A Fuzzy Control Chart Approach for Attributes and Variables

Authors

  • N. Pekin Alakoc College of Business Administration, American University of The Middle East, Kuwait
  • A. Apaydin Department of Insurance and Actuary Sciences, Ankara University, Ankara, Turkey
Volume: 8 | Issue: 5 | Pages: 3360-3365 | October 2018 | https://doi.org/10.48084/etasr.2192

Abstract

The purpose of this study is to present a new approach for fuzzy control charts. The procedure is based on the fundamentals of Shewhart control charts and the fuzzy theory. The proposed approach is developed in such a way that the approach can be applied in a wide variety of processes. The main characteristics of the proposed approach are: The type of the fuzzy control charts are not restricted for variables or attributes, and the approach can be easily modified for different processes and types of fuzzy numbers with the evaluation or judgment of decision maker(s). With the aim of presenting the approach procedure in details, the approach is designed for fuzzy c quality control chart and an example of the chart is explained. Moreover, the performance of the fuzzy c chart is investigated and compared with the Shewhart c chart. The results of simulations show that the proposed approach has better performance and can detect the process shifts efficiently.

Keywords:

component, fuzzy set theory, statistical process control, fuzzy control charts, average run length

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References

D. C. Montgomery, Introduction to Statistical Quality Control, 7th edition, John Wiley & Sons Inc., NY, USA, 2013

L. A. Zadeh, “Fuzzy sets”, Information and Control, Vol. 8, No. 3, pp. 338-353, 1965 DOI: https://doi.org/10.1016/S0019-9958(65)90241-X

T. Raz, J. H. Wang, “Probabilistic and memberships approaches in the construction of control charts for linguistic data”, Production Planning & Control, Vol. 1, No. 3, pp. 147-157, 1990 DOI: https://doi.org/10.1080/09537289008919311

J. H. Wang, T. Raz, “On the construction of control charts using linguistic variables”, International Journal of Production Research, Vol. 28, No. 3, pp. 477-487, 1990 DOI: https://doi.org/10.1080/00207549008942731

A. Kanagawa, F. Tamaki, H. Ohta, “Control charts for process average and variability based on linguistic data”, International Journal of Production Research, Vol. 31, No. 4, pp. 913-922, 1993 DOI: https://doi.org/10.1080/00207549308956765

H. Taleb, M. Limam, “On fuzzy and probabilistic control charts”, International Journal of Production Research, Vol. 40, No. 12, pp. 2849-2863, 2002 DOI: https://doi.org/10.1080/00207540210137602

F. Franceschine, D. Romano, “Control chart for linguistic variables: a method based on the use of linguistic quantifiers”, International Journal of Production Research, Vol. 37, No. 16, pp. 3791-3800, 1999 DOI: https://doi.org/10.1080/002075499190059

M. Gulbay, C. Kahraman, D. Ruan, “-Cuts fuzzy control charts for linguistic data”, International Journal of Intelligent Systems, Vol. 19, No. 12, pp. 1173-1196, 2004 DOI: https://doi.org/10.1002/int.20044

K. Thaga, R. Sivasamy, “Control chart based on transition probability approach”, Journal of Statistical and Econometric Methods, Vol. 4, No. 2, pp. 61-82, 2015

J. H. Wang, C .H. Chen, “Economic statistical np-control chart designs based on fuzzy optimization”, International Journal of Quality & Reliability Management., Vol. 12, No. 1, pp. 88-92, 1995 DOI: https://doi.org/10.1108/02656719510076276

P. Grzegorzewski, O. Hryniewicz, “Soft methods in statistical quality control”, Control Cybernet, Vol. 29, No. 1, pp. 119-140, 2000

W. Woodall, K. L. Tsui, G. L. Tucker, “A review of statistical and fuzzy control charts based on categorical data”, in: Frontiers in Statistical Quality Control, Vol. 5, pp. 83-89, Springer-Verlag, Berlin Heidelberg, 1997 DOI: https://doi.org/10.1007/978-3-642-59239-3_7

Y. K. Chen, C. Yeh, “An enhancement of DSI control charts using a fuzzy genetic approach”, The International Journal of Advanced Manufacturing Technology, Vol. 24, No. 1-2, pp. 32-40, 2004

C. B. Cheng, “Fuzzy process control: construction of control charts with fuzzy numbers”, Fuzzy Sets and Systems, Vol. 154, No. 2, pp. 287-303, 2005 DOI: https://doi.org/10.1016/j.fss.2005.03.002

M. Gulbay, C. Kahraman, “An alternative approach to fuzzy control charts: direct fuzzy approach”, Information Sciences, Vol. 77, No. 6, pp. 1463-1480, 2007 DOI: https://doi.org/10.1016/j.ins.2006.08.013

O. Hryniewicz, “Statistics with fuzzy data in statistical quality control”, Soft Computing, Vol. 12, No. 3, pp. 229-234, 2007 DOI: https://doi.org/10.1007/s00500-007-0203-x

M. H. Zavvar Sabegh, Z. Sabegha, A. Mirzazadeha, S. Salehiana, G. W. Weber, “A literature review on the fuzzy control chart; classifications & analysis”, International Journal of Supply and Operations Management, Vol. 1, No. 2, pp. 167-189, 2014

D. J. Fonseca, M. E. Elam, L. Tibbs, “Fuzzy short-run control charts”, Mathware & Soft Computing, Vol. 14, pp. 81-101, 2007

K. L. Hsieh, L. I. Tong, M. C. Wang, “The application of control chart for defects and defect clustering in IC manufacturing based on fuzzy theory”, Expert Systems with Applications, Vol. 32, No. 3, pp. 765-776, 2007 DOI: https://doi.org/10.1016/j.eswa.2006.01.050

V. Amirzadeh, M. Mashinchi, A. Parchami, “Construction of p-charts using degree of nonconformity”, Information Sciences, Vol. 179, No. 1-2, pp. 1501-1560, 2009 DOI: https://doi.org/10.1016/j.ins.2008.09.010

M. H. Shu, H. C. Wu, “Monitoring imprecise fraction of nonconforming items using p control charts”, Journal of Applied Statistics, Vol. 37, No. 8, pp. 1283-1297, 2010 DOI: https://doi.org/10.1080/02664760903030205

D. Wang, P. Li, M. Yasuda, “Construction of fuzzy control charts based on weighted possibilistic mean”, Communications in Statistics - Theory and Methods, Vol. 43, No. 15, pp. 3186-3207, 2014 DOI: https://doi.org/10.1080/03610926.2012.695852

M. H. Fazel Zarandi, I. B. Turksen, H. Kashan, “Fuzzy control charts for variable and attribute quality characteristic”, Iranian Journal of Fuzzy Systems, Vol. 3, No. 1, pp. 31-44, 2006

A. Faraz, M. B. Moghadam, “Fuzzy control chart a better alternative for Shewhart average chart”, Quality & Quantity, Vol. 41, No. 3, pp. 375-385, 2007 DOI: https://doi.org/10.1007/s11135-006-9007-9

A. Faraz, R.B. Kazemzadeh, M. B. Moghadam, A. Bazdar, “Constructing a fuzzy Shewhart control chart for variables when uncertainty and randomness are combined”, Quality & Quantity, Vol. 44, No. 5, pp. 905-914, 2009 DOI: https://doi.org/10.1007/s11135-009-9244-9

A. Faraz, A. F. Shapiro, “An application of fuzzy random variables to control charts”, Fuzzy Sets and Systems, Vol. 161, pp. 2684-2694, 2010 DOI: https://doi.org/10.1016/j.fss.2010.05.004

M. H. Shu, H. C. Wu, “Fuzzy and R control charts: Fuzzy dominance approach”, Computers & Industrial Engineering, Vol. 61, No. 3, pp. 676-686, 2011 DOI: https://doi.org/10.1016/j.cie.2011.05.001

S. B. Akhundjanov, F. Pascual, “Moving range EWMA control charts for monitoring the Weibull shape parameter”, Journal of Statistical Computation and Simulation, Vol. 85, No. 9, pp. 1864-1882, 2015 DOI: https://doi.org/10.1080/00949655.2014.907574

J. D. T. Tannock, “A fuzzy control charting method for individuals”, International Journal of Production Research, Vol. 41. No. 5, pp. 1017-1032, 2003 DOI: https://doi.org/10.1080/0020754021000049808

M. Gulbay, C. Kahraman, “Development of fuzzy process control charts and fuzzy unnatural pattern analyses”, Computational Statistics & Data Analysis, Vol. 51, No. 1, pp. 434-451, 2006 DOI: https://doi.org/10.1016/j.csda.2006.04.031

N. Pekin Alakoc, A. Apaydin, “Sensitizing rules for fuzzy control charts”, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, Vol. 7, No. 5, pp.931-935, 2013

M. N. Pastuizaca Fernandez, A. Carrion Garcia, O. Ruiz Barzola, “Multivariate multinomial T2 control chart using fuzzy approach”, International Journal of Production Research, Vol. 53, No. 7, pp. 2225–2238, 2015 DOI: https://doi.org/10.1080/00207543.2014.983617

D. Wang, O. Hryniewicz, “A fuzzy nonparametric Shewhart chart based on the bootstrap approach”, International Journal of Applied Mathematics and Computer Science, Vol. 25, No. 2, pp. 389-401, 2015 DOI: https://doi.org/10.1515/amcs-2015-0030

B. Sadeghpour Gildeh, N. Shafiee, “X-MR control chart for autocorrelated fuzzy data using Dp,q-distance”, The International Journal of Advanced Manufacturing Technology, Vol. 81, No. 5-8, pp. 1047-1054, 2015 DOI: https://doi.org/10.1007/s00170-015-7199-7

L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning - 1”, Information Sciences, Vol. 8, No. 3, pp. 199-249, 1975 DOI: https://doi.org/10.1016/0020-0255(75)90036-5

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How to Cite

[1]
Pekin Alakoc, N. and Apaydin, A. 2018. A Fuzzy Control Chart Approach for Attributes and Variables. Engineering, Technology & Applied Science Research. 8, 5 (Oct. 2018), 3360–3365. DOI:https://doi.org/10.48084/etasr.2192.

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