Reliability-Box of Systems Under Model Parameter Uncertainty Based on Evidential Variable and Evidential Network

Abstract

Advanced engineering systems possess a large number of components with complicated failure dependencies. To accurately assess the system reliability, the degradation models of components should be known in advance and the model parameters should be accurately estimated via a large quantity of historical time-to-failure data. In real-world situations, due to limited data, lack of knowledge, and vague judgments from experts, components’ degradation model parameters are, however, inevitably encountered with epistemic uncertainty and oftentimes quantified as evidential variables. In this article, upper and lower bounds of system reliability, termed as reliability-box, are estimated when components’ degradation model parameters are elicited from experts and quantified by evidential variables. In the first place, the constrained optimization model is leveraged to assess the reliability-box of each component by giving the evidential variable of the component’s degradation model parameters. Next, based on the system structure, the evidential network of the system is constructed to propagate the epistemic uncertainty from the component level to the system level. Therefore, the focal elements of the evidential variable of system reliability, i.e., the system reliability bounds, can be assessed via the belief and plausibility functions to the mass function of the leaf node of the evidential network. The effectiveness of the proposed methods is demonstrated by a rolling system in the chip cutting detection module.

Keywords

• Reliability-box
• epistemic uncertainty
• evidential variable
• evidential network
• Dempster-Shafer theory
• chip cutting detection system