Design of Control Charts for Number of Defects Based on Pythagorean Fuzzy Sets

Yıl 2020, Cilt: 3 Sayı: 1, 115 - 121, 15.12.2020

İhsan Kaya Ali Karaşan Esra İlbahar Beyza Cebeci

Öz

Control charts (CCs) are completely useful techniques to monitor the process’ stability and control. If the process is stable and in statistical control, it only displays a variation that is inherent to the process. So, usage of them is completely critical for the process’ improvements. Two types of attribute control charts (ACCs) are related to the total count of defects that are the designs of the non--measurable characteristics and they are called $u$ and $c$ control charts. If the process related to evaluations about defects includes some uncertainty, the ACCs are insufficient to reflect the available data in design stages. The fuzzy set theory (FST) is a tool for representing uncertainty by assigning membership functions. In case of quality engineers' intuitive behaviours, ordinary fuzzy sets are incapable of the representation of the data. In this type of data, Pythagorean fuzzy sets (PFSs), which is an extension of FST is a proper way of representing not only uncertainty in the data but also hesitancy of the quality engineers. Through that, in this paper, the design of control charts for the number of defects based on PFSs has been proposed. An extension of $u$ and $c$ control charts based on PFSs are constructed and the design of these control charts has been detailed. Moreover, a descriptive example is introduced to check the applicability of the proposed method.

Anahtar Kelimeler

c control chart, Fuzzy logic, Pythagorean fuzzy sets, u control chart

Destekleyen Kurum

TUBITAK

Proje Numarası

119K408

Teşekkür

This study is supported by The Scientific and Technological Research Council of Turkey (TUBITAK) under Project Number 119K408.

Kaynakça

• 1 L. Zadeh, Fuzzy sets, Inf. Sci., 8(3) (1965), 338–35.
• 2 H. E. Teksen, A. S. Anagün, Interval type-2 fuzzy c-control charts using ranking methods, Hacettepe Journal of Mathematics and Statistics, 48(2) (2019), 510-520.
• 3 S. Senturk, Construction of fuzzy c control charts based on fuzzy rule method, Anadolu University Journal of Science and Technology–A Applied Sciences and Engineering, 18(3), 563–572, 2017.
• 4 M. H. Shu, C. C. Chiu, T. L.Nguyen, B. M. Hsu, W. I. Hsiao, T. H. Lam, Monitoring welding discontinuities with fuzzy control chart, 893, Advanced Materials Research, 2014.
• 5 A. Aslangiray, G. Akyüz, Fuzzy control charts: An application in a textile company, Istanbul University Management Faculty Journal, 43(1) (2014), 70–89.
• 6 S. Fadaei, A. Pooya, Fuzzy U control chart based on fuzzy rules and evaluating its performance using fuzzy OC curve, The TQM Journal, 30(3) (2018), 232–247.
• 7 M. Gulbay, C. Kahraman, An alternative approach to fuzzy control charts: Direct fuzzy approach, Inform. Sci., 177(6) (2007), 1463–1480.
• 8 M.F. Zarandi, A. Alaeddini, I.B. Turksen, A hybrid fuzzy adaptive sampling—run rules for Shewhart control charts, Inform. Sci., 178(4) (2008), 1152–1170.
• 9 R.R. Yager, Pythagorean fuzzy subsets, Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), (2013), 57–61.
• 10 E. Haktanır, C. Kahraman, A novel interval-valued Pythagorean fuzzy QFD method and its application to solar photovoltaic technology development, Comput. Ind. Eng., 132 (2019), 361–372.
• 11 A.V. Feigenbaum, Total quality control, 3, Mc. Graw–Hill, New York, 1991.
• 12 O. Engin, A. Celik, I. Kaya, A fuzzy approach to define sample size for attributes control chart in multistage processes: An application in engine valve manufacturing process, Appl. Soft Comput., 8(4) (2008), 1654—1663.
• 13 J. Hintze, NCSS and PASS number crucher statistical systems, http://www.NCSS.com, 2001.
• 14 M. Gulbay, C. Kahraman, D. Ruan, α–cut fuzzy control charts for linguistic data, Int J Intell Syst., 19(12) (2004), 1173—1195.
• 15 S. Senturk, N. Erginel, I. Kaya, C. Kahraman, Design of fuzzy u ̃ control charts, J. Mult. Log. Soft Comput., 17 (2011), 459—473.
• 16 T.T. Huang, L.H. Chen, Y.W. Wang, Y.S. Su, Design of fuzzy quality control charts for attributes based on triangular fuzzy numbers, Sixth International Conference on Genetic and Evolutionary Computing, (2012), 449—452.
• 17 S.S. Pandian, P. Puthiyanayagam, Triangular fuzzy multinomial control chart with variable sample size using α-–cuts, Int. J. Eng. Sci. Technol., 5(3) (2013), 699-–707.
• 18 N. Erginel, S. Senturk, G. Yildiz, Modeling attribute control charts by interval type–2 fuzzy sets, Soft Comput., 22(15) (2018), 5033—5041.
• 19 H. Teksen, A.S. Anagun, Interval type–2 fuzzy c–control charts using likelihood and reduction methods, Soft Comput., 22(15) (2018), 4921—4934.
• 20 T. Zhao, J. Xiao, Type–2 intuitionistic fuzzy sets, Control Theory Technol., 29(9) (2012), 1215–1222.