Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A type-2 fuzzy-statistical clustering approach for estimating the multiple change points in a process mean with monotonic change

  • 146 Accesses

  • 2 Citations


Identifying the real time of the change in a process, recognized as change point problem, simplifies the removal of change causes. In most of the change point models, the existence of different uncertainty levels is either ignored or paid a little attention to. This paper tries to address an appropriate model to estimate the multiple change points in a monotonic change process in an uncertain condition and for a known number of change points. In this regard, a novel set of membership functions and a novel objective function, based on using interval type-2 fuzzy sets, are introduced in a fuzzy-statistical clustering approach. The proposed approach, in addition to the ability of managing various amount of uncertainty, is free from the distribution of the process variables, and in the case of existence, a certain variable distribution, it is independent from it. Finally, extensive simulation studies are conducted to evaluate the performance of the proposed approach in simple step change, multiple step change, and linear trend change in the presence of isotonic change in the process mean. The results are compared with some of the powerful change point approaches.

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


  1. 1.

    Ahmadzadeh F (2009) Change point detection with multivariate control charts by artificial neural network. Int J Adv Manuf Technol:1–12. doi:10.1007/s00170-009-2193-6

  2. 2.

    Aisbett J, Rickard JT, Morgenthaler D (2010) Type-2 fuzzy sets as functions on spaces. IEEE Trans Fuzzy Syst 18(4):841–844

  3. 3.

    Alaeddini A, Ghazanfari M, Amin Nayeri M (2009) A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts. Inf Sci 179(11):1769–1784

  4. 4.

    Amiri A, Allahyari S (2012) Change Point Estimation Methods for Control Chart Post signal Diagnostics: A Literature Review. Qual Reliab Eng Int 28(7):673–685

  5. 5.

    Bradshaw CW (1983) A fuzzy set theoretic interpretation of economic control limits. Eur J Oper Res 13(4):403–408

  6. 6.

    Castillo, O, Melin, P, (2008), Introduction to Type-2 Fuzzy Logic, in Type-2 Fuzzy Logic: Theory and Applications (book), Studies in Fuzziness and Soft Computing, Springer-Verlag, Berlin, Heidelberg.

  7. 7.

    Chang CW, Wu CR, Chen HC (2007) Using expert technology to select unstable slicing machine to control wafer slicing quality via fuzzy AHP. Expert Syst Appl 34(3):2210–2220

  8. 8.

    Fahmy HM, Elsayed EA (2006) Detection of Linear Trends in Process Mean. Int J Prod Res 44(3):487–504

  9. 9.

    Fahmy HM, Elsayed EA (2006) Drift time Detection and Adjustment Procedures for Processes Subject to Linear Trend. Int J Prod Res 44(16):3257–3278

  10. 10.

    Ghazanfari M, Alaeddini A, Niaki ST, Aryanezhad MB (2008) A clustering approach to identify the time of a step change in Shewhart control charts. Qual Reliab Eng Int 24(7):765–778

  11. 11.

    Gülbay M, Kahraman C (2007) An alternative approach to fuzzy control charts: direct fuzzy approach. Inf Sci 177(6):1463–1480

  12. 12.

    Harnish P, Nelson B, Runger G (2009) Process partitions from time-ordered clusters. J Qual Technol 41(1):3–17

  13. 13.

    Hawkins DM, Qui P, Kang CW (2003) The change-point model for statistical process control. J Qual Technol 35(4):355–366

  14. 14.

    Kazemi MS, Bazargan H, Yaghoobi MA (2014) Estimating the drift time for processes subject to linear trend disturbance using fuzzy statistical clustering. Int J Prod Res 52(11):3317–3330

  15. 15.

    Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 8(5):535–550

  16. 16.

    Melin P, Castillo O (2007) An intelligent hybrid approach for industrial quality control combining neural networks. Fuzzy Logic Fractal Theory Inf Sci 177(7):1543–1557

  17. 17.

    Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 4(6):808–821

  18. 18.

    Mendel JM (2007) Type-2 fuzzy sets and systems: an overview. IEEE Comput Intell Mag 2(2):20–29

  19. 19.

    Montgomery DC (2005) Introduction to Statistical Quality Control, 5th edn. Wiley, New York, pp 470–472

  20. 20.

    Nishina K (1992) A Comparison of Control Charts from the Viewpoint of Change-point Estimation. Qual Reliab Eng Int 8(6):537–541

  21. 21.

    Noorossana R, Atashgar K, Saghaee A (2011) An integrated solution for monitoring process mean vector. Int J Adv Manuf Technol 56(5):755–765

  22. 22.

    Noorossana R, Heydari M (2012) Change point estimation of a normal process variance with a monotonic change. ScientiaIranica Trans E-Ind Eng 19(3):885–894

  23. 23.

    Noorossana R, Shadman A (2009) Estimating the change point of a normal process mean with a monotonic change. Qual Reliab Eng Int 25(1):79–90

  24. 24.

    Page E (1954) Continuous Inspection Schemes. Biometrika 41(1/2):100–115

  25. 25.

    Perry MB, Pignatiello JJ (2006) Estimation of the change point of a normal process mean with a linear trend disturbance. Qual Technol Quant Manag 3(3):101–115

  26. 26.

    Perry MB, Pignatiello JJ, Simpson JR (2007) Change point estimation for monotonically changing Poisson rates in SPC. Int J Prod Res 45(8):1791–1813

  27. 27.

    Perry MB, Pignatiello JJ Jr, Simpson JR (2007) Estimation of the changepoint of the process fraction nonconforming with a monotonic changedisturbance in SPC. Qual Reliab Eng Int 23(3):327–339

  28. 28.

    Samuel TR, Pignatiello JJ, Calvin JA (1998) Identifying the time of a step change with \( \overline{X} \) control charts. Qual Eng 10(3):521–527

  29. 29.

    Sedgewick R, Flajolet P (2013) An Introduction to the Analysis of Algorithms, 2nd edn. Addison-Wesley Professional, Boston

  30. 30.

    Soltys M (2012) An Introduction to the Analysis of Algorithms, 2nd edn. World Scientific Publishing Company, Singapore

  31. 31.

    Sullivan JH (2002) Detection of multiple change-points from clustering individual observations. J Qual Technol 34(4):371–383

  32. 32.

    Zadeh LA (2008) Is there a need for fuzzy logic? Inf Sci 178(13):2751–2779

  33. 33.

    Zarandi MHF, Alaeddini A (2010) A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts. Inf Sci 180(16):3033–3044

  34. 34.

    Zarandi MHF, Alaeddini A, Turksen IB (2008) A hybrid fuzzy adaptive sampling—run rules for Shewhart control charts. Inf Sci 178(4):1152–1170

  35. 35.

    Zarandi MHF, Alaeddini A, Turksen IB (2007) A neuro-fuzzy multi-objective design of Shewhart control charts. In: IFSA 2007 World Congress, Cancun, Mexico

Download references

Author information

Correspondence to Mohammad Hossein Fazel Zarandi.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zarandi, M.H.F., Najafi, S. A type-2 fuzzy-statistical clustering approach for estimating the multiple change points in a process mean with monotonic change. Int J Adv Manuf Technol 77, 1751–1765 (2015).

Download citation


  • Control chart
  • Statistical process control (SPC)
  • Monotonic change
  • Multiple change points
  • Fuzzy set theory
  • Type-2 fuzzy set
  • Fuzzy clustering