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Mathematical Problems in Engineering
Volume 2015, Article ID 217406, 8 pages
Research Article

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

Department of Industrial Engineering, Faculty of Engineering, Islamic Azad University, Semnan Branch, Semnan 3519744571, Iran

Received 19 June 2014; Revised 28 October 2014; Accepted 31 October 2014

Academic Editor: Mohamed Abd El Aziz

Copyright © 2015 Mohammad Abdolshah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Loss-based process capability indices are appropriate and realistic tools in order to measure the process capability. Among them, index and its generation 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 and there are some uncertainties in observations, so fuzzy logic can be employed to manage the uncertainties. This paper investigates fuzzification of process capability index and its generation . In order to find the membership function of process capability indices and , the α-cuts of fuzzy observation were employed. Then with an example of fuzzy process capability index, and were calculated and compared. Results showed that fuzzy was more sensitive compared with and was increased while the target departs (asymmetric tolerance). This example also showed that, with departure from the target, variation of fuzzy and consequently its fuzziness were increased.