Series-system reliability-estimation using very small binomial samples

This investigation explored the effect of incorporating prior information into series-system reliability estimates, where the inferences are made using very small sets (less than 10 observations) of binomial test-data. To capture this effect, the performance of a set of Bayes interval estimators was compared to that of a set of classical estimators over a wide range of subsystem beta prior-distribution parameters. During a Monte Carlo simulation, the Bayes estimators tended to provide shorter interval estimators when the mean of the prior system-reliability differed from the true reliability by 20 percent of less, but the classical estimators dominated when the difference was greater. Based on these results, the authors conclude that there is no clear advantage to using Bayes interval estimation for sample sizes less than 10 unless the poor mean system reliability is believed to be within 20 percent of the true system reliability. Otherwise, the Lindstrom-Madden estimator, a useful classical alternative for very small samples, should be used.