Evaluation and comparison of estimation methods for failure rates and probabilities

An updated parametric robust empirical Bayes (PREB) estimation methodology is presented as an alternative to several two-stage Bayesian methods used to assimilate failure data from multiple units or plants. PREB is based on prior-moment matching and avoids multi-dimensional numerical integrations. The PREB method is presented for failure-truncated and time-truncated data. Erlangian and Poisson likelihoods with gamma prior are used for failure rate estimation, and Binomial data with beta prior are used for failure probability per demand estimation. Combined models and assessment uncertainties are accounted for. One objective is to compare several methods with numerical examples and show that PREB works as well if not better than the alternative more complex methods, especially in demanding problems of small samples, identical data and zero failures. False claims and misconceptions are straightened out, and practical applications in risk studies are presented.