Skip to main content
Log in

Statistics with fuzzy data in statistical quality control

  • Focus
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Statistical quality control (SQC) is an important field where both theory of probability and theory of fuzzy sets may be used. In the paper we give a short overview of basic problems of SQC that have been solved using both these theories simultaneously. Some new results on the applications of fuzzy sets in SQC are presented in details. We also present problems which are still open, and whose solution should definitely increase the applicability of fuzzy sets in quality control.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arnold BF (1996) An approach to fuzzy hypothesis testing. Metrika 44:119–126

    Article  MATH  MathSciNet  Google Scholar 

  • Cai KY (1996) System failure engineering and fuzzy methodology. An introductory overview. Fuzzy Sets Syst 83:113–133

    Article  Google Scholar 

  • Chang SI, Aw CA (1996) A neural fuzzy control chart for detecting and classifying process mean shifts. Int J Prod Res 34:2265–2278

    Article  MATH  Google Scholar 

  • Cheng CB (2005) Fuzzy process control: construction of control charts with fuzzy numbers. Fuzzy Sets Syst 154:287–303

    Article  Google Scholar 

  • de Cooman G (2005) A behavioral model for vague probability assessments. Fuzzy Sets Syst 154:305–358

    Article  MATH  Google Scholar 

  • Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30:1983:183–224

    Article  MathSciNet  Google Scholar 

  • Dubois D, Prade H (2002) Quantitative Possibility Theory and its Probabilistic Connections. In: Grzegorzewski P, Hryniewicz O, Gil MA (eds) Soft methods in probability, statistics and data analysis. Physica-Verlag, Heidelberg, pp 3–26

    Google Scholar 

  • Grzegorzewski P (1997) Control charts for fuzzy data. In: Proceedings of the 5th European congress EUFIT’97, Aachen, pp 1326–1330

  • Grzegorzewski P (2001) Acceptance sampling plans by attributes with fuzzy risks and quality levels. In: Wilrich PTh, Lenz HJ (eds) Frontiers in statistical quality control, vol 6. Physica-Verlag, Heidelberg, pp 36–46

  • Grzegorzewski P (2002) Acceptance sampling plans by variables for vague data. In: Grzegorzewski P, Hryniewicz O, Gil MA (eds) Soft methods in probability, statistics and data analysis. Physica-Verlag, Heidelberg, pp 197–206

    Google Scholar 

  • Grzegorzewski P, Hryniewicz O (2000) Soft methods in statistical quality control. Control Cybern 29:119–140

    MATH  MathSciNet  Google Scholar 

  • Hald A (1981) Statistical theory of sample inspection by attributes. Academic, New York

    Google Scholar 

  • Hryniewicz O (1994) Statistical decisions with imprecise data and requirements. In: Kulikowski R, Szkatula K, Kacprzyk J (eds) Systems analysis and decisions support in economics and technology. Omnitech Press, Warszawa, pp 135–143

    Google Scholar 

  • Hryniewicz O (2003) User-preferred solutions of fuzzy optimization problems—an application in choosing user-preferred inspection intervals. Fuzzy Sets Syst 137:101–111

    Article  MATH  MathSciNet  Google Scholar 

  • Hryniewicz O (2005) Evaluation of reliability using shadowed sets and fuzzy lifetime data. In: Kolowrocki K (ed) Advances in safety and reliability. A.A.Balkema, Amsterdam, pp 881–886

    Google Scholar 

  • Kanagawa A, Ohta H (1990) A design for single sampling attribute plan based on fuzzy sets theory. Fuzzy Sets Syst 37:173–181

    Article  MathSciNet  Google Scholar 

  • Kanagawa A, Tamaki F, Ohta H (1993) Control charts for process average and variability based on linguistic data. Int J Prod Res 31:913–922

    Article  MATH  Google Scholar 

  • Krätschmer V (2005) Sampling inspections by attributes which are based on soft quality standards. In: Proceedings of EUSFLAT’2005, Barcelona, September 2005, pp 611–614

  • Ohta H, Ichihashi H (1988) Determination of single-sampling attribute plans based on membership functions. Int J Prod Res 26:1477–1485

    Article  MATH  Google Scholar 

  • Pedrycz W (1998) Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern Part B: Cybern 28:103–109

    Article  Google Scholar 

  • Raz T, Wang JH (1990) Probabilistic and membership approaches in construction of control charts for linguistic data. Prod Plann Control 1:147–157

    Article  Google Scholar 

  • Taleb H, Limam M (2002) On fuzzy and probabilistic control charts. Int J Prod Res 40:2849–2863

    Article  Google Scholar 

  • Tamaki F, Kanagawa A, Ohta H (1991) A fuzzy design of sampling inspection plans by attributes. Jpn J Fuzzy Theory Syst 3:315–327

    MathSciNet  Google Scholar 

  • Tannock TDT (2003) A fuzzy control charting methods for individuals. Int J Prod Res 41:1017–1032

    Article  Google Scholar 

  • Wang D (2006) A CUSUM control chart for fuzzy quality data. In: Lawry J, Miranda E, Bugarin A, Li S, Gil MA, Grzegorzewski P, Hryniewicz O (eds) Soft methods for integrated uncertainty modelling. Springer-Verlag, Heidelberg, pp 357–364

    Google Scholar 

  • Wang JH, Raz T (1990) On the construction of control charts using linguistic variables. Int J Prod Res 28:477–487

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olgierd Hryniewicz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hryniewicz, O. Statistics with fuzzy data in statistical quality control. Soft Comput 12, 229–234 (2008). https://doi.org/10.1007/s00500-007-0203-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-007-0203-x

Keywords

Navigation