|Abstract To overcome the deficiency that the safety membership function of a structure or a system in safety engineering sometimes involves subjectivity in the application of profust reliability theory, a preliminary study was made for finding out the rootstock of the performance fuzziness of a random system. The performance fuzziness for a general random structure system was quantified by translating random vectors into standard interval vectors, that is, the density functions of random vectors was intercepted by an equivalent horizontal cut set. A non-probabilistic reliability index was proposed to measure the fuzziness of the structural performance, and the index was defined in a convex domain a subspace of the standard interval vector space and in its extended space. Not only does the index offer to what extent the structure is safe but also depicts to what extent the structure has been failure. Consequently the index is proposed to characterize the fuzziness for the structural performance.