Advertisement

Soft Computing

, Volume 22, Issue 15, pp 5033–5041 | Cite as

Modeling attribute control charts by interval type-2 fuzzy sets

Focus
  • 32 Downloads

Abstract

Fuzzy attribute control charts, where data are classified into conforming/nonconforming product units, are used to monitor fuzzy fractions of nonconforming units for variable sample sizes and the fuzzy number of nonconforming units for constant sample sizes. Data defined as quality characteristics can be imprecise due to the subjective decisions of the quality control operator. Type-2 fuzzy set theory deals with ambiguity associated with the uncertainty of membership functions by incorporating footprints and modeling high-level uncertainty. In this paper, the structure of an interval type-2 fuzzy p-control chart and interval type-2 fuzzy np-control chart with constant sample size are developed and applied to real data. The main advantage in using interval type-2 fuzzy sets in control charts is the flexibility allowed in determining control limits for process monitoring by incorporating fuzzy set theory. Therefore, fuzzy control charts with interval type-2 fuzzy numbers afford the decision maker the opportunity to see and detect process defects.

Keywords

Fuzzy set theory Interval type-2 fuzzy sets Fraction nonconforming Number of nonconforming units Fuzzy control charts 

Notes

Compliance with ethical standards

Conflict of interest

Author N. Erginel is a member of the Turkish Operations Research Society. Authors S. Şentürk and G. Yıldız declare that they have no conflict of interest.

Human Participants

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Chen L-H, Huang C-H (2016) Design of a fuzzy zone control chart for improving the process variation monitoring capability. J Appl Sci 16:201–208CrossRefGoogle Scholar
  2. Cheng CB (2005) Fuzzy process control: construction of control charts with fuzzy numbers. Fuzzy Sets Syst 154:287–303MathSciNetCrossRefGoogle Scholar
  3. Erginel N (2008) Fuzzy individual and moving range control charts with \(\alpha \)-cuts. J Intell Fuzzy Syst 19:373–383MATHGoogle Scholar
  4. Erginel N, Şentürk S, Kahraman C, Kaya İ (2011) Evaluating the packing process in food industry using fuzzy \(\bar{X}\) and S control charts. Int J Comput Intell Syst 4(4):509–520Google Scholar
  5. Erginel N (2014) Fuzzy rule based p–np control charts. J Intell Fuzzy Syst 27:159–171MathSciNetMATHGoogle Scholar
  6. Gülbay M, Kahraman C (2006a) Development of fuzzy process control charts and fuzzy unnatural pattern analyses. Comput Stat Data Anal 51:434–451MathSciNetCrossRefMATHGoogle Scholar
  7. Gülbay M, Kahraman C (2006b) An alternative approach to fuzzy control charts: direct fuzzy approach. Inf Sci 77(6):1463–1480CrossRefMATHGoogle Scholar
  8. Gülbay M, Kahraman C, Ruan D (2004) \(\alpha \)-cut Fuzzy control charts for linguistic data International. J Intell Syst 19:1173–1196CrossRefMATHGoogle Scholar
  9. Hou S, Wang H, Feng S (2016) Attribute control chart construction based on fuzzy score number. Symmetry 8:3–13MathSciNetCrossRefGoogle Scholar
  10. Kahraman C, Oztayşi B, Sarı IU, Turanoglu E (2014) Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowl Based Syst 59:48–57CrossRefGoogle Scholar
  11. Kanagawa A, Tamaki F, Ohta H (1993) Control charts for process average and variability based on linguistic data. Intell J Prod Res 31(4):913–922CrossRefMATHGoogle Scholar
  12. Karnik NN, Mendel JM (2001) Operations on type-2 fuzzy sets. Fuzzy Sets Syst 122:327–348MathSciNetCrossRefMATHGoogle Scholar
  13. Kaya İ, Kahraman C (2011) Process capability analyses based on fuzzy measurement and fuzzy control charts. Expert Syst Appl 38:3172–3184CrossRefGoogle Scholar
  14. Kaya İ, Erdoğan M, Yıldız C (2017) Analysis and control of variability by using fuzzy individual control charts. Appl Soft Comput 51:370–381CrossRefGoogle Scholar
  15. Khademi M, Amirzadeh V (2014) Fuzzy rules for fuzzy \(\bar{X}\) and R control charts. Iran J Fuzzy Syst 11(5):55–56MathSciNetGoogle Scholar
  16. Mendel JM, John RI (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127CrossRefGoogle Scholar
  17. Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821CrossRefGoogle Scholar
  18. Mizumoto M, Tanaka K (1976) Some properties of fuzzy sets of type-2. Inf Control 31:312–340MathSciNetCrossRefMATHGoogle Scholar
  19. Montgomery DC (1991) Introduction to statistical quality control. Wiley, New YorkMATHGoogle Scholar
  20. Raz T, Wang JH (1990) Probabilistic and memberships approaches in the construction of control chart for linguistic data. Prod Plan Control 1(3):147–157CrossRefGoogle Scholar
  21. Rowlands H, Wang LR (2000) An approach of fuzzy logic evaluation and control in SPC. Qual Reliab Eng Intell 16:91–98CrossRefGoogle Scholar
  22. Şentürk S (2010) Fuzzy regression control chart based on \(\alpha \)-cut approximation. Int J Comput Intell Syst 3(1):123–140Google Scholar
  23. Şentürk S, Antucheviciene J (2017) Interval type-2 fuzzy c-control charts: an application in a food company. Informatica 28(2):269–283CrossRefGoogle Scholar
  24. Şentürk S, Erginel N (2009) Development of fuzzy \(\tilde{\bar{X}}-R\) and \(\tilde{\bar{X}}-S\) control charts using \(\alpha \)-cuts. Inf Sci 179:1542–1551CrossRefGoogle Scholar
  25. Şentürk S, Erginel N, Kaya İ, Kahraman C (2010) Design of fuzzy \(\tilde{u}\) control chart. J Mult Valued Logic Soft Comput 17:459–473Google Scholar
  26. Wang D, Hyrnıewıcz O (2015) A fuzzy nonparametric Shewhart charts based on the bootstrap approach. Int J Appl Math Comput Sci 25:389–401MathSciNetCrossRefGoogle Scholar
  27. Wang JH, Raz T (1990) On the construction of control charts using linguistic variables. Intell J Prod Res 28:477–487CrossRefGoogle Scholar
  28. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nihal Erginel
    • 1
  • Sevil Şentürk
    • 2
  • Gülay Yıldız
    • 3
  1. 1.Industrial Engineering DepartmentAnadolu UniversityEskisehirTurkey
  2. 2.Statistic DepartmentAnadolu UniversityEskisehirTurkey
  3. 3.Institute of ScienceAnadolu UniversityEskisehirTurkey

Personalised recommendations