Reliability assessment under uncertainty using Dempster-Shafer and vague set theories

Abstract

Analyzing reliability of a system in design stage requires expertpsilas estimations and statistical data with various degrees of epistemic uncertainty and doing aggregation in a coherent framework. Dempster-Shafer (DS) theory is theorypotentially valuable tool for combination of evidence obtained from multiple different sources. One approach for fuzzy reliability assessment is using Vague set (VS) theory. DS theory has many similarities with VS theory. Uncertain raw data about the component reliability of a system can be combined using different combination methods of DS theory and can be represented in the form of triangular fuzzy vague number. Using the proper methods and equations, the fuzzy reliability of the system can be computed with triangular vague numbers of components reliability. Combining these two theories eliminates the gap between the representation of combined evidences and the way of representing the reliability of components in the VS theory for reliability assessment. Our proposed method eliminates this gap in very convenient form. Because of closed relevance of these two theories we can represent the output of DS combination in the form of vague triangular number in the VS theory. With this method we eliminate the loss of meaningful information in this conversion.