kanpur, Kanpur, India).Google Scholar
- Kundu, D., Kannan, N. and Balakrishnan, N. (2004). Analysis of progressively censored competing risks data, 23. Elsevier, Amsterdam, Balakrishnan, N. and Rao, C. R. (eds.), p. 331–348. Handbook of Statistics.Google Scholar
- Ng, H. K. T., Duan, F. and Chan, P. S. (2015). Ordered data analysis, modeling and health research methods. In honor of H. N. Nagaraja’s 60th birthday. (Chap. On Conditional Moments of Progressively Censored Order Statistics with a Time Constraint, pp. 55–71).Google Scholar
- Samanta, D., Kundu, D. and Ganguly, A (2017). Order restricted Bayesian analysis of a simple step stress model. Sankhya B, to appear.Google Scholar