Soft Computing

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

Modeling attribute control charts by interval type-2 fuzzy sets

  • Nihal ErginelEmail author
  • Sevil Şentürk
  • Gülay Yıldız


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.


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


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.


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Copyright information

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

Authors and Affiliations

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

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