On the Behavior of Some Quantities Used in Bayesian Reliability Demonstration Tests

Equipment mean time between failures (MTBF) is assumed to be a frequency random variable. The goodness of fit of the uniform prior as a probability model for the MTBF is compared to the goodness of fit of the inverted gamma prior for actual failure data. These distributions can both be adequately fitted to the same failure data when the method of moments is used to fit the distributions. A comparison of posterior producer and consumer risks in a Bayesian reliability demonstration test is made using the fitted inverted gamma and uniform distributions as the priors. There can be rather large differences in the values of the posterior risks even when the two priors fit the data equally well or equally poorly.