Hierarchical Bayesian Reliability Analysis of Binomial Distribution based on Zero-Failure Data

doi:10.23940/ijpe.18.09.p16.20762082

Abstract

Abstract: The aim of this paper is to develop a new hierarchical Bayesian estimation method under symmetric entropy loss function for reliability of the binomial distribution. With the rapid development of manufacturing techniques, some electric products are highly reliable, and thus zero-failure data often occur when putting them in censored lifetime tests. Based on zero-failure data, the reliability analysis is very important for manufacturing. The hierarchical Bayesian estimator is regarded as a robust estimating method, but many existing robust Bayes estimators are complex and difficult to be utilized in practice. The contribution of this article is to present an easy hierarchical Bayesian estimator for reliability of the binomial distribution when reliability has a negative log-gamma prior distribution. Finally, a practical example is provided to show the feasibility and robustness of different estimators.

Key words: binomial distribution, bayes estimation, symmetric entropy loss function, hierarchical bayesian estimation

Shixiao Xiao and Haiping Ren. Hierarchical Bayesian Reliability Analysis of Binomial Distribution based on Zero-Failure Data [J]. Int J Performability Eng, 2018, 14(9): 2076-2082.

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References

[1] H. F.Martz and R. A.Waller, “Bayesian Zero-Failure (BAZE) Reliability Demonstration Testing Procedure,” Journal of Quality Technology, Vol. 11, No. 3, pp. 128-138, July 1979
[2] H. Nagata, Y. Li,D. R. Maack, et al., “Reliability Estimation from Zero-Failure LiNbO3, Modulator Bias Drift Data,” IEEE Photonics Technology Letters, Vol. 16, No. 6, pp. 1477-1479, June 2004
[3] X. T. Xia, “Reliability Analysis of Zero-Failure Data with Poor Information,” Quality & Reliability Engineering International, Vol. 28, No. 8, pp. 981-990, December 2012
[4] Y. C. Yin, H. Z. Huang,W. Peng, et al., “An E-Bayesian Method for Reliability Analysis of Exponentially Distributed Products with Zero-Failure Data,” Eksploatacja i Niezawodnosc - Maintenance and Reliability, Vol. 18, No. 3, pp. 445-449, June 2016
[5] X. Jia, X. Wang,B. Guo, “Reliability Assessment for Very Few Failure Data and Zero-Failure Data,” Journal of Mechanical Engineering, Vol. 52, No. 2, pp. 182-190, January 2016
[6] L. Jiang, C. Li,S. Wang, et al., “Deep Feature Weighting for NAIVE BAYES and its Application to Text Classification,” Engineering Applications of Artificial Intelligence, Vol. 52, No. C, pp. 26-39, June 2016
[7] Y. K. Gu, Y. G. Xiong,J. Li, “A Reliability Analysis of Crank Rod System based on Bayesian Network,” Nonferrous Metals Science & Engineering, Vol. 3, No. 2, pp. 96-100, April 2012
[8] P. Mehta, M. Kuttolamadom,L. Mears,“Mechanistic Force Model for Machining Process-Theory and Application of Bayesian Inference,” International Journal of Advanced Manufacturing Technology, Vol. 91, No. 9-12, pp. 3673-3682, August 2017
[9] J. Wang, W. Yan,H. Xu, et al., “Investigation of the Probability of a Safe Evacuation to Succeed in Subway Fire Emergencies based on Bayesian Theory,” Ksce Journal of Civil Engineering, Vol. 22, No. 3, pp. 877-886, May 2018
[10] B. H. Do, C. Langlotz,C. F. Beaulieu, “Bone Tumor Diagnosis using a Naïve Bayesian Model of Demographic and Radiographic Features,” Journal of Digital Imaging, Vol. 30, No. 5, pp. 640-647, October 2017
[11] J. Górecki, M. Hofert,M. Holeňa, “An Approach to Structure Determination and Estimation of Hierarchical Archimedean Copulas and its Application to Bayesian Classification,” Journal of Intelligent Information Systems, Vol. 46, No. 1, pp. 21-59, February 2016
[12] D. V.Lindley and A. F. M. Smith, “Bayesian Estimation for the Linear Model,” Journal of the Royal Statistical Society. Series B: Methodological, Vol. 30, No. 1, pp. 453-455, January 1972
[13] M. Han, “The Structure of Hierarchical Prior Distribution and Its Applications,” Chinese Operations Research & Managementence, Vol. 6, No. 3, pp. 31-40, June 1997
[14] J. Wang, D. Cheng,E. Yang, et al., “Reliability Life Assessment of Spring Contact with Incomplete Gamma Distribution,” Mechanical Science & Technology for Aerospace Engineering, Vol. 36, No. 1, pp. 39-45, January 2017
[15] T. Zhu, Z. Z. Yan,X. Peng, “A Weibull Failure Model to the Study of the Hierarchical Bayesian Reliability,” Eksploatacja i Niezawodnosc - Maintenance and Reliability, Vol. 18, No. 4, pp. 501-506, September 2016
[16] Y. Shibuya, K. Okada,T. Ogawa, et al., “Hierarchical Bayesian Models for the Autonomic-based Concealed Information Test,” Biological Psychology, Vol. 132, pp. 81-90, February 2018
[17] S. Kim, W. S. Desarbo,D. K. H.Fong, “A Hierarchical Bayesian Approach for Examining Heterogeneity in Choice Decisions,” Journal of Mathematical Psychology, Vol. 82, pp. 56-72, February 2018
[18] M. Han, “The E-Bayesian Estimation and Hierarchical Bayesian Estimation of Shape Parameter for Pareto Distribution and Its Applications,” Pure & Applied Mathematics, Vol. 32, No. 3, pp. 235-242, June 2016
[19] M. Han, “The E-Bayesian Estimation of the Parameter for Poisson Distribution and its Properties,” Acta Mathematica Scientia, Vol. 36, No. 5, pp. 1010-1016, October 2016
[20] M. Han, “Properties of E-Bayesian Estimation for the Reliability Derived from Binomial Distribution,” Acta Mathematica Scientia, Vol. 33, No. 1, pp. 62-70, February 2013
[21] M. Chacko, “Bayesian Estimation based on Ranked Set Sample from Morgenstern Type Bivariate Exponential Distribution when Ranking Is Imperfect,” Metrika, Vol. 80, No. 3, pp. 1-17, April 2017
[22] N. S. Farsipour, “Admissibility of Estimators in the Non-Regular Family under Entropy Loss Function,” Statistical Papers, Vol. 44, No. 2, pp. 249-256, April 2003
[23] A. T. P.Najafabadi and M. O.Najafabadi, “On the Bayesian Estimation for Cronbach's Alpha,” Journal of Applied Statistics, Vol. 43, No. 13, pp. 2416-2441, March 2016
[24] B. Xu, D. H. Wang,R. T. Wang, “Estimator of Scale Parameter in a Subclass of the Exponential Family under Symmetric Entropy Loss,” Journal of Northeastern Mathematical, Vol. 24, No. 5, pp. 447-457, October 2008
[25] H. P. Ren, “Bayesian Estimation of Parameter of Rayleigh Distribution under Symmetric Entropy Loss Function,” Journal of Jiangxi University of Science & Technology, Vol. 31, No. 5, pp. 64-66, October 2010
[26] J. O. Berger, “Statistical Decision Theory and Bayesian Analysis,” Springer-Verlag, New York, 1985
[27] W. B.Yu and H. P. Ren, “Hierarchical Bayesian Analysis for the Success-and-Failure Test with Zero-Failure Data,” Journal of Nanchang University, Vol. 33, No. 2, pp. 130-132, March 2009