An empirical Bayesian based approach to delay time inspection model parameters estimation using both subjective and objective data

This paper presents a model on the estimation of delay time inspection model parameters using both subjective and objective data. Delay time based inspection modelling has been increasingly reported in the literature. This has primarily concerned the modelling of inspection intervals, while estimating model parameters is an important task. When either subjective data such as expert judgements or objective data of failure and maintenance interventions are available, approaches to estimate the parameters associated in the delay time inspection model are available to each of the data types. If, however, we have subjective data in the first instance and then objective data become available later, a method using both available information sources is required. This paper reports on a new development of such an approach using a standard hierarchical Bayesian method. The approach starts with subjective data first, and then updates the estimates when objective data become available. The initial estimates are made using the empirical Bayesian method matching with few subjective summary statistics provided by the experts, which differs from previously reported subjective approaches in delay time modelling. Then the updating mechanism enters the process, which requires a repeated evaluation of the likelihood function. Examples based on real and simulated data are presented and findings are discussed. Copyright © 2007 John Wiley & Sons, Ltd.