失效模式與效應分析(failure mode and effects analysis, FMEA)是一種預防性的風險管理技術，主要應用於分析與辨認產品設計系統的潛在失效模式，並根據風險優先指數(risk priority number, RPN)決定失效模式的改善順序，藉由適當的改善措施來降低失效率與提高可靠度。由於傳統RPN 是以嚴重性、發生率、以及難檢度等三個風險因子的乘積來衡量，雖然具有計算簡單與容易比較的優點，但也使FMEA 引發眾多爭議。為了改進RPN 的缺失而使失效模式的評比結果具有代表性，本研究基於資料包絡分析法(data envelopment analysis, DEA)適用於決定多準則決策分析問題(multiple criteria decision making, MCDM)評估屬性權重之特性，將失效模式的嚴重性、發生率、以及難檢度等風險因子視為評估屬性，在DEA 的概念下，考量失效模式風險評估屬性之理想值(ideal) 與反理想值(anti-ideal)，建立以距離函數為基礎的妥協規劃共同權重模式來決定嚴重性、發生率、以及難檢度等風險因子的共同權重。採用共同權重來計算失效模式的RPN，不僅使得全部失效模式能在相同的基準下確認改善的先後順序，並且讓全部失效模式不論以理想值或反理想值為評估基準均有一致的排序結果。

Failure mode and effects analysis (FMEA) is a preventive technology of risk management that is applied to analyze and to identify the potential failure modes in a system. The risk priorities of the failure modes are determined through the risk priority number (RPN), and appropriate improvement actions can be taken for decreasing the error. In other words, the failure modes are ranked by their RPN. Failure modes having higher RPN are assumed to be more important and assigned a higher priority than those with lower RPN. Traditionally, the RPN is the multiplication of three risk factors that are the severity, the occurrence, and the detection of a failure mode. It has the advantage of easy calculation and comparison, but the RPN has been criticized to have some drawbacks. In order to improve the disadvantages, this study considers the three risk factors as the attributes of a multiple criteria decision making (MCDM) problem and the RPN is the criterion for comparing different failure modes. The characteristic of data envelopment analysis (DEA) is applied to determine the weights of the attributes. Based on the concepts of DEA and the distance of the failure modes to the ideal and the anti-ideal, a compromise programming model is proposed to determine the common weights of the three risk factors. The RPNs of all failure modes are calculated from the common weights. All failure modes could not only be compared on the same basis, but also have consistent rakings when they are ranked based on the distance to the ideal and the anti-ideal.