A PROPOSED RESPONSE SURFACE-BASED ROBUST DESIGN MODEL FOR QUALITY ENGINEERING PROBLEMS

Abstract

  The aim of robust design models is to reduce the variability reduction as small as possible. The process bias defined as a difference between the desired target value and the process mean is an important concern for quality engineering problems. In addition, the selection of different variability measures may also change optimal operating conditions for a response variable. Therefore, this paper is three-fold. One, another view of dual response model is proposed with the three different variability measures in order to determine optimum robust design solutions for input variables while minimizing the process bias. Two, the linearization of constraints is performed using the sequential quadratic programming method as an effective optimization method. Three, a printing process from the literature is conducted to obtain the best optimal settings for input variables. Finally, the results of the proposed model show approximately % 16 more variance reduction than traditional models.

Keywords

• robust design,dual response model,response surface design,variability measures,sequential quadratic programming

KALİTE MÜHENDİSLİĞİ PROBLEMLERİ İÇİN ÖNERİLEN BİR YANIT YÜZEYİ TABANLI SAĞLAM TASARIM MODELİ

Öz

  Sağlam tasarım modellerinin amacı değişkenliği mümkün olduğu kadar azaltmaktır. İstenen hedef değer ile işlem ortalaması arasındaki fark olarak tanımlanan işlem yanlılığı, kalite mühendisliği problemleri için önemli bir husustur. Ek olarak, farklı değişkenlik ölçümlerinin seçimi bir yanıt değişkeni için en uygun çalışma koşullarını da değiştirebilir. Bu nedenle, bu makalenin üç amaçlıdır. Birincisi, yanıt modelinin bir başka görünümü işlem yanlılığını en aza indirirken girdi değişkenleri için en iyi sağlam tasarım çözümlerini belirlemek amacıyla üç farklı değişkenlik ölçüsüyle önerilmiştir. İkincisi, kısıtlamaların doğrusallaştırılması, etkin bir optimizasyon yöntemi olarak sıralı ikinci dereceden programlama yöntemi kullanılarak gerçekleştirilir. Üçüncüsü, girdi değişkenleri için en uygun ayarları elde etmek için literatürden bir baskı işlemi süreci araştırılmıştır. Son olarak, önerilen modelin sonuçları geleneksel modellere göre yaklaşık % 16 daha fazla varyansın azaldığını gösterir.

Anahtar Kelimeler

• : sağlam tasarım,ikili tepki modeli,yanıt yüzey tasarımı,farklı değişkenlik ölçüleri,sıralı ikinci dereceden programlama

Kaynakça

1. [1] TAGUCHI, G., Introduction to Quality Engineering, UNIPUB/Kraus International, New York, US, 1986.
2. [2] VINING, G.G., MYERS, R.H., “Combining Taguchi and Response Surface Philosophies: A Dual Response Approach”, Journal of Quality Technology, 22, 38-45, 1990.
3. [3] DEL CASTILLO, E., MONTGOMERY, D.C., “A Nonlinear Programming Solution to the Dual Response Problem”, Journal of Quality Technology, 25, 199-204, 1993.
4. [4] LIN, D.K.J., TU, W., “Dual Response Surface Optimization”, Journal of Quality Technology, 27, 34-39, 1995.
5. [5] CHO, B.R., PHILIPS, M.D., KAPUR, K.C., “Quality Improvement by RSM Modelling for Robust Design”, Proceedings of the Fifth Industrial Engineering Research Conference, 650-655. Minnesota, US, 1996.
6. [6] COPELAND, K.A.F., NELSON, P.R., “Dual Response Optimization via Direct Function Minimization”, Journal of Quality Technology, 28, 331-336, 1996.
7. [7] KIM, K.J., LIN, D.K., “Dual Response Surface Optimization: A Fuzzy Modelling Approach”, Journal of Quality Technology, 30, 1-10, 1998.
8. [8] CHO, B.R., KIM, Y.J., KIMBLER, D.L., PHILLIPS, M.D., “An Integrated Joint Optimization Procedure for Robust and Tolerance Design”, International Journal of Production Research, 38, 2309-2325, 2000.

9. [9] TANG, L.C., XU, K., “A Unified Approach for Dual Response Surface Optimization”, Journal of Quality Technology, 34, 437-447, 2002.
10. [10] KIM, Y.J., CHO, B.R., “Development of Priority-based Robust Design”, Quality Engineering, 14, 355-363, 2002.
11. [11] KÖKSOY, O., DOGANAKSOY, N., “Joint Optimization of Mean and Standard Deviation Using Response Surface Methods”, Journal of Quality Technology, 35, 239-252, 2003.
12. [12] DING, R., LIN, D.K.J., WEI, D., “Dual-Response Surface Optimization: A Weighted MSE Approach”, Quality Engineering, 16, 377-385, 2004.
13. [13] ROMANO, D., VARETTO, M., VICARIO, G., “Multiresponse Robust Design: A General Framework based on Combined Array”, Journal of Quality Technology, 36, 27-37, 2004.
14. [14] SHIN, S., CHO, B.R., “Bias-Specified Robust Design Optimization and Its Analytical Solutions”, Computers & Industrial Engineering, 48, 129-140, 2005.
15. [15] Köksoy, O., “Multiresponse Robust Design: Mean Square Error (MSE) Criterion”, Applied Mathematics and Computation, 175, 1716-1729, 2006.
16. [16] PARK, H., PARK, S.H., KONG, H.B., LEE, I., “Weighted Sum MSE Minimization Under per-BS Power Constraint for Network MIMO Systems”, Communications Letters, IEEE, 16, 360-363, 2012.
17. [17] ROBINSON, T.J., WULFF, S.S., MONTGOMERY, D.C., KHURI, A.I., “Robust Parameter Design Using Generalized Linear Mixed Models”, Journal of Quality Technology, 38, 65-75, 2006.
18. [18] SHAIBU, A.B., CHO, B.R., “Another View of Dual Response Surface Modeling and Optimization in Robust Parameter Design”, The International Journal of Advanced Manufacturing Technology, 41, 631-641, 2009.
19. [19] Costa, N.R.P., “Simultaneous Optimization of Mean and Standard Deviation”, Quality Engineering, 22, 140-149, 2010.
20. [20] OZDEMIR, A., CHO, B.R., “A Nonlinear Integer Programming Approach to Solving the Robust Parameter Design Optimization Problem”, Quality and Reliability Engineering International, 32, 2859-2870, 2016.
21. [21] Box, G.E.P., Draper, N.R., Empirical Model Building and Response Surfaces, Wiley, New York, US, 1987.
22. [22] Goethals, P., Aragon, L., Cho, B.R., “Experimental Investigations of Estimated Response Surface Functions with Different Variability Measures”, International Journal of Experimental Design and Process Optimisation, 1, 123-163, 2009.
23. [23] Ruszczyński, A.P., Nonlinear Optimization, Princeton University Press, New Jersey, US, 2006.
24. [24] Fishback, P.E., Linear and Nonlinear Programming with Maple: An Interactive, Applications-Based Approach, Chapman and Hall/CRC, Florida, US, 2009.
25. [25] SAS Institute, Using JMP 11, SAS Institute, Cary, NC, US, 2013.
26. [26] Maple, V., Waterloo Maple Software. University of Waterloo, Version, 17, Waterloo, ON, Canada, 2013.