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It is impossible to calculate fuzzy reliability by using much more mature conventional reliability theory so far. Therefore, after fuzzy strength that took commonly used membership functions was transformed to an equivalent random strength and its equivalent probability density function and probability distribution function were obtained. A method to compute fuzzy reliability in the case of random stress and fuzzy strength via advanced first order second moment method and equivalent normal distribution method of convectional reliability theory has been put forwards so that the reliability index to measure fuzzy reliability could be obtained. The method is of theoretical significance and practical value. An example was given to show its reasonableness and feasibility.