Possibilistic methods for uncertainty treatment

Abstract

The authors propose a method for assessing the performance of a maintenance policy whilst accounting for uncertainty in various parameters of the degradation model. The method is appropriate for the representation and propagation of epistemic uncertainty which is elicited from an expert, who can provide a family of confidence intervals for each uncertain parameter. Information elicited from the expert is described using possibility distributions and propagated through the degradation model using fuzzy random variables and the Dempster-Shafer Theory of Evidence.

In classical approaches to uncertainty propagation based on probability theory, probability distributions are used to represent information obtained from experts. However, expert judgment is often expressed using imprecise linguistic statements, and the imposition of specific probability distributions over-constrains this uncertain information in an arbitrary and unjustified manner. Possibility theory allows the epistemic uncertainty arising from expert opinion to be represented in an arguably more rigorous manner, without introducing additional bias.

A practical case study concerning the maintenance of a check valve of a turbo-pump lubricating system in a nuclear power plant illustrates the method. A rupture failure model caused by fatigue is modeled, and a Condition-Based Maintenance policy is applied to the component over a fixed time horizon. The performance of the maintenance policy is assessed in terms of cost and component unavailability. The method produces plausibility and belief distributions for the output values of interest. Further work is necessary to help decision-makers interpret this information and integrate it in decision-support procedures.