SERIES-SYSTEM RELIABILITY-ESTIMATION USING VERY SMALL BINOMIAL SAMPLES

This investigation explored the effect of incorporating prior informat ion into series-system reliability estimates, where the inferences are made using very small sets (less than 10 observations) of binomial te st-data. To capture this effect, the performance of a set of Bayes int erval estimators was compared to that of a set of classical estimators over a wide range of subsystem beta prior-distribution parameters. Du ring a Monte Carlo simulation, the Bayes estimators tended to provide shorter interval estimates when the mean of the prior system-reliabili ty differed from the true reliability by 20 percent or less, but the c lassical estimators dominated when the difference was greater. Based o n these results, we conclude that there is no clear advantage to using Bayes interval estimation for sample sizes less than 10 unless the pr ior 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.