On Analytic Empirical Bayes Estimation of Failure Rates
- 1 September 1987
- journal article
- Published by Wiley in Risk Analysis
- Vol. 7 (3) , 329-338
- https://doi.org/10.1111/j.1539-6924.1987.tb00468.x
Abstract
The estimation of plant accident rates and component failure rates is addressed within the framework of a parametric empirical Bayes approach. The observables, the numbers of failures recorded in various similar systems, obey the Poisson probability law. The parameters of a common gamma prior distribution are determined by a special moment matching method such that the results are consistent with classical (fiducial) confidence limits. Relations between Bayesian, classical, and Stein's estimation are discussed. The theory of the method is fully developed, although the suggested procedure itself is relatively simple. Solutions exist and they are in allowed ranges for all practical cases, including small samples and clustered data. They are also unbiased for large samples. Numerical examples are analyzed to illustrate the method and to allow comparisons with other methods.Keywords
This publication has 9 references indexed in Scilit:
- On robust methods for failure rate estimationReliability Engineering, 1986
- Analytic Bayesian Solution of the Two-Stage Poisson-Type Problem in Probabilistic Risk AnalysisRisk Analysis, 1985
- Natural Exponential Families with Quadratic Variance Functions: Statistical TheoryThe Annals of Statistics, 1983
- Parametric Empirical Bayes Inference: Theory and ApplicationsJournal of the American Statistical Association, 1983
- Parametric Empirical Bayes Confidence IntervalsPublished by Elsevier ,1983
- Fiducial estimation of probabilities for reliability and risk assessmentAnnals of Nuclear Energy, 1981
- Data Analysis Using Stein's Estimator and its GeneralizationsJournal of the American Statistical Association, 1975
- Stein's Estimation Rule and Its Competitors--An Empirical Bayes ApproachJournal of the American Statistical Association, 1973
- Confidence Sets for the Mean of a Multivariate Normal DistributionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1962