Handling the epistemic uncertainty in the selective maintenance problem

Abstract

Nowadays, both continuous and discontinuous operating systems require higher and higher reliability levels in order to avoid the occurrence of dangerous or even disastrous consequences. Accordingly, the definition of appropriate maintenance policies and the identification of components to be maintained during the planned system's downtimes are fundamental to ensure the reliability maximization. Therefore, the present paper proposes a mathematical programming formulation of the selective maintenance problem with the aim to maximize the system's reliability under an uncertain environment. Specifically, the aleatory model related to the components’ failure process is well known, whereas some model parameters are affected by epistemic uncertainty. Uncertain parameters are hence gathered from experts in an interval form, and the Dempster-Shafer Theory (DST) of evidence is proposed as a structured methodology to properly deal with the interval-valued experts’ opinions. An exact and efficient algorithm is finally used to solve the optimization model.