Measuring Loss-Based Process Capability Index Le and Its Generation Le" with Fuzzy Numbers

Loss-based process capability indices are appropriate and realistic tools in order to measure the process capability. Among them, index L-e and its generation L-e '' are well-known loss-based process capability indices, whose concepts are based on the worth (the opposite concept of loss). Sometimes, in order to calculate L-e and L-e '' there are some uncertainties in observations, so fuzzy logic can be employed to manage the uncertainties. This paper investigates fuzzification of process capability index (L) over tilde (e) and its generation (L) over tilde (e)'' In order to find the membership function of process capability indices (L) over tilde (e) and (L) over tilde (e)'', the alpha-cuts of fuzzy observation were employed. Then with an example of fuzzy process capability index, (L) over tilde (e) and (L) over tilde (e) were calculated and compared. Results showed that fuzzy (L) over tilde (e)'' wasmore sensitive compared with (L) over tilde (e) and was increased while the target departs (asymmetric tolerance). This example also showed that, with departure from the target, variation of fuzzy (L) over tilde (e '') and consequently its fuzziness were increased.