T2: An Introduction to Belief Reliability Theory


Abstract


How to measure reliability by a reasonable metric is a basic problem in reliability science. Since in reality, components/systems are usually affected by both aleatory and epistemic uncertainties, professor Kang from Beihang University proposed a new reliability metric, named belief reliability, which is defined as the chance that a system state is within a feasible domain. Mathematically, the metric can degenerate to either probability theory-based reliability, which mainly copes with aleatory uncertainty, or uncertainty theory-based reliability, which mainly considers the effect of epistemic uncertainty. Based on the proposed metric, belief reliability theory is proposed, including commonly used belief reliability indexes, belief reliability modeling and analysis for components, belief reliability modeling and analysis for systems, the design and optimization of belief reliability, and the application of belief reliability theory in accelerated degradation testing.

This short course will give a brief introduction of belief reliability theory, and can be divided into three parts:

Part 1: Background, Preliminaries and Belief Reliability Metric and Indexes

In this part, we will first introduce the definition of reliability, classical probabilistic reliability metric and current reliability metrics considering the epistemic uncertainty, and gives the requirements for reliability metric. Then we will introduce the mathematic bases of belief reliability theory, including uncertainty theory and chance theory. At last we will introduce the belief reliability metric and indexes.

Part 2: Belief Reliability Modeling and Analysis for Components and Systems

In this part, we will first introduce the belief reliability modeling and analysis for components, and give the corresponding illustrative examples. Then we will introduce the belief reliability modeling and analysis for systems based on the reliability block diagram and the fault tree respectively.

Part 3: Application of Belief Reliability Theory in Accelerated Degradation Testing

In accelerated degradation testing, there exist limited data in unit dimension, time dimension and stress dimension, which will cause epistemic uncertainties correspondingly. The existing accelerated degradation models can either quantify the epistemic uncertainties or just quantify epistemic uncertainties by subjective methods. So we introduce uncertainty theory into the field of accelerated degradation modeling.

In this part, we will introduce how to quantify the epistemic uncertainty caused by limited data in time dimension based on uncertainty theory, and build up a new accelerated degradation model, derive its reliability and lifetime functions, and present the corresponding statistical method based on belief reliability theory.

Speaker


Rui Kang avatar
Rui Kang China

Beihang University, China


Rui Kang is a Changjiang Scholars of Chinese Ministry of Education and Distinguished Professor in the School of Reliability and Systems Engineering of Beihang University, Beijing, China. He received his Bachelor's and Master's degree in Electrical Engineering in 1987 and 1990 from Beihang University, respectively. His main research interests include reliability and resilience for critical infrastructures, system prognosis and health management (PHM) and Belief Reliability Theory. Now, he is the director of the Center for Resilience and Safety of Critical Infrastructure (CRESCI) and Sino-French Risk Science and Engineering Lab. He is also an Associate Editor (AE) of the IEEE Transaction on Reliability (ITR) and Journal of Risk and Reliability (JRR). He has developed six courses and published eight books and more than 200 research papers. He received several awards from the Chinese government for his outstanding scientific contributions.


Xiaoyang Li avatar
Xiaoyang Li China

Beihang University, China


Xiaoyang Li is an associate professor at the School of Reliability and Systems Engineering, Beihang University. And also, she is the executive director of Center for resilience and safety of critical infrastructure. She received her PhD degree in Aerospace Systems Engineering from Beihang University in 2007 and visited the IMS center of University of Cincinnati from 2010- 2011. Her research interests include reliability of cloud data center, reliability testing and modeling, and resilience modeling and evaluation. She is the PIs of about 15 funding and projects, including National Science foundation of China, the sub-project of National Program on Key Basic Research, etc. Now, she published about 30 SCI indexed academic papers focused on reliability testing and owned more than 20 authorized patents.