Existing software and hardware integrated systems reliability evaluation methods ignore the problem of different failure mechanisms of hardware and software; thus, there are some limitations. In view of the above problems, this paper firstly studies time/state-based failure. Moreover, for the problem of reliability measurement in the presence of epistemic uncertainty, a calculation method of epistemic uncertainty factor of software and hardware integrated systems based on failure mode and effect analysis application effect and software and hardware comprehensive reliability test application effect is proposed. Furthermore, a belief reliability evaluation method with comprehensive consideration of design margin, aleatory uncertainty and epistemic uncertainty is presented. Finally, the proposed method is demonstrated and verified through application case. The results show that the existence of epistemic uncertainty will reduce people's trust in "system reliability".