×

zbMATH — the first resource for mathematics

Two-sided M-Bayesian credible limits of reliability parameters in the case of zero-failure data for exponential distribution. (English) Zbl 1428.62460
Summary: In this paper, we study the interval estimation of failure rate and reliability for exponential distribution, in the case of zero-failure data, using the method of two-sided Modified Bayesian (M-Bayesian) credible limit. We discuss the properties of two-sided M-Bayesian credible limits which include the impact of the value of upper bound \(c\) of hyper parameter, and the influence of different prior distributions of hyper parameter on two-sided M-Bayesian credible limits. The paper obtains the relationship between three kinds of two-sided M-Bayesian credible limits and two-sided classical confidence limits. Finally, we use a real data set to verify the properties of two-sided M-Bayesian credible limits, and the computing results indicate that the method is efficient and easy to operate.

MSC:
62N05 Reliability and life testing
62F15 Bayesian inference
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Martz, H. F.; Waller, R. A., A Bayes zero-failure (BAZE) reliability demonstration testing procedure, Qual. Technol., 11, 3, 128-137 (1979)
[2] Lindley, D. V.; Smith, A. F., Bayes estimation for the linear model, R. Stat. Soc. - Ser. B, 34, 1-41 (1972)
[3] Han, M.; Ding, Y. Y.; Chen, T., The hierarchical Bayesian analysis of zero-failure data of exponential distribution, Chin. Appl. Stat. Manage., 17, 4, 24-27 (1998)
[4] Brooks, S. P., Markov chain Monte Carlo method and its application, The Statistician, 47, 1, 69-100 (1998)
[5] Han, M., E-Bayesian estimation and hierarchical Bayesian estimation of failure rate, Appl. Math. Model., 33, 1915-1922 (2009)
[6] Jiang, P.; Lim, J. H.; Zuo, M. J.; Guo, B., Reliability estimation in a weibull lifetime distribution with zero-failure field data, Qual. Reliab. Eng. Int., 26, 691-701 (2010)
[7] John, Q.; Matthew, R., Estimating the probability of rare events: addressing zero-failure data, Risk Anal., 31, 7, 1120-1132 (2011)
[8] Nagata, H.; Li, Y. G.; Maack, D. R.; Bosenberg, W. R., Reliability estimation from zero-failure \(linbo_3\) modulator bias drift data, IEEE Photonics Technol. Lett., 16, 6, 1477-1479 (2004)
[9] Mao, S. S.; Wang, L. L., Reliability Statistics (1984), East China Normal University Press: East China Normal University Press Shanghai
[10] Han, M., Two-sided M-Bayesian credible limits method of reliability parameters and its applications, Commun. Stat. Methods, 37, 1659-1670 (2008)
[11] Chen, J. D., Survial analysis and reliability (2005), Peking University Press: Peking University Press Beijing
[12] Han, M., The M-Bayesian credible limits of the reliability derived from binomial distribution, Commun. Stat. - Theory Methods, 41, 21, 3814-3830 (2012)
[13] Niu, S. W.; Zhan, W., Analysis of confidence lower limits of reliability and hazard rate for electronic stability control systems, Qual. Reliab. Eng. Int., 29, 621-629 (2013)
[14] Fu, H. M.; Zhang, Y. B., Method of reliability analysis for time truncated zero-failure data based on weibull distribution, Chin. Aerosp. Power, 25, 12, 2807-2810 (2010)
[15] Han, M., Confidence limit of reliability parameters in the case of zero-failure data, Chin. Eng. Math., 21, 2, 245-248 (2004)
[16] Berger, J. O., Statistical Decision Theory and Bayesian Analysis (1985), Springer-Verlag: Springer-Verlag New York
[17] Lawless, J. F., Statistical Models and Method for lifetime Data (1982), Wiley: Wiley New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.