1984 · 13 citations · 0 references
ComputingNuclear EngineeringBayesian Data AnalysisNuclear Safety AnalysisStatisticsBayesian InferenceBayesian ModelingBayesian StatisticsEmpirical BayesProbabilistic ModelingReliability ModelingFailure ProbabilityMaximum Likelihood EstimatorMaximum Likelihood InferencePoisson DistributionProbabilistic Reliability AnalysisProbabilistic Reliability AssessmentProbability Of Failure AnalysisReliability Data Analysis
This report is the result of a preliminary feasibility study of the applicability of Stein and related parametric empirical Bayes (PEB) estimators to the Nuclear Plant Reliability Data System (NPRDS). A new estimator is derived for the means of several independent Poisson distributions with different sampling times. This estimator is applied to data from NPRDS in an attempt to improve failure rate estimation. Theoretical and Monte Carlo results indicate that the new PEB estimator can perform significantly better than the standard maximum likelihood estimator if the estimation of the individual means can be combined through the loss function or through a parametric class of prior distributions.