Empirical Bayes inference with nonlinear homogenizations and correlated intensity functions: use in asset degradation modelling

We develop and evaluate a method to estimate the frequency of an asset failure when experience event data are available for multiple assets of a given type. Typically such data contains information on assets of mixed ages, operating in different environments and in many cases the number of recorded events might be few or even zero. Assets are known to have slow age-related degradation and we have access to engineering experts who are able to provide judgment about the degradation rates. An empirical Bayes method is developed to allow us to estimate the failure rates for an asset on a particular site by using the available observational data pool together with structured engineering judgment of the degradation rate for the asset type. Our method aims to address the challenges of asset pool heterogeneity and environmental conditions across sites. We describe our practical motivation which is informed by a real problem facing a water utility. We explain the principles and mathematics underpinning the new methods, before describing a simulation based evaluation of their accuracy. We show that the empirical Bayes methods provide accurate estimates of the failure intensities for a range of parameters considered in this controlled study and that empirical Bayes estimators can compensate for bias in initial judgmental assessments of degradation rates. We discuss how the method can be applied in the industry context.