Abstarct: Statistical quality control is one of the most important and applicable topics of statistics science, part of which relates to capability and incapability indices. Process capability and incapability indices are useful tools for measuring product quality and process status using process capability analysis. The advantage of using incapability indices is to divide the information into two indices of imprecision and inaccuracy. On the other hand, the incapability index is in some cases not able to accurately express the incapability (or capability) of the process. Therefore, a generalization of the incapability index has been introduced which can eliminate this problem. Now, if the data is not crisp, fuzzy logic can be used. In this case, conventional incapability indices cannot be used, so for fuzzy indices, fuzzy estimation of imprecision and inaccuracy indices must first be calculated. In this thesis, we have two considerations for this. The first case, when the specification limit and target value are not fuzzy, and the second case, when the specification limit and value target are fuzzy. Finally, by presenting a real example, we examine the application of these two indices of fuzzy incapability in the industry and compare them.