Keywords: dynamic programming, decision analysis, Markov processes, epistemic uncertainty, maintenance policy.

The decision process regarding an optimal maintenance policy is often very sensitive to the input statistical parameters (e.g. mean values, standard deviations, Markovian transition matrices) describing the probabilistic models. However, these parameters are estimated by classical interference methods, where the available data is often very limited. This lack of data leads to second-order uncertainties due to the inevitable difference between the observed sample from which inference is made and the real population. This second-order statistical uncertainty is usually quantified by several means, such as confidence intervals, maximum likelihood methods, Bayesian updating methods and fuzzy sets. It can be shown that the expected costs increase with full uncertainty consideration. Therefore, neglecting the epistemic uncertainty leads in general to misleading low life cycle costs.

In this paper we present an extension to the generalized partially observable Markov decision process (GPOMDP) taking into account the second-order epistemic uncertainties, where the decision analysis is combined with dynamic programming. The GPOMDP allows for easy mathematical modelling to optimize a complex sequence of actions to be undertaken during each time period. In our case, the "sequence of actions" consists of two inspection decisions followed by one maintenance decision. This type of modelling is relevant to maintenance problems, as an inexpensive inspection may be first carried out, in order to decide whether more precise, and costly, inspection is required before taking the decision relating to the type of repair technology to apply. By taking into account the costs of the different inspection and maintenance techniques, GPOMDP allows us to optimize the planning of imperfect inspections and probabilistic actions along the prescribed time horizon of the POMDP. Although the proposed methodology was motivated by inspection, maintenance and rehabilitation, the formulation is quite general and can be relevant to any POMDP.

In order to take into account second-order epistemic uncertainties, several techniques have been proposed and implemented, such as Dirichlet distributions, fuzzy sets, etc. This modeling allows us to consider the second-order uncertainties relating the imperfectness of the inspection techniques, the stochastic deterioration and the probabilistic outcomes of the maintenance actions.

In a POMDP, the state of the system at the beginning of each time period cannot be fully observed. Thus, the manager of the system must rely on a characterization of a partially observed state (i.e. a belief state) which is usually described by a probabilistic distribution.

The proposed model is applied to a concrete bridge subject to degradation, in order to provide the optimal strategy for inspection and maintenance. The influence of epistemic uncertainties on the optimal solution is underlined through sensitivity analysis regarding the input data.

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