Skip to main content
SpringerLink
Log in

Fuzzy maximum likelihood change-point algorithms for identifying the time of shifts in process data

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Process data provide important information for monitoring product quality. A common problem of process readings is their deviation from in-control values due to systematic errors or instrument biases. Timely detection and modification of instrument fault is crucial for process manipulation. Monitoring changes in process mean and variance simultaneously is important because special causes can evoke changes in both at once. Many existing methods identify either the mean or variance only; some even inaccurately assumes that the in-control parameters are known. We propose a new method called fuzzy maximum likelihood change-point (FMLCP) algorithm that allows detection of the time of shifts in mean and variance simultaneously without knowing the in-control parameters. The fuzzy c-partition concept is embedded into change-point formulation to deal with the vagueness of boundaries between adjacent segments. An FMLCP procedure is constructed and suitable for processes following any distribution. The FMLCP algorithm can be applied to both phase I and II processes in quality control without any information of in-control parameters; multiple change points are allowed and the shifts in each individual segment can be estimated simultaneously. Our experimental results demonstrate the preferred utility of FMLCP over traditional statistical maximum likelihood approaches. We used real datasets to demonstrate the effectiveness of FMLCP. Using FMLCP to detect small shifts is particularly beneficial for identifying root causes quickly and correctly in phase II applications where small changes occur more often and the average run length tends to be long.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Gan FF, Ting KW, Chang TC (2004) Interval charting schemes for joint monitoring of process mean and variance. Qual Reliab Eng Int 20:291–303

    Article  Google Scholar 

  2. Keshavarz M, Huang B (2015) Expectation maximization method for multivariate change point detection in presence of unknown and changing covariance. Comput Chem Eng 69:128–146

    Article  Google Scholar 

  3. Niaki STA, Khedmati M (2013) Change point estimation of high-yield processes with a linear trend disturbance. Int J Adv Manuf Technol 69:491–497

    Article  Google Scholar 

  4. Niaki STA, Khedmati M (2014) Change point estimation of high-yield processes experiencing monotonic disturbances. Comput Ind Eng 67:82–92

    Article  Google Scholar 

  5. Eyvazian M, Noorossana R, Saghaei A, Amiri A (2011) Phase II monitoring of multivariate multiple linear regression profiles. Qual Reliab Eng Int 27(3):281–296

    Article  Google Scholar 

  6. Shams I, Ajorlou S, Yang K (2013) Modeling clustered non-stationary Poisson processes for stochastic simulation inputs. Comput Ind Eng 64:1074–1083

    Article  Google Scholar 

  7. Dogu E (2014) Change point estimation based statistical monitoring with variable time between events (TBE) control charts. Qual Technol Quant Manag 11:383–400

    Article  Google Scholar 

  8. Hawkins DM, Qiu PH, Kang CW (2003) The changepoint model for statistical process control. J Qual Technol 35:355–366

    Article  Google Scholar 

  9. Hawkins DM, Zamba KD (2005) A change-point model for a shift in variance. J Qual Technol 37:21–31

    Article  Google Scholar 

  10. Ross GJ, Adams NM, Tasoulis DK, Hand DJ (2011) A nonparametric change point model for streaming data. Technometrics 53:379–389

    Article  MathSciNet  Google Scholar 

  11. Ross GJ, Adams NM (2012) Two nonparametric control charts for detecting arbitrary distribution changes. J Qual Technol 44:102–116

    Article  Google Scholar 

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

    Google Scholar 

  13. Amiri A, Niaki STA, Moghadam AT (2015) A probabilistic artificial neural network-based procedure for variance change point estimation. Soft Comput 19:691–700

    Article  Google Scholar 

  14. Chen CWS, Chan JSK, Gerlach R, Hsieh WYL (2011) A comparison of estimators for regression models with change points. Stat Comput 21:395–414

    Article  MathSciNet  MATH  Google Scholar 

  15. Keshavarz M, Huang B (2015) Expectation maximization method for multivariate change pointdetection in presence of unknown and changing covariance. Comput Chem Eng 69:128–146

    Article  Google Scholar 

  16. Fearnhead P (2006) Exact and efficient Bayesian inference for multiple change point problems. Stat Comput 16:203–213

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Lu KP, Chang ST, Yang MS (2016) Change-point detection for shifts in control charts using fuzzy shift change-point algorithms. Comput Ind Eng 93:12–27

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Hawkins DM, Zamba KD (2005) Statistical process control for shifts in mean or variance using a changepoint formulation. Technometrics 47:164–173

    Article  MathSciNet  Google Scholar 

  24. Park J, Park S (2004) Estimation of the change-point in the \(\bar{X}\) and S control charts. Commun Stat Simul Comput 33:1115–1132

  25. Montgomery DC (2013) Introduction to statistical quality control, 7th edn. Wiley, New York

    MATH  Google Scholar 

  26. Chang ST, Lu KP (2016) Detecting change-points in statistical process control using EM change-point algorithm. Qual Reliab Eng Int 32:889–900

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  28. Wang D, Li P, Yasuda M (2014) Construction of fuzzy control charts based on weighted possibilistic mean. Commun. Stat. Theory Methods 43:3186–3207

    Article  MathSciNet  MATH  Google Scholar 

  29. Sentürk S, Erginel N, Kaya I, Kahraman C (2014) Fuzzy exponentially weighted moving average control chart for univariate data with a real case application. Appl Soft Comput 22:1–10

    Article  Google Scholar 

  30. Faraz A, Shapiro AF (2010) An application of fuzzy random variables to control charts. Fuzzy Set Syst 161:2684–2694

    Article  MathSciNet  MATH  Google Scholar 

  31. Chen YK, Chang HH, Chiu FR (2008) Optimization design of control charts based on minimax decision criterion and fuzzy process shifts. Expert Syst Appl 35:207–213

    Article  Google Scholar 

  32. Hsieh KL, Tong LI, Wang MC (2007) The application of control chart for defects and defect clustering in IC manufacturing based on fuzzy theory. Expert Syst Appl 32:765–776

    Article  Google Scholar 

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

    Article  Google Scholar 

  34. Hawkins DM (2001) Fitting multiple change-point models to data. Comput Stat Data Anal 37:323–341

    Article  MathSciNet  MATH  Google Scholar 

  35. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  36. Ruspini EH (1969) A new approach to clustering. Inf Control 15:22–32

    Article  MATH  Google Scholar 

  37. Yang MS (1994) On a class of fuzzy classification maximum likelihood procedures. Fuzzy Set Syst 57:365–375

    Article  MathSciNet  MATH  Google Scholar 

  38. Venter JH, Steel SJ (1996) Finding multiple abrupt change points. Comput Stat Data Anal 22:481–504

    Article  MathSciNet  MATH  Google Scholar 

  39. Hsu DA (1979) Detection shifts of parameter in gamma sequences with application to and air traffic flow analysis. J Am Stat Assoc 74:31–46

    Article  Google Scholar 

  40. Lee CB (1998) Bayesian analysis of a change-point in exponential families with applications. Comput Stat Data Anal 27:195–208

    Article  MathSciNet  MATH  Google Scholar 

  41. Habibi R (2011) Change point detection using bootstrap methods. Adv Model Optim 13:341–347

    MathSciNet  MATH  Google Scholar 

  42. Jandhyala VK, Fotopoulos SB, Hawkins DM (2002) Detection and estimation of abrupt changes in the variability of a process. Comput Stat Data Anal 40:1–19

    Article  MathSciNet  MATH  Google Scholar 

  43. Lombard F (1987) Rank tests for changepoint problems. Biometrika 74:15–624

    Article  MathSciNet  Google Scholar 

  44. Fearnhead P, Clifford P (2003) Online inference for hidden Markov models. J R Stat Soc Ser B 65:887–899

    Article  MATH  Google Scholar 

  45. Ruanaidh JJK, Fitzgerald WJ (1996) Numerical Bayesion methods applied to signal processing. Springer, New York

    Book  MATH  Google Scholar 

  46. Neubauer J, Vesely V (2013) Detection of multiple changes in mean by sparse parameter estimation. Nonlinear Anal Model Control 18:177–190

    MathSciNet  MATH  Google Scholar 

  47. Gustafsson F (2000) Adaptive filtering and change detection. Wiley, Hoboken. ISBN 978-0-470-85340-5

    Google Scholar 

  48. Bai X, Yao W, Boyer JE (2012) Robust fitting of mixture regression models. Comput Stat Data Anal 56:2347–2359

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This study was partially supported by the Ministry of Science and Technology, Taiwan [Grant Number Most 105-2118-M-025-002 and Most 105-2118-M-003-001] and National Taiwan Normal University [Grant Number 104000138].

Author information

Authors and Affiliations

  1. Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, Taiwan

    Kang-Ping Lu

  2. Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan

    Shao-Tung Chang

Authors
  1. Kang-Ping Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shao-Tung Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shao-Tung Chang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, KP., Chang, ST. Fuzzy maximum likelihood change-point algorithms for identifying the time of shifts in process data. Neural Comput & Applic 31, 2431–2446 (2019). https://doi.org/10.1007/s00521-017-3200-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-3200-8

Keywords

Search

Navigation