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Uncertain random variables provide a tool to deal with phenomena in which uncertainty and randomness simultaneously exist. This paper proposes a concept of value-at-risk to quantify the risk of an uncertain random system. In addition, a value-at-risk theorem is proved in order to calculate the value-at-risk, and is applied to series systems, parallel system, k-out-of-n system, standby system, and...
Uncertain random variable is a main tool to deal with phenomena in which uncertainty and randomness are present simultaneously. This paper proposes a concept of expected loss to quantify the risk of an uncertain random system. In addition, an expected loss theorem is proved and applied to series system, parallel system, k-out-of-n system, standby system and structural system.
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