Belief reliability analysis of multi-state deteriorating systems under epistemic uncertainty

Abstract

Due to the growing complexity of multi-state deteriorating systems and the lack of data, information and knowledge, epistemic uncertainty cannot be ignored anymore. Although there already exist some reliability metrics to deal with epistemic uncertainty problems in multi-state deteriorating systems, the final results provided by these methods are always probability intervals, which will suffer from the interval extension challenge in the subsequent operation. In this paper, we propose a reliability analysis method for the multi-state deteriorating system based on belief reliability theory, which can provide more conservative estimations and avoid interval extension problems. To describe the state transition process of multi-state deteriorating systems under the effect of epistemic uncertainty, a mathematical model called uncertain state transition chain is proposed. Under the framework of uncertainty theory, a total uncertainty inequality is given to assist the calculation of belief reliability. Using the proposed model and inequality, an algorithm of belief reliability for multi-state deteriorating systems considering the uncertainty of inspection time is provided. As a numerical example, the calculating process, the evaluation result and some discussions of a specific deteriorating system are given at last.