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The lifetimes of components in unrepairable systems are considered as random fuzzy variablessince randomness and fuzziness are often merged with each other. Then we establish the fundamentalmathematical models of random fuzzy unrepairable systems, including series systems, parallel systems,series-parallel systems, parallel-series systems, and cold standby systems with absolutely reliable conversionswitches. Furthermore, the expressions of reliability and mean time to failure (MTTF) are given forthe above five random fuzzy unrepairable systems, respectively. Finally, numerical examples are given toshow the application in a lighting lamp system and a hi-fi system

Reliability Analysis of Random Fuzzy Unrepairable Systems