Summary: In view of the process of failures being a fuzzy random phenomenon including randomness and fuzziness concurrently, the life of electronic products would be a fuzzy random variable. Applying the theory of fuzzy random probability, the conventional random probability analysis method is improved, a new fuzzy random probability the life distribution function is established, and a criterion of choosing the membership function of the fuzzy variable is introduced according to the life characteristics. Then, the possibility distribution of the failure is studied as to confirm the possibility that the product will fail at a certain time. By analyzing the example, it is found that the new fuzzy random probability life distribution function can provide more life information intuitionisticly and concretely than the conventional one, and the established possibility distribution can reflect the level of the possibility that the product will fail actually.