Point and Interval Estimation of Series System Reliability Using Small Data Sets

摘要

This investigation explored the relative performance of several small-samplepoint and interval estimators for series system reliability. Among point estimators, the maximum likelihood estimator (MLE) was compared to the corresponding Bayes estimator. In addition, four interval estimators were compared: Easterling's modified maximum likelihood integer estimator, the Lindstrom-Madden estimator, and Bayesian probability interval estimators constructed using approximate beta and Bayes Monte Carlo empirical posterior densities. The relative performance of the point estimators was assessed by comparing their mean square errors. For the four interval estimators, the interval coverage probability and the average interval lower bound were examined. The values of these performance measures were generated for 32 representative series systems using Monte Carlo simulation. The results of the Monte Carlo study showed that the accuracy of the available prior information determines whether a Bayesian or a classical approach should be used to estimate series system reliability. If there is high confidence that the mean of each component prior distribution is within 20 percent of the true component reliability, Bayesian point and interval estimators constructed from an approximate beta posterior should be used. Otherwise, the MLE point estimator and the Lindstrom-Madden interval estimator should be chosen. Reliability, Statistical inference, Bayes' theorem, Maximum likelihood estimation, Weapon system effectiveness.