Fuzzy Multivariate Process Capability Index for Measuring Process Capability

Abstract

Abstract. In the case of process capability index several methods are identified. In this paper ,a new process capability index using fuzzy number and fuzzy probability concept, in order to remove the weakness of other famous method is suggested. After introduction of fuzzy index in univariate case, fuzzy multivariate process capability index is investigated. Finally, this new method is compared to three well-known methods in literature review, with numerical example.

Keywords


References

[1]Boyles, R. A. (1991). “The Taguchi Capability Index”, Journal of Quality Technology 23, pp.17–26.

[2]Carr, W. E. (1991). “A New Process Capability Index: Parts per Million”. Quality Progress 24, p. 152.

[3]Cengiz Kahraman, ─░hsan Kaya, (2010) ‘Fuzzy Process Capability Analysis and Applications’, Springer Berlin Heidelberg, pp 483-513, DOI: 10.1007/978-3-642-12052-7—20

[4]Cha n, L.K., Chen , S.W. and Spring .F.A.(1988): "Anew measure of process capability :Cpm, Journal of Quality Technology, 20:132-175.

[5]Chan, L. K.; Cheng, S. W.; and Spiring, F. A. (1991), “A Multivariate Measure of Process Capability”. International Journal of Modeling and Simulation 11, pp. 1–6.

[6]Chen, H. (1994). “A Multivariate Process Capability Index over a Rectangular Solid Tolerance Zone”. Statistica Sinica4, pp. 749–758.the 4th Industrial Engineering Research Conference, Institute of Industrial Engineers, pp. 304–309.

[7]Hubele, N. F.; Shahriari, H.; and Cheng, C. S. (1991), “A Bivariate Process Capability Vector, in Statistics and design in Process Control” in Statistical Process Control in Manufacturing  edited by J. B. Keats, and D. C. Montgomery. Marcel Dekker, NewY ork, NY. pp. 299–310.

[8]Ihsan Kaya, Cengiz Kahraman, (2009)’ Fuzzy robust process capability indices for risk assessment of air pollution’, Journal Stochastic Environmental Research and Risk Assessment , Volume 23, Issue 4, pp 529-541, DOI: 10.1007/s00477-008-0238-2

[9]Johnson, R. A. and Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. Prentice Hall, Englewood Cli.s, NJ.

[10]        Kane, V. E. (1986). “Process Capability Indices”. Journal of Quality Technology 18, pp. 41–52.

[11]        KLIR, G.J. and BO, Y. (1995) .Fuzzy set and Fuzzy Logic, Theory and application. Prentice-hall Inc, New Jersey

[12]         KOTZ S., JOHNSON N. L., (2002), Process Capability Indices—A Review, 1992–2000 , Journal of Quality Technology  Vol. 34, No. 1.

[13]        Ming-Hung Shu, Hsien-Chung Wu, (2012), ‘Manufacturing process performance evaluation for fuzzy data based on loss-based capability index’, Journal of Soft Computing, Volume 16, Issue 1, pp 89-99, DOI: 10.1007/s00500-011-0736-x

[14]        .Montgomery, D. C. (1996). Introduction to Statistical Quality Control, 3rd ed. John Wiley & Sons, New York, NY.

[15]        Pearn, W.; Kotz, L. S.; and Johnson, N. L. (1992). “Distributional and Inferential Properties of Process Capability Indices”. Journal of Quality Technology 24, pp. 216–231.

[16]        SULLIVAN , L. P. (1985) Letters, Quality Progress, 18:7-8.

[17]        Sadegh pour Gildeh, B. and Moradi, V (2012): Fuzzy Tolerance Region and Process Capability Analysis, Advances in Intelligent and Soft Computing 147, 2012, pp: 183-193

[18]        Tam, W.; Subbaiah, P.; and Lady, J. W. (1993). “A Note on Multivariate Capability Indices”. Journal of Applied Statistics 20, pp. 339–351.

[19]        Wang F.K.; Lawrence; Misruling, John; Shahriari. (2000). "Comparison of three multivariate process capability indices".  Journal of quality technology. Vol 32, No 3.  263-275.

[20]        YONGTING, C. (1996): Fuzzy quality and analysis on fuzzy probability. fuzzy set and system, 83:283-290.

[21]        Zadeh, L.A. (1967): Fuzzy Set. Inform. Control 8:338-3.

Zeinab Ramezani, Panchami & Masha Allah Mashinchi, (2011), ‘Fuzzy confidence regions for the Taguchi capability index’, International Journal of system scince, Vol. 42, No. 06, June 2011, 977-987