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Title: Two-sided M-Bayesian limits of credibility of reliability parameters in the case of zero-failure data and a case study

Authors: Wanyi Dai; Siqi Li; Mei Zhang; Yueming Hu; Dongfang Mei

Addresses: Department of Mathematics, California State University, Fullerton, Fullerton, California, USA ' Providence St. Joseph Health, 3345 Michelson Dr #100, Irvine, CA 92612, USA ' School of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong, China ' School of Automation Science and Engineering, South China University of Technology, Guangzhou, Guangdong, China ' College of Public Management, South China University of Technology, Guangzhou, Guangdong, China

Abstract: In this paper, a novel method of two-sided M-Bayesian credible limit is proposed to deal with the interval estimation problem of reliability parameters with exponential distribution in the case of zero-failure data. The properties of two-sided M-Bayesian limits of credibility are discussed and some new theorems are proven including the impact of the upper bound c of hyper parameters and the influence of different prior distributions of hyper parameters on two-sided M-Bayesian limits of credibility when the reliability of estimation was determined by the exponential distribution. The paper extended the conclusions drawn in two previous studies regarding the relationships among the many kinds of two-sided M-Bayesian limits of credibility and two-sided classical confidence. Finally, a real dataset about engines is discussed with different model parameters. By means of an example, the presented method of this paper is compared with the classical confidence limits. The results verify the properties of two-sided M-Bayesian limits of credibility and indicate that the method is efficient and easy to perform.

Keywords: reliability; estimation; two-sided M-Bayesian limits of credibility; zero-failure data.

DOI: 10.1504/IJSPM.2020.106976

International Journal of Simulation and Process Modelling, 2020 Vol.15 No.1/2, pp.89 - 99

Received: 28 Aug 2018
Accepted: 17 May 2019

Published online: 21 Apr 2020 *

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