不确定环境下的系统可靠性理论
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摘要
本文首先研究了模糊不可修系统的可靠性,将系统的寿命看作模糊变量.分别用系统可靠度和平均寿命作为衡量模糊不可修系统可靠性的主要数量指标,其中系统可靠度定义为系统在t时刻正常工作的可信性,平均寿命定义为模糊不可修系统寿命的期望值.基于这两种数量指标,建立了模糊不可修系统的基本模型,包括模糊串联系统、模糊并联系统、模糊串—并联系统、模糊并—串联系统以及模糊冷贮备系统,并分别对每种情况下的模糊不可修系统进行分析,给出了可靠度和平均寿命的具体表达式.
考虑到实际应用中系统的寿命可能具有随机和模糊双重不确定性,本文进一步考虑不可修系统的寿命为随机模糊变量的情形.仍用可靠度和平均寿命作为衡量随机模糊不可修系统可靠性的主要数量指标,将系统可靠度定义为可修系统在t时刻正常工作的平均机会,平均寿命定义为随机模糊不可修系统寿命的期望值.相应地,也建立了随机模糊不可修系统的基本模型,包括随机模糊串联系统、随机模糊并联系统、随机模糊串—并联系统、随机模糊并—串联系统以及随机模糊冷贮备系统,且分别对各个随机模糊不可修系统基本模型进行分析,给出了可靠度和平均寿命的具体表达式.此外,本文也对随机模糊可修串联系统进行了分析,将系统稳态可用度作为衡量随机模糊可修系统可靠性的主要数量指标,定义为系统长期运行下,系统正常工作的平均机会.在串联系统各部件和相应的维修时间服从随机模糊指数分布的情况下,给出了该串联系统的稳态可用度.
最后,本文定义了随机模糊冲击模型以及随机模糊致命冲击模型,并由随机模糊致命冲击模型导出了随机模糊二维指数分布,给出了该随机模糊二维指数分布的基本定理.
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.
考虑到实际应用中系统的寿命可能具有随机和模糊双重不确定性,本文进一步考虑不可修系统的寿命为随机模糊变量的情形.仍用可靠度和平均寿命作为衡量随机模糊不可修系统可靠性的主要数量指标,将系统可靠度定义为可修系统在t时刻正常工作的平均机会,平均寿命定义为随机模糊不可修系统寿命的期望值.相应地,也建立了随机模糊不可修系统的基本模型,包括随机模糊串联系统、随机模糊并联系统、随机模糊串—并联系统、随机模糊并—串联系统以及随机模糊冷贮备系统,且分别对各个随机模糊不可修系统基本模型进行分析,给出了可靠度和平均寿命的具体表达式.此外,本文也对随机模糊可修串联系统进行了分析,将系统稳态可用度作为衡量随机模糊可修系统可靠性的主要数量指标,定义为系统长期运行下,系统正常工作的平均机会.在串联系统各部件和相应的维修时间服从随机模糊指数分布的情况下,给出了该串联系统的稳态可用度.
最后,本文定义了随机模糊冲击模型以及随机模糊致命冲击模型,并由随机模糊致命冲击模型导出了随机模糊二维指数分布,给出了该随机模糊二维指数分布的基本定理.
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.
引文
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[11]Cai K., Wen C., Zhang M., A critical review on software reliability modeling, Reliability Engineering and System Safety,1991,32(3):357-371.
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