In order to enhance quality and reliability of mechanical and electrical products, the methods of taking corresponding corrective measures to eliminate or alleviate product failure in advance have been widely concerned. Failure mode and effects analysis (FMEA) is a typical prevention reliability analysis method. However, there are some drawbacks in traditional FMEA method. To overcome these drawbacks, we propose a hybrid risk evaluation method, which combines picture fuzzy sets (PFSs), the PF-linear programming model (PF-LPM) method and the PF-weighted aggregated sum product assessment (PF-WASPAS) method. We adopt PFSs to evaluate risks of products. In order to overcome drawback of the traditional distance between PFSs, some new distance measures between PFSs based on the Dice similarity and the Jaccard similarity are proposed by us. The PF-LPM method which considers the subjective weights of risk factors and calculates synthetical deviation with the Dice similarity-based distance is utilized to calculate the weights of risk factors. Moreover, the PFWA operator and the PFWG operator are used by us to fuse experts’ evaluation information. Then, the PF-WASPAS method is utilized to rank failure modes. Finally, an illustrative example with respect to pallet exchange rack is introduced, and the rationality, effectiveness and applicability of the proposed method are verified by a discussion and comparison.