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GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION

Year 2015, Volume: 16 Issue: 1, 23 - 37, 24.08.2015

Sevil Şentürk

https://doi.org/10.18038/btd-a.93366

Abstract

In statistical process control, if there is a consistent increase or decrease in process average and variation and there is a tool wear in process, the regression control chart is the most suitable control chart. Therefore, classical control chart is used in the situation that the data is precise. In case that the monitoring process includes vagueness which arises from measurement system or environmental conditions, fuzzy control charts based on fuzzy set theory are useful tools used to model process. The fuzzy regression control chart is a functional technique to evaluate the process in which the avarege has a trend and data represents a linguistic or aprroximate value. The theoratical structure of fuzzy regression control chart and fuzzy range control chart was generated by Şentürk (2010) and an application was carried out for triangular fuzzy number by using α-cut fuzzy midrange technique. In this paper, the theoretical structure of fuzzy regression control chart and fuzzy range control chart are generated for fuzzy mode and fuzzy median by using trapezoidal fuzzy numbers for the first time. An application based on fuzzy median technique carried out for fuzzy regression control chart and fuzzy range control chart. The results are interpreted

Keywords

Fuzzy transformation techniques Trapezoidal fuzzy numbers Control charts Regression control chart

References

  • Chakravarty, A. K. and Shtub A., (1985)“New Technology Investments in Multistage Production Systems”, Decision Science, vol. 16(3), 248-264.
  • Burnak ,N. (1997). Toplam kalite yönetimi-istatistiksel süreç kontrolü, Osmangazi Üniversitesi Mühendislik Mimarlık Fakültesi, TEKAM yayın No: TS-97-008-NB.
  • Cheng.,C.B. (2005). Fuzzy Process Control: Construction of Control Charts with Fuzzy Numbers, Fuzzy Sets and Systems,154 ,287-303.
  • El-Shal ,S.M. and Morris, A.S. (2000). A Fuzzy Rule-Based Algorithm to Improve The Performance of Statistical Process Control in Quality Systems, Journal of Intelligent Fuzzy Systems, 9 ,207-223.
  • Erginel, N. (2008). Fuzzy Individual and Moving Range Control Charts with α-cuts, Journal of Intelligent Fuzzy Systems, 19, 373-383.
  • Erginel, N; Şentürk, S; Kahraman, C ve Kaya İ. (2011). Evaluating the Packing Process in Food Industry using FuzzyX Systems, 4, 509-520.
  • Control Charts, International Journal of Computational Intelligence
  • Erginel, N. (2014).Fuzzy Rule Based p-np Control Charts, Journal of Intelligent Fuzzy Systems, 27, 159- 171.
  • Faraz A. and Moghadam.M.B. (2007). Fuzzy Control Chart A Beter Alternative for Shewhart Average Chart, Quality & Quantity, 41,375-385.
  • Gülbay M. and Kahraman, C.(2006a) Development of Fuzzy Process Control Charts and fuzzy Unnatural Pattern Analyses, Computational Statistics and Data Analysis,51, 434-451.
  • Gülbay M. and Kahraman.C. (2006b). An Alternative Approach to Fuzzy Control Chart: Direct Fuzzy Approach, Information Sciences,77, 1463-1480.
  • Gülbay,M; Kahraman C. and Ruan D. (2004).α-Cut Fuzzy Control Chart for Linguistic Data, International Journal of Intelligent Systems, 19, 1173-1196.
  • Hsu, H.M. and Chen, Y.K. (2001). A Fuzzy Reasoning Based Diagnosis System for X Control Charts,
  • Journal of Intelligent Manufacturing,12, 57-64.
  • Kanagawa, A ;Tamaki, F. and Ohta, H. (1993).Control Charts for Process Average And Variability Based on Linguistic Data, Intelligent Journal of Production Research, 3, 913-922.
  • Klir, J.G. and Yuan, B. (1995).Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentice Hall , New Jersey.
  • Kolarik W J. (1995), Creating Quality Concepts, Systems, Strategies and Tools, McGraw Hill.
  • Mandel, J. (1969). The Regression Control Chart, Journal of Quality Technology, 1 .
  • Montgomery, D.C. (1991). Introduction to Statistical Quality Control, John Wiley & Sons. Inc. USA.
  • Özdamar, İ.H. (2013).Regrsyon Kontrol Kartı ve Bir Çalışma, Süleyman Demirel Üniversitesi Orman Fakültesi Dergisi, 14, 134-137.
  • Raz ,T. and Wang,J.H. (1990). Probabilistic and memberships approaches in the construction of control chart for linguistic data, Production Planning and Control,1,147-157.
  • Rowland, H. and Wang, L.R. (2000). An Approach of Fuzzy Logic Evaluation and Control in SPC, Quality Reliability Engineering Intelligent,16, 91-98.
  • Şenol, F. (2000). Bulanık Mantık Kontrolcüsü, Gazi Üniversitesi Lisans Tezi, Ankara,
  • Şentürk,S. and Erginel,N.(2009). Development of fuzzy ~ XR and XS
  • control charts using
  • cuts, Information Sciences, 179, 1542-1551.
  • Şentürk, S, Erginel, N Kaya, İ and Kahraman, C.(2011).Design of fuzzy u~
  • Control charts, Journal of
  • Multiple-Valued Logic and Soft Computing, 17,459-473.
  • Şentürk, S. (2010). Fuzzy Regression Control Chart Based on α -Cut Approximation, International Journal of Computational Intelligence Systems, 3, 123-140.
  • Taheri, S.M.( 2003).Trends in Fuzzy Statistics, Austrian Journal of Statistics, 32, 239-257.
  • Timothy, J.R. (1995). Fuzzy Logic with Engineering Applications, Mc Graw-Hill, Newyork,
  • Türkbey, O. (2003). Makina Sıralama Problemlerinde çok Amaçlı Bulanık Küme Yaklaşımı, Gazi Üniversitesi, Mühendislik. Mimarlık. Fakülte Dergisi, 18, 63-77.
  • Wang, J.H. and Raz, T. (1990). On The Construction of Control Charts using Linguistic Variables, Intelligent Journal of Production Research, 28, 477-487.
  • Zadeh, L.A.( 1965).Fuzzy Sets, Information and Control, 8, 338-353.

BULANIK REGRESYON KONTROL GRAFİĞİNİN BULANIK MOD VE BULANIK MEDYAN DÖNÜŞÜM TEKNİKLERİ KULLANILARAK OLUŞTURULMASI VE BİR UYGULAMA

Year 2015, Volume: 16 Issue: 1, 23 - 37, 24.08.2015

Sevil Şentürk

https://doi.org/10.18038/btd-a.93366

Abstract

İstatistiksel süreç kontrolünde eğer sürecin ortalamasında ve değişkenliğinde kararlı bir artma veya
azalma gözlemleniyorsa ve süreçte bir aşınma söz konusuysa regresyon kontrol grafiği kullanılabilecek en
uygun kontrol grafiği tekniğidir. Bununla birlikte, klasik kontrol grafikleri süreçten alınan verilerin kesin
ve tam olarak bilindiği durumlarda kullanılmaktadır. İlgilenilen süreç, ölçüm sisteminden veya çevresel
etkenlerden kaynaklanan bir belirsizlik içeriyorsa bulanık küme teorisine dayalı, bulanık kontrol grafikleri
süreci modellemede daha etkin bir araç olarak kullanılabilmektedir. Bulanık regresyon kontrol grafiği,
verilerin yaklaşık değer olarak ya da dilsel olarak ifade edildiği ve ortalamanın bir trende sahip olduğu
süreçleri değerlendirmede kullanılan bir kontrol grafiğidir. Şentürk (2010) tarafından bulanık regresyon
kontrol grafiğinin ve bulanık değişim aralığı kontrol grafiğinin teorik yapısı oluşturulmuş ve üçgen bulanık
sayılar için α-kesim bulanık orta değişim tekniği kullanılarak uygulaması yapılmıştır. Bu çalışmada ise,
yamuk bulanık sayılar kullanılarak, bulanık mod ve bulanık medyan transformasyon teknikleri için bulanık
regresyon kontrol grafiğinin ve bulanık değişim aralığı kontrol grafiğinin teorik yapısı ilk defa
oluşturulmuştur. Bulanık regresyon kontrol grafiği ve bulanık değişim aralığı kontrol grafiği için bulanık
medyan tekniğine dayalı bir uygulama yapılmış ve uygulama sonuçları yorumlanmıştır.

Keywords

Bulanık dönüşüm teknikleri Yamuk bulanık sayılar Kontrol grafikleri Regresyon kontrol grafiği

References

  • Chakravarty, A. K. and Shtub A., (1985)“New Technology Investments in Multistage Production Systems”, Decision Science, vol. 16(3), 248-264.
  • Burnak ,N. (1997). Toplam kalite yönetimi-istatistiksel süreç kontrolü, Osmangazi Üniversitesi Mühendislik Mimarlık Fakültesi, TEKAM yayın No: TS-97-008-NB.
  • Cheng.,C.B. (2005). Fuzzy Process Control: Construction of Control Charts with Fuzzy Numbers, Fuzzy Sets and Systems,154 ,287-303.
  • El-Shal ,S.M. and Morris, A.S. (2000). A Fuzzy Rule-Based Algorithm to Improve The Performance of Statistical Process Control in Quality Systems, Journal of Intelligent Fuzzy Systems, 9 ,207-223.
  • Erginel, N. (2008). Fuzzy Individual and Moving Range Control Charts with α-cuts, Journal of Intelligent Fuzzy Systems, 19, 373-383.
  • Erginel, N; Şentürk, S; Kahraman, C ve Kaya İ. (2011). Evaluating the Packing Process in Food Industry using FuzzyX Systems, 4, 509-520.
  • Control Charts, International Journal of Computational Intelligence
  • Erginel, N. (2014).Fuzzy Rule Based p-np Control Charts, Journal of Intelligent Fuzzy Systems, 27, 159- 171.
  • Faraz A. and Moghadam.M.B. (2007). Fuzzy Control Chart A Beter Alternative for Shewhart Average Chart, Quality & Quantity, 41,375-385.
  • Gülbay M. and Kahraman, C.(2006a) Development of Fuzzy Process Control Charts and fuzzy Unnatural Pattern Analyses, Computational Statistics and Data Analysis,51, 434-451.
  • Gülbay M. and Kahraman.C. (2006b). An Alternative Approach to Fuzzy Control Chart: Direct Fuzzy Approach, Information Sciences,77, 1463-1480.
  • Gülbay,M; Kahraman C. and Ruan D. (2004).α-Cut Fuzzy Control Chart for Linguistic Data, International Journal of Intelligent Systems, 19, 1173-1196.
  • Hsu, H.M. and Chen, Y.K. (2001). A Fuzzy Reasoning Based Diagnosis System for X Control Charts,
  • Journal of Intelligent Manufacturing,12, 57-64.
  • Kanagawa, A ;Tamaki, F. and Ohta, H. (1993).Control Charts for Process Average And Variability Based on Linguistic Data, Intelligent Journal of Production Research, 3, 913-922.
  • Klir, J.G. and Yuan, B. (1995).Fuzzy Sets and Fuzzy Logic Theory and Applications, Prentice Hall , New Jersey.
  • Kolarik W J. (1995), Creating Quality Concepts, Systems, Strategies and Tools, McGraw Hill.
  • Mandel, J. (1969). The Regression Control Chart, Journal of Quality Technology, 1 .
  • Montgomery, D.C. (1991). Introduction to Statistical Quality Control, John Wiley & Sons. Inc. USA.
  • Özdamar, İ.H. (2013).Regrsyon Kontrol Kartı ve Bir Çalışma, Süleyman Demirel Üniversitesi Orman Fakültesi Dergisi, 14, 134-137.
  • Raz ,T. and Wang,J.H. (1990). Probabilistic and memberships approaches in the construction of control chart for linguistic data, Production Planning and Control,1,147-157.
  • Rowland, H. and Wang, L.R. (2000). An Approach of Fuzzy Logic Evaluation and Control in SPC, Quality Reliability Engineering Intelligent,16, 91-98.
  • Şenol, F. (2000). Bulanık Mantık Kontrolcüsü, Gazi Üniversitesi Lisans Tezi, Ankara,
  • Şentürk,S. and Erginel,N.(2009). Development of fuzzy ~ XR and XS
  • control charts using
  • cuts, Information Sciences, 179, 1542-1551.
  • Şentürk, S, Erginel, N Kaya, İ and Kahraman, C.(2011).Design of fuzzy u~
  • Control charts, Journal of
  • Multiple-Valued Logic and Soft Computing, 17,459-473.
  • Şentürk, S. (2010). Fuzzy Regression Control Chart Based on α -Cut Approximation, International Journal of Computational Intelligence Systems, 3, 123-140.
  • Taheri, S.M.( 2003).Trends in Fuzzy Statistics, Austrian Journal of Statistics, 32, 239-257.
  • Timothy, J.R. (1995). Fuzzy Logic with Engineering Applications, Mc Graw-Hill, Newyork,
  • Türkbey, O. (2003). Makina Sıralama Problemlerinde çok Amaçlı Bulanık Küme Yaklaşımı, Gazi Üniversitesi, Mühendislik. Mimarlık. Fakülte Dergisi, 18, 63-77.
  • Wang, J.H. and Raz, T. (1990). On The Construction of Control Charts using Linguistic Variables, Intelligent Journal of Production Research, 28, 477-487.
  • Zadeh, L.A.( 1965).Fuzzy Sets, Information and Control, 8, 338-353.
There are 35 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sevil Şentürk

Publication Date August 24, 2015
Published in Issue Year 2015 Volume: 16 Issue: 1

Cite

APA Şentürk, S. (2015). GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 16(1), 23-37. https://doi.org/10.18038/btd-a.93366
AMA Şentürk S. GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION. AUJST-A. August 2015;16(1):23-37. doi:10.18038/btd-a.93366
Chicago Şentürk, Sevil. “GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 16, no. 1 (August 2015): 23-37. https://doi.org/10.18038/btd-a.93366.
EndNote Şentürk S (August 1, 2015) GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 16 1 23–37.
IEEE S. Şentürk, “GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION”, AUJST-A, vol. 16, no. 1, pp. 23–37, 2015, doi: 10.18038/btd-a.93366.
ISNAD Şentürk, Sevil. “GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 16/1 (August 2015), 23-37. https://doi.org/10.18038/btd-a.93366.
JAMA Şentürk S. GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION. AUJST-A. 2015;16:23–37.
MLA Şentürk, Sevil. “GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 16, no. 1, 2015, pp. 23-37, doi:10.18038/btd-a.93366.
Vancouver Şentürk S. GENERATING FUZZY REGRESSION CONTROL CHART BY USING FUZZY MOD AND FUZZY MEDIAN TRANSFORMATION TECHNIQUES AND AN APPLICATION. AUJST-A. 2015;16(1):23-37.
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