Skip to main content

Monitoring Fraction Nonconforming in Process with Interval Type-2 Fuzzy Control Chart

  • Conference paper
  • First Online:
Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Abstract

Fuzzy set theory is particularly appropriate approach when data include imprecise. Type-2 fuzzy set theory captures ambiguity that associates the uncertainty of membership functions by incorporating footprints and models high level uncertainty. If the quality characteristic is a binary classification into conforming/non-conforming of product, this decision depends on human subjectivity that have ambiguity or vague. In this situation, monitoring the process with statistical control charts based on interval type-2 fuzzy sets, a special case of type-2 fuzzy sets, is more suitable due to the human imprecise judgments on quality characteristics. In this paper, interval type-2 fuzzy p-control chart is developed into the literature for the first time. Due to the interval type-2 fuzzy sets modelled more uncertainty for defining membership functions, in this paper interval type-2 fuzzy fraction nonconforming numbers used for handling more uncertainty in process. Real word application is implemented with developed fuzzy control chart.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  2. Montgomery, D.C.: Introduction to Statistical Quality Control, p. 351. Wiley, New York (1991)

    Google Scholar 

  3. Erginel, N.: Fuzzy individual and moving range control charts with α-cuts. J. Intell. Fuzzy Syst. 19, 373–383 (2008)

    MATH  Google Scholar 

  4. Şentürk, S., Erginel, N.: Development of fuzzy \( \tilde{\bar{X}} - R \) and \( \tilde{\bar{X}} - S \) control charts using α-cuts. Inf. Sci. 179, 1542–1551 (2009)

    Google Scholar 

  5. Şentürk, S.: Fuzzy regression control chart based on α-cut approximation. Int. J. Comput. Intell. Syst. 3(1), 123–140 (2010)

    Google Scholar 

  6. Kaya, İ., Kahraman, C.: Process capability analyses based on fuzzy measurement and fuzzy control charts. Expert Syst. Appl. 38, 3172–3184 (2011)

    Article  Google Scholar 

  7. Gülbay, M., Kahraman, C., Ruan, D.: α-cut fuzzy control charts for linguistic data. Int. J. Intell. Syst. 19, 1173–1196 (2004)

    Article  MATH  Google Scholar 

  8. Gülbay, M., Kahraman, C.: Development of fuzzy process control charts and fuzzy unnatural pattern analyses. Comput. Stat. Data Anal. 51, 434–451 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Şentürk, S., Erginel, N., Kaya, İ., Kahraman, C.: Design of fuzzy \( \tilde{u} \) control chart. J. Multiple-Valued Log. Soft Comput. 17, 459–473 (2010)

    Google Scholar 

  10. Erginel, N.: Fuzzy rule based p−np control charts. J. Intell. Fuzzy Syst. 27, 159–171 (2014)

    MathSciNet  MATH  Google Scholar 

  11. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEE Trans. Fuzzy Syst. 14(6), 808–821 (2006)

    Article  Google Scholar 

  12. Kahraman, C., Oztayşi, B., Sarı, I.U., Turanoglu, E.: Fuzzy analytic hierarchy process with interval type-2 fuzzy sets. Knowl. Based Syst. 59, 48–57 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nihal Erginel .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Erginel, N., Şentürk, S., Yıldız, G. (2018). Monitoring Fraction Nonconforming in Process with Interval Type-2 Fuzzy Control Chart. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_62

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-66830-7_62

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66829-1

  • Online ISBN: 978-3-319-66830-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics