multivariate process incapability index considering measurement error in fuzzy environment

Process capability indices (pci) show that the process conforms to the specification limits; when the product quality depends on more than one characteristic, multivariate process capability indices (mcpi) are used. by modifying the process capability indices, the process incapability indices are created; these indices then provide information about the accuracy and precision of the process separately. in the real world, in most cases, the parameters cannot be specified precisely; therefore, the use of fuzzy sets can solve this problem in statistical quality control. the purpose of this paper is to present, for the first time, a multivariate process incapability index by considering the measurement error in a fuzzy environment. the presented index is shown for practical examples solved by considering triangular fuzzy numbers; then the capability of the model is compared to the time when fuzzy logic is not used. the obtained results emphasize that ignoring the measurement error also leads to the incorrect calculation of process capability, causing a lot of damage to manufacturing industries, especially high-tech ones.