Measuring process capability index C pm with fuzzy data

Abstract

The process capability index Cpm, which considers the process variance and departure of the process mean from the target value, is important in the manufacturing industry to measure process potential and performance. This paper extends its applications to calculate the process capability index \({\tilde {C}_{pm} }\) of fuzzy numbers. In this paper, the α-cuts of fuzzy observations are first derived based on various values of α. The membership function of fuzzy process capability index \({\tilde {C}_{pm} }\) is then constructed based on the α-cuts of fuzzy observations. An example is presented to demonstrate how the fuzzy process capability index \({\tilde {C}_{pm} }\) is interpreted. When the quality characteristic cannot be precisely determined, the proposed method provides the most possible value and spread of fuzzy process capability index \({\tilde {C}_{pm} }\). With crisp data, the proposed method reduces to the classical method of process capability index Cpm.