System Reliability Theory In Uncertain Environments

Firstly, this dissertation regards the lifetime of the unrepairable sys-tem as fuzzy variable. In a fuzzy analysis of unrepairable system, system behavior is described by reliability and mean time to failure (MTTF). Reli-ability is defined as the credibility of the fuzzy event "system is functioning at time t", and MTTF the expected value of fuzzy lifetime of unrepairable system. In addition, the basic mathematical models of unrepairable system with fuzzy lifetime are established, including fuzzy series system, fuzzy paral-lel system, fuzzy series-parallel system, fuzzy parallel-series system and fuzzy cold standby system, each of which has been analyzed and given the specific formula regarding its reliability and MTTF.Given that in the practical application, the lifetime of unrepairable sys-tem contain both randomness and fuzziness, so the lifetime of unrepairable system is considered as random fuzzy variables. System behavior is also described by reliability and MTTF. But reliability is defined by the aver-age chance of the fuzzy event "system is functioning at time t", and MTTF the expected value of random fuzzy lifetime of unrepairable system. Cor-respondingly, the basic mathematical models of unrepairable system with random fuzzy lifetime are established. The reliability and MTTF of ran-dom fuzzy series system, random fuzzy parallel system, random fuzzy series-parallel system, random fuzzy parallel-series system and random fuzzy cold standby system are discussed, respectively. Furthermore, a repairable series system is considered, in which the lifetimes and repair times of components are assumed to have random fuzzy exponential distributions. Repairable sys-tem behavior is described by limit availability. Then a theorem on the limit availability of the repairable series system is proposed.Finally, random fuzzy shock model and random fuzzy fatal shock model are defined, respectively. Then bivariate random fuzzy exponential distri-bution is derived from the random fuzzy fatal shock model. In addition, some properties of the bivariate random fuzzy exponential distribution are proposed.