Fuzzy-based functional process capability indices for simple linear profile

Process capability indices (PCIs) are numerical quantities that measure how the process products meet the required specifications considered for them‎. ‎In some processes‎, ‎the quality of a process or product can be characterized by a functional relationship between a response quality characteristic and one or more explanatory variables‎. ‎This relationship is usually known as a profile‎. When this relationship is as a linear function based on only independent, is named simple linear profile. One type capability indices for this process is functional capability indices. Then, the specification limits, natural tolerance intervals, mean and target are as simple linear function of the independent variable. In the present paper, two new functional process capability indices are introduced that for calculating them, fuzzy numbers are engaged to weigh the levels of the independent variable by membership degree.The performance of the proposed indices in comparison with the two available indices are investigated in simulation scheme, in terms of bias and mean square error (MSE). Results show that the new indices perform better that their competitors. Some graphics are presented to show this matter, obviously. Furthermore, a real example are presented to show how the new indices applied to measure the capability of process.