Risk Index in Uncertain Random Risk Analysis

In many systems, randomness and uncertainty are present simultaneously. Uncertain random variables provide a tool to deal with these inexact phenomena. This paper proposes a concept of risk index to quantify the risk of an uncertain random system. In addition, a risk index theorem is proved in order to calculate the risk index, and is applied to series systems, parallel systems and standby systems. Finally, a concept of expected loss is suggested for an uncertain random system.