Evaluation of Empirical Bayes Estimators of Correlated Event Rates and Implications for Predicting new Product Reliability

Abstract

A method for estimating the reliability of a new product based on a comparative analysis of observed data for similar existing products has been motivated by an industry problem; see Quigley and Walls (to appear). Such estimates are required as part of contractual discussions with customers, as well as to inform the reliability program management for the new design. An empirical Bayes inference method has been developed based on a multivariate Poisson-Gamma probability model. The model aims to capture both aleatory and epistemic uncertainties. The latter are those which have the potential to be bought down by gathering more information such as learning about the existence of a potential design weaknesses. The model is multivariate since it involves modelling elements of the new product design reliability in relation to a set of relevant elements from multiple similar products. See, Quigley et al (2013) for more details of probability modelling of correlated events which provides a theoretical framework, and Quigley and Walls (2017) for an approach to construct prior distributions using empirical data.