| Fuzzy reliability of the standby system is very important in the research of reliability. This paper which adopts fuzzy mathematical principles and methods has researched some system reliability of repairable and unrepairable standby models, and gives some system reliability indexes.Firstly, on the base of the cold standby repairable system which the system fails we give the relations between membership function and conventional reliability index using Fuzzy Probability Theory and fuzzy reliability mathematics theory, so we can obtain the formula of some fuzzy reliability indexes. Then give the Fuzzy reliability index of the cold standby system with two different components when the switch is completely reliable and the switch is unreliable (Switch life 0-1and Exponential distribution).Secondly, this paper discusses the fuzzy reliability when two failures repair is homology. of the warm standby repairable system, make a study of a warm standby repairable system which was consisted of two same components and a repairman by using the Markov process theory, the method of Laplace transformation theory and the method of Laplace-Stieltjes transformation theory, A repairable model of this system is set up where both the lifetime and repaired time of the components and the switch obey the exponential distribution, some reliability indexes of this system are obtained. Then we make fuzzy reliability analysis, especially the fuzzy reliability is obtained when two failures repair is homology.Finally, this paper gives the membership function of the fuzzy wok state and fuzzy failure state by using fuzzy mathematic theory and method, then discusses the fuzzy reliability of the k/n(G) repairable system. Compare the result to traditional reliability index, we find the fuzzy reliability index is closed to reality, the difference indicates that the fuzzy reliability presses close to the practicality, it can be said that the fuzzy reliability fully describes the action of the system reliability.
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