Reliability And Mean Time To Failure Analysis Of Fuzzy Random Unrepairable Systems

System reliability has been widely studied in the literature because of its prevalence in power plants, manufacturing systems, and industrial systems. Maintaining a high level of reliability is often an essential requisite. In classical reliability theory, the lifetimes of systems and components have been assumed to be random variables. In a probabilistic analysis of unrepairable systems, system behavior is described by reliability and mean time to failure (MTTF), in which the reliability is defined by the probability of the random event "system is functioning at time t", and MTTF the expected value of random lifetime of system.In practice, the lifetimes of unrepairable systems contain both randomness and fuzziness. So it is appropriate to assume the lifetimes of systems to be fuzzy random variables. In this paper, the definitions of reliability and MTTF of unrepairable systems with fuzzy random lifetimes are given, respectively. Then basic mathematical models of unrepairable systems with fuzzy random lifetimes are established. Furthermore, the reliability and MTTF of fuzzy random series systems, parallel systems, series-parallel systems, parallel-series systems and cold standby systems are discussed, respectively.Finally, some numerical examples are presented to illustrate how to calculate the reliability and MTTF of a fuzzy random series system, a fuzzy random parallel system and a fuzzy random cold standby system.