Design of EWMA and CUSUM Control Charts Based On Type-2 Fuzzy Sets

Abstract

A Shewhart control chart is a completely critical tool used for monitoring process’ stability. The superiority of EWMA and CUSUM control charts over Shewhart control charts is their ability to handle small process shifts. Although fuzzy sets can manage uncertainties related to processes, the extensions of fuzzy sets can be used to improve the ability of these control charts. The main advantage of type-2 fuzzy sets is that they can effectively model uncertainty even when the membership functions are not crisp. For these reasons, type-2 fuzzy sets are used to design of CUSUM and EWMA control charts. Therefore, in this study, the control limits and center lines in EWMA and CUSUM control diagrams have been re-formulated based on type-2 fuzzy sets. Furthermore, an illustrative example is provided to show the applicability of the proposed techniques.

Keywords

• CUSUM
• EWMA
• Type-2 fuzzy sets
• Quality control

Kaynakça

1. 1 D. C. Montgomery, Statistical quality control, Wiley Global Education, 2012.
2. 2 I. W. Burr, Statistical quality control methods, CRC Press, 1976.
3. 3 R. S. Leavenworth, E. L. Grant, Statistical quality control, Tata McGraw-Hill Education, 2000.
4. 4 S. F. Yang, J. S. Lin, S. W. Cheng, A new nonparametric EWMA sign control chart, Expert Syst. Appl., 38(5) (2011), 6239–6243.
5. 5 E. S. Page, Continuous inspection schemes, Biometrika, 41(1/2) (1954), 100-115.
6. 6 S. W. Roberts, Control chart tests based on geometric moving averages, Technometrics, 1(3) (1959), 239–250.
7. 7 L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning—-I, Inform. Sci., 8(3) (1975), 199–249.
8. 8 M. Kilic, I. Kaya, Investment project evaluation by a decision making methodology based on type–2 fuzzy sets, Appl. Soft Comput., 27 (2015), 399–410.

9. 9 L. A. Zadeh, Fuzzy sets, Inform. and Control, 8(3) (1965), 338–353.
10. 10 M. Gülbay, C. Kahraman, An alternative approach to fuzzy control charts: Direct fuzzy approach, Inf. Sci., 177(6) (2007), 1463–1480.
11. 11 A. Moraditadi, S. Avakhdarestani, Development of fuzzy individual x and moving range control chart, Int. J. Product. Qual. Manage., 17(1) (2016), 82.
12. 12 I. Kaya, C. Kahraman, Process capability analyses based on fuzzy measurements and fuzzy control charts, Expert Syst. Appl., 38(4) (2011), 3172—3184.
13. 13 N. Erginel, S. Senturk, Fuzzy EWMA and Fuzzy CUSUM Control Charts, Fuzzy Statistical Decision-Making, Springer Cham., 2016.
14. 14 N. Erginel, S. Senturk, G. Yıldız, Monitoring fraction nonconforming in process with interval type–2 fuzzy control chart, Adv. in Fuzzy Log. and Technol, Springer Cham., 2017.
15. 15 A. Dos Santos Mendes, M. A. G. Machado, P. M. S. Rocha Rizol, Fuzzy control chart for monitoring mean and range of univariate processes, Pesquisa Operacional, 39(2) (2019), 339–357.
16. 16 G. Hesamian, M. G. Akbari, E. Ranjbar, Exponentially weighted moving average control chart based on normal fuzzy random variables, Int. J. Fuzzy Syst., 21(4) (2019) 1187–1195.
17. 17 H. E. Teksen, A. S. Anagün, Interval type–2 fuzzy c–control charts using ranking methods, Hacettepe J. of Math. and Stat., 48(2) (2019), 510–520.
18. 18 H. Ercan-Teksen, A. S. Anagun, Intuitionistic fuzzy c-control charts using fuzzy comparison methods, Int. Conf. on Intell. and Fuzzy Syst., (2019), 1161–1169.
19. 19 M. Erdoğan, I.Kaya, A combined fuzzy approach to determine the best region for a nuclear power plant in Turkey, Appl. Soft Comput., 39 (2016), 84–93.
20. 20 G. Kose, Prioritization of perceived quality parameters: The application of fuzzy quality function deployment in white goods sector, MSc Thesis, Yildiz Teknik University, 2016.
21. 21 T. Tuncinan, Proposal of interval type–2 fuzzy models for replacement analysis, MSc Thesis, Istanbul Teknik University, 2016.
22. 22 S. M. Chen, L. W. Lee, Fuzzy multiple attributes group decision–making based on the interval type–2 TOPSIS method, Expert Syst. Appl., 37(4) (2010), 2790–2798.
23. 23 C. Kahraman, B. Oztaysi, I. U. Sari, E. Turanoglu, Fuzzy analytic hierarchy process with interval type–2 fuzzy sets, Knowl. Based Syst., 59 (2014), 48–57.
24. 24 D. C. Montgomery, L. A. Johnson, J. S. Gardiner, Forecasting and time series analysis, McGraw-Hill Companies, 1990.
25. 25 D. Trietsch, Statistical quality control: a loss minimization approach, World Scientific, 1999.
26. 26 T. Colak, Statistical process control and its apllications, MSc Thesis, Cukurova University, 2007.