The effect of model uncertainty on maintenance optimization

Much operational reliability data available, e.g., in the nuclear industry, is heavily right-censored by preventive maintenance. The common methods for dealing with right-censored data (total time on test statistic, Kaplan-Meier estimator, adjusted rank methods) assume the s-independent competing-risk model for the underlying failure process and the censoring process, even though there are, many s-dependent competing-risk models that can also interpret the data. It is not possible to identify the 'correct' competing risk model from censored data. A reasonable question is whether this model uncertainty is of practical importance. This paper considers the impact of this model-uncertainty on maintenance optimization, and shows that it can be substantial. Three competing-risk model classes are presented which can be used to model the data, and determine an optimal maintenance policy. Given these models, then consider the error that is made when optimizing costs using the wrong model. Model uncertainty can be expressed in terms of the 'dependence between competing risks' which can be quantified by expert judgment. This enables reformulating the maintenance optimization problem to account for model uncertainty.