Document Type : Research Paper

**Authors**

Department of Industrial Engineering, Yazd University, Yazd, Iran

**Abstract**

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 in 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.

**Keywords**

[1] Yongting, C., (1996), Fuzzy quality and analysis on fuzzy probability*.* *Fuzzy sets systems*. 83(2): p. 283-290.

[2] Lee, Y.-H., Wei, C.-C. and Chang, C.-L., (1999), Fuzzy design of process tolerances to maximise process capability*.* *The International Journal of Advanced Manufacturing Technology*. 15(9): p. 655-659.

[3] Lee, H.T., (2001), Cpk index estimation using fuzzy numbers*.* *European Journal of Operational Research*. 129(3): p. 683-688.

[4] Sadeghpour Gildeh, B. (Year) Comparison of Cp, Cpk and Cp- tilde process capability indices in the case of measurement error occurrence. in *10th IFSA World Congress*. *of Conference*.

[5] Parchami, A., Mashinchi, M. and Maleki, H.R., (2006), Fuzzy confidence interval for fuzzy process capability index*.* *Journal of Intelligent Fuzzy Systems*. 17(3): p. 287-295.

[6] Parchami, A., Mashinchi, M., Yavari, A.R., and Maleki, H.R., (2005), Process capability indices as fuzzy numbers*.* *Austrian Journal of Statistics*. 34(4): p. 391–402-391–402.

[7] Parchami, A. and Mashinchi, M., (2007), Fuzzy estimation for process capability indices*.* *Information Sciences*. 177(6): p. 1452-1462.

[8] Parchami, A. and Mashinchi, M., (2010), A new generation of process capability indices*. Journal of Applied Statistics*. 37(1): p. 77-89.

[9] Hsu, B.-M. and Shu, M.-H., (2008), Fuzzy inference to assess manufacturing process capability with imprecise data*.* *European Journal of Operational Research*. 186(2): p. 652-670.

[10] Kahraman, C. and Kaya, I., (2009), Fuzzy process accuracy index to evaluate risk assessment of drought effects in Turkey*.* *Human Ecological Risk Assessment*. 15(4): p. 789-810.

[11] Kahraman, C. and Kaya, I., (2009), Fuzzy process capability indices for quality control of irrigation water*.* *Stochastic Environmental Research Risk Assessment*. 23(4): p. 451-462.

[12] Kaya, I. and Kahraman, C., (2011), Process capability analyses with fuzzy parameters*.* *Expert systems with applications*. 38(9): p. 11918-11927.

[13] Kaya, İ. and Kahraman, C., (2010), A new perspective on fuzzy process capability indices: Robustness*.* *Expert systems with applications*. 37(6): p. 4593-4600.

[14] Kaya, İ. and Kahraman, C., (2010), Fuzzy process capability analyses with fuzzy normal distribution*. Expert Systems with Applications*. 37(7): p. 5390-5403.

[15] Kaya, İ. and Kahraman, C., (2011), Process capability analyses based on fuzzy measurements and fuzzy control charts*.* *Expert systems with applications*. 38(4): p. 3172-3184.

[16] Kaya, İ. and Kahraman, C., (2011), Fuzzy process capability indices with asymmetric tolerances*.* *Expert systems with applications*. 38(12): p. 14882-14890.

[17] Kaya, I. and Kahraman, C., (2009), Air pollution control using fuzzy process capability indices in the six-sigma approach*.* *Human Ecological Risk Assessment*. 15(4): p. 689-713.

[18] Kaya, İ. and Kahraman, C., (2010), Development of fuzzy process accuracy index for decision making problems*.* *Information Sciences*. 180(6): p. 861-872.

[19] Kaya, I. and Kahraman, C., (2008), Fuzzy process capability analyses: An application to teaching processes*.* *Journal of Intelligent Fuzzy Systems*. 19(4, 5): p. 259-272.

[20] Kaya, I. and Kahraman, C., (2009), Fuzzy robust process capability indices for risk assessment of air pollution*.* *Stochastic Environmental Research Risk Assessment*. 23(4): p. 529-541.

[21] Ramezani, Z., Parchami, A. and Mashinchi, M., (2011), Fuzzy confidence regions for the Taguchi capability index*.* *International Journal of Systems Science*. 42(6): p. 977-987.

[22] Gildeh, B.S. and Moradi, V., *Fuzzy tolerance region and process capability analysis*, in *Fuzzy engineering and operations research*. 2012, Springer. p. 183-193.

[23] Sadeghpour Gildeh, B. and Angoshtari, T., (2013), Monitoring Fuzzy Capability Index by Using the EWMA Control Chart with Imprecise Data*.* *Iranian Journal of fuzzy* *systems*. 10(2): p. 111-132.

[24] Abbasi Ganji, Z. and Sadeghpour Gildeh, B., (2016), On the multivariate process capability vector in fuzzy environment*.* *Iranian Journal of fuzzy systems*. 13(5): p. 147-159.

[25] Abbasi Ganji, Z. and Sadeghpour Gildeh, B., (2016), Fuzzy multivariate process capability vector*.* *Journal of Intelligent Fuzzy Systems*. 30(2): p. 1007-1017.

[26] Ganji, Z.A. and Gildeh, B.S., (2017), A new fuzzy process capability index for asymmetric tolerance interval*.* *International Journal of Fuzzy* *System Applications*. 6(3): p. 74-104.

[27] Hesamian, G. and Akbari, M.G., (2019), A process capability index for normal random variable with intuitionistic fuzzy information*.* *Operational Research*.

[28] Ganji, Z.A., (2019), Multivariate process incapability vector*.* *Quality Reliability Engineering International*. 35(4): p. 902-919.

[29] Sadeghpour Gildeh, B. and Abbasi Ganji, Z., (2020), The effect of measurement error on the process incapability index*.* *Communications in Statistics-Theory Methods*. 49(3): p. 552-566.

[30] Kahraman, C. and Kaya, I. (Year) Fuzzy estimations of process incapability index. in *Proceedings of the World Congress on Engineering*. *of Conference*.

[31] Kaya, I. and Baracli, H., (2012), Fuzzy Process Incapability Index with Asymmetric Tolerances*. Journal of Multiple-Valued Logic Soft Computing*. 18.

[32] Kaya, İ., (2014), The process incapability index under fuzziness with an application for decision making*.* *international Journal of computational intelligence systems*. 7(1): p. 114-128.

[33] Abbasi Ganji, Z. and Sadeghpour Gildeh, B., (2016), Assessing process performance with incapability index based on fuzzy critical value*.* *Iranian Journal of fuzzy systems*. 13(5): p. 21-34.

[34] Dubois, D.J., (1980) Fuzzy sets and systems: theory and applications. Vol. 144. *Academic press*.

[35] Klir, G.J. and Yuan, B., (1994) Fuzzy sets and fuzzy logic: theory and applications. *Prentice-Hall, Inc*.

[36] Dehghan, M., Ghatee, M. and Hashemi, B., (2008), Some computations on fuzzy matrices: An application in fuzzy analytical hierarchy process*.* *International Journal of Uncertainty, Fuzziness Knowledge-Based Systems*. 16(05): p. 715-733.

[37] Fortemps, P. and Roubens, M., (1996), Ranking and defuzzification methods based on area compensation*.* *Fuzzy sets systems*. 82(3): p. 319-330.

[38] Searle, S.R. and Khuri, A.I., (2017) Matrix algebra useful for statistics. *John Wiley & Sons*.

[39] Shishebori, D., & Hamadani, A. Z. (2009). The effect of gauge measurement capability on MCp and its statistical properties. *International Journal of Quality & Reliability Management*.

[40] Shishebori, D. and Hamadani, A.Z., (2010a), Properties of multivariate process capability in the presence of gauge measurement errors and dependency measure of process variables*.* *Journal of manufacturing systems*. 29(1): p. 10-18.

[41] Shishebori, D., & Zeinal Hamadani, A. (2010b). The effect of gauge measurement capability and dependency measure of process variables on the MCp. *Journal of Industrial and Systems Engineering*, *4*(1), 59-76.

[42] Shishebori, D., Akhgari, M. J., Noorossana, R., & Khaleghi, G. H. (2015). An efficient integrated approach to reduce scraps of industrial manufacturing processes: a case study from gauge measurement tool production firm. *The International Journal of Advanced Manufacturing Technology*, *76*(5-8), 831-855.

[43] Jackson, J.E., (1956), Quality control methods for two related variables*.* *Industrial Quality Control*. 12(7): p. 4-8.

[44] Sultan, T., (1986), An acceptance chart for raw materials of two correlated properties*.* *Quality Assurance*. 12(3): p. 70-72.

April 2020

Pages 205-220

- XML
- PDF 798.44 K
- Supplementary File
- 1765-Rezaee-final.pdf