This paper introduces a new method, E-Bayesian estimation method, to estimate the reliability in
zero-failure data. The definition of E-Bayesian estimation of the reliability is given. Based on the definition,
the formulas of E-Bayesian estimation and hierarchical Bayesian estimation of the reliability are provided, and
property of the E-Bayesian estimation, i.e. relation between E-Bayesian estimation and hierarchical Bayesian
estimation, is discussed. Calculations performed on practical problems show that the proposed new method is
feasible and easy to operate.
HAN Ming (韩明)
. Estimation of Reliability Derived from Binomial Distribution in Zero-Failure Data[J]. Journal of Shanghai Jiaotong University(Science), 2015
, 20(4)
: 454
-457
.
DOI: 10.1007/s12204-015-1648-1
[1] Lindley D V, Smith A F. Bayes estimates for the linear model [J]. Journal of the Royal Statistical Society Series B, 1972, 34(1): 1-41.
[2] Han Ming. The structure of hierarchical prior distribution and its applications [J]. Operations Research and Management Science, 1997, 6(3): 31-40 (in Chinese).
[3] Ando T, Zellner A. Hierarchical bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct monte carlo and importance sampling techniques [J].Bayesian Analysis, 2010, 5(1): 65-96.
[4] Yau C, Holmes C. Hierarchical bayesian nonparametric mixture models for clustering with variable relevance determination [J]. Bayesian Analysis, 2011,6(2): 329-352.
[5] Han M. E-bayesian estimation and hierarchical bayesian estimation of failure probability [J]. Communications in Statistics-Theory and Methods, 2011,40(18): 3303-3314.
[6] Han Ming. The advances of reliability for zero-failure data [J]. Advances in Mathematics, 2002, 31(1): 7-19(in Chinese).
[7] Miller K W, Morell L J, Noonan R E, et al. Estimating the probability of failure when testing reveals no failures [J]. IEEE Transaction on Software Engineering,1992, 18(1): 33-43.
[8] Han Ming. Reliability analysis of zero-failure data [M].Beijing: China Statistics Press, 1999 (in Chinese).
[9] Han M. E-bayesian estimation of the reliability derived from binomial distribution [J]. Applied Mathematical Modelling, 2011, 35: 2419-2424.
[10] Han M. The M-bayesian credible limits of the reliability derived from binomial distribution [J]. Communications in Statistics-Theory and Methods, 2012, 41(21):3814-3830.
