Skip to main content

A Neuro-fuzzy Multi-objective Design of Shewhart Control Charts

  • Chapter

Part of the book series: Advances in Soft Computing ((AINSC,volume 41))

Abstract

Control charts are widely used to establish statistical process control (SPC) and maintain manufacturing processes in desired operating conditions. Effective use of a control chart requires finding the best parameters for the optimal operation of the chart, which is called design of control chart. The design of control chart involves the selection of three parameters namely, the sample size, the sampling interval, and the control limits coefficients. Conventional approaches to design control charts include complex mathematical models and associated optimization schemes. Also, Conventional approaches usually use point estimators of the input parameters which are not able to represent the true parameters sufficiently. The input parameters are suffered from ambiguity uncertainty, which can be effectively modeled by using fuzzy set theory. In this paper a fuzzy multi-objective model for economic-statistical design of X-bar control chart, in which the input parameters are expressed by fuzzy membership functions, is proposed. Moreover, an ANFIS approach is used to transform the complex fuzzy multi-objective model into a fuzzy rule-base. Next, a genetic algorithm (GA) has been developed to find the best design (input) parameters of control charts. Finally, the proposed approach is tested and validated by using a numerical example.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Montgomery, D.C.: Introduction to statistical quality control, 5th edn. Wiley, New York (2005)

    MATH  Google Scholar 

  2. Girshick, M.A., Rubin, H.A.: Baysian to a quality control model. Annals of Mathematical Statistics 23(1), 114–125 (1952)

    MathSciNet  Google Scholar 

  3. Duncan, A.J.: The economic design of _X charts to maintain current control of a process. Journal of the American Statistical Association 51, 228–242 (1956)

    Article  MATH  Google Scholar 

  4. Lorenzen, T.J., Vance, L.C.: The economic design of control charts: a unified approach. Technometrics 28, 3–10 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Woodall, W.H.: Weaknesses of the economic designof control charts. Technometrics 28, 408–409 (1986)

    Article  Google Scholar 

  6. Saniga, E.M.: Economic Statistical Control Chart Designs with an Application to X and R Charts. Technometrics 31, 313–320 (1989)

    Article  Google Scholar 

  7. Montgomery, D.C., et al.: Statistically constrained economic design of the ewma control chart. Journal of Quality Technology 27, 250–256 (1995)

    Google Scholar 

  8. Del Castillo, E.: A multivariate self-tuning controller for run-to-run process control under shift and trend disturbances. IIE Transactions 28, 1011–1021 (1996)

    Google Scholar 

  9. Del Castillo, E., Mackin, P., Montgomery, D.C.: Multiple-criteria optimal design of x-bar control charts. IIE Transactions 28, 467–474 (1996)

    Article  Google Scholar 

  10. Celano, G., Fichera, S.: Multiobjective economic design of an x control chart. Computers & Industrial Engineering 37, 129–132 (1999)

    Article  Google Scholar 

  11. Chena, Y.K., Liaob, H.C.: Multi-criteria design of an X-bar control chart. Computers & Industrial Engineering 46, 877–891 (2004)

    Article  Google Scholar 

  12. Pignatiello Jr., J.J., Tsai, A.: A Optimal economic design of control charts when cost model parameters are not precisely known. IIE Transactions 20, 103–110 (1988)

    Article  Google Scholar 

  13. Vommi, V.B., Seetala, M.S.N.: A new approach to robust economic design of control charts. Applied Soft Computing, ARITCLE IN PRESS (2006)

    Google Scholar 

  14. Linderman, K., Choo, A.S.: Robust economic control chart design. IIE Transactions 34, 1069–1078 (2002)

    Google Scholar 

  15. Vommi, V.B., Seetala, M.S.N.: A simple approach for robust economic design of control charts. Computers & Operations Research, ARITCLE IN PRESS (2006)

    Google Scholar 

  16. Saniga, E.M., Shirland, L.E.: Quality control in practice-a survey. Quality Progress 10(5), 30–33 (1977)

    Google Scholar 

  17. Keats, J.B., et al.: Economic modeling for statistical process control. J. Qual. Technol. 29(2), 144–147 (1997)

    Google Scholar 

  18. Taguchi, G.: Introduction to Quality Engineering. Asian Productivity Organization, UNIPUB, White Plains, NY (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Patricia Melin Oscar Castillo Eduardo Gomez Ramírez Janusz Kacprzyk Witold Pedrycz

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zarandi, M.H.F., Alaeddini, A., Turksen, I.B., Ghazanfari, M. (2007). A Neuro-fuzzy Multi-objective Design of Shewhart Control Charts. In: Melin, P., Castillo, O., Ramírez, E.G., Kacprzyk, J., Pedrycz, W. (eds) Analysis and Design of Intelligent Systems using Soft Computing Techniques. Advances in Soft Computing, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72432-2_84

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72432-2_84

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72431-5

  • Online ISBN: 978-3-540-72432-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics