The “Bayesian Anomaly” and Its Practical Mitigation

A fundamental logical problem in the Bayesian inference of a series system´s failure probability is described, a practical means for its mitigation is discussed, and its application to space launch vehicles is illustrated. The problem is the ldquoBayesian Anomaly,rdquo the difference in the system´s failure probability per operation inferred from prior estimates, and test or operational experience applied at a lower-level of the system; and from the convolution of the same priors, and of the same experience applied at the system level (or any level above the first). In particular, unlike in a classical inference, the mean estimates differ critically. Although it is not possible to entirely resolve the problem, a practical procedure for mitigating it, establishing consistency among the mean and variance estimates at the two levels, is delineated.