Robust parameter design using the weighted metric method - The case of 'the smaller the better'
Mostafa Kamali Ardakani ; Rassoul Noorossana ; Seyed Taghi Akhavan Niaki ; Homayoun Lahijanian
International Journal of Applied Mathematics and Computer Science, Tome 19 (2009), p. 59-68 / Harvested from The Polish Digital Mathematics Library

In process robustness studies, it is desirable to minimize the influence of noise factors on the system and simultaneously determine the levels of controllable factors optimizing the overall response or outcome. In the cases when a random effects model is applicable and a fixed effects model is assumed instead, an increase in the variance of the coefficient vector should be expected. In this paper, the impacts of this assumption on the results of the experiment in the context of robust parameter design are investigated. Furthermore, two criteria are considered to determine the optimum settings for the control factors. In order to better understand the proposed method and to evaluate its performances, a numerical example for the case of 'the smaller the better' is included.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:207921
@article{bwmeta1.element.bwnjournal-article-amcv19i1p59bwm,
     author = {Mostafa Kamali Ardakani and Rassoul Noorossana and Seyed Taghi Akhavan Niaki and Homayoun Lahijanian},
     title = {Robust parameter design using the weighted metric method - The case of 'the smaller the better'},
     journal = {International Journal of Applied Mathematics and Computer Science},
     volume = {19},
     year = {2009},
     pages = {59-68},
     zbl = {1169.93403},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv19i1p59bwm}
}
Mostafa Kamali Ardakani; Rassoul Noorossana; Seyed Taghi Akhavan Niaki; Homayoun Lahijanian. Robust parameter design using the weighted metric method - The case of 'the smaller the better'. International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) pp. 59-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv19i1p59bwm/

[000] Asgharpour, M. J., (1998). Multiple Criteria Decision Making, Tehran University Press, Tehran.

[001] Borkowski, J. J. and Lucas, J. M., (1997). Designs of mixed resolution for process robustness studies, Technometrics 39(1): 63-70. | Zbl 0869.62070

[002] Borror, C. M. and Montgomery, D. C., (2000). Mixed resolution designs as alternatives to Taguchi inner/outer array designs for robust design problems, Quality and Reliability Engineering International 16(2): 117-127.

[003] Box, G. E. P., Bisgaard S., and Fung C., (1988). An explanation and critique of Taguchi's contributions to quality engineering, Quality and Reliability Engineering International 4(2): 123-131.

[004] Box, G. E. P. and Jones, S., (1992). Split-plot designs for robust product experimentation, Journal of Applied Statistics 19(1): 3-26.

[005] Copeland, K. and Nelson, P. R., (1996). Dual response optimization via direct function minimization, Journal of Quality Technology 28(3): 331-336.

[006] Chankong, V. and Haimes, Y., (1983). Multiobjective Decision Making: Theory and Methodology, North Holland, New York, NY. | Zbl 0622.90002

[007] Deb, k., (2001). Multi-objective Optimization Using Evolutionary Algorithms, Wiley, New York, NY. | Zbl 0970.90091

[008] Del Castillo, E., Alvarez, M. J., Ilzarbe, L. and Viles, E., (2007). A new design criterion for robust parameter experiments, Journal of Quality Technology 39(3): 279-295.

[009] Del Castillo, E. and Montgomery, D. C., (1993). A nonlinear programming solution to the dual response problem, Journal of Quality Technology 25(2): 199-204.

[010] Drain, D., Borror, C. M., Anderson-Cook, C. M and Montgomery, D. C., (2005). Response surface design for correlated noise variables, Journal of Probability and Statistical Science 3(2): 247-281.

[011] Draper, N. R. and Smith, H., (1998). Applied Regression Analysis, 2nd Ed., Wiley, New York, NY. | Zbl 0895.62073

[012] Fan, S. K. and Del Castillo, E., (1999). Calculation of an optimal region of operation for dual response systems fitted from experimental data, Journal of the Operational Research Society 50(8): 826-836. | Zbl 1054.90532

[013] Fathi, Y., (1991). A nonlinear programming approach to the parameter design problem, European Journal of Operational Research 53(3): 371-381. | Zbl 0729.90594

[014] Hwang, C. L. and Masud, A. S. Md., (1979). Multiple Objective Decision Making Methods and Applications, Springer, Berlin. | Zbl 0397.90001

[015] Jeong, I. and Kim, K., (2005). D-STEM: A modified step method with desirability function concept, Computers and Operations Research 32(12): 3175-3190. | Zbl 1178.90307

[016] Khattree, P., (1996). Robust parameter design: A response surface approach, Journal of Quality Technology 28(2): 187-198.

[017] Khuri A. I., (1996). Response surface models with mixed effects, Journal of Quality Technology 28(2): 177-186.

[018] Kim, Y. J., and Cho, B. R., (2002). Development of prioritybased robust design, Quality Engineering 14(3): 355-363.

[019] Kim, K. and Lin, D. K. J., (1998). Dual response surface optimization: A fuzzy modeling approach, Journal of Quality Technology 30(1): 1-10.

[020] Koksoy, O. and Doganaksoy, N., (2003). Joint optimization of mean and standard deviation using response surface methods, Journal of Quality Technology 35(3): 239-252.

[021] Kunert, J., Auer, C., Erdbrugge, M. and Ewers, R., (2007). An experiment to compare Taguchi's product array and the combined array, Journal of Quality Technology 39(1): 17-34.

[022] Lin, D. and Tu, W., (1995). Dual response surface optimization, Journal of Quality Technology 27(1): 34-39.

[023] Lucas, J. M., (1994). How to achieve a robust process using response surface methodology, Journal of Quality Technology 25(3): 248-260.

[024] Montgomery, D. C., (1990). Using fractional factorial designs for robust process development, Quality Engineering 3(2): 193-205.

[025] Montgomery, D. C., (1999). Experimental design for product and process design and development, Journal of the Royal Statistical Society D 48(2): 159-177.

[026] Myers, R. H., Kim, Y. and Griffiths, K. L., (1997). Response surface methods and the use of noise variables, Journal of Quality Technology 29(4): 429-440.

[027] Myers, R. H., Khuri, A. I. and Vining, G. G., (1992). Response surface alternatives to the Taguchi robust parameter design approach, The American Statistician 46(2): 131-139.

[028] Myers, R. H., Montgomery, D. C., Vining, G. G., Kowalski, S. M. and Borror, C. M. (2004). Response surface methodology: A retrospective and current literature review, Journal of Quality Technology 36(1): 53-77.

[029] Myers, R. H. and Montgomery, D. C. (2002). Response Surface Methodology: Process and Product Optimization using Designed Experiments, 2nd Ed., Wiley, New York, NY. | Zbl 1161.62393

[030] Nair, V. N., (1992). Taguchi's parameter design: A panel discussion, Technometrics 34(2): 127-161.

[031] Nelder, J. A. and Mead, R., (1965). A simplex method for function minimization, Computer Journal 7(4): 308-313. | Zbl 0229.65053

[032] Pignatiello, J. J. Jr. and Ramberg, J. S., (1991). The topten triumphs and tragedies of Genichi Taguchi, Quality Engineering 4(2): 211-225.

[033] Pledger, M., (1996). Observable uncontrollable factors in parameter design, Journal of Quality Technology 28(2): 153-162.

[034] Romano, D., Varetto, M. and Vicario, G., (2004). Multiresponse robust design: A general framework based on combined array, Journal of Quality Technology 36(1): 27-37.

[035] Shoemaker, A. C., Tsui, K. L. and Wu, C. F. J., (1991). Economical experimentation methods for robust parameter design, Technometrics 33(4): 415-427.

[036] Taguchi, G., (1987), System of Experimental Design: Engineering Methods to Optimize Quality and Minimize Cost, Quality Resources, White Plains, NJ.

[037] Tang, L. C. and Xu, K., (2002). A unified approach for dual response optimization, Journal of Quality Technology 34(4): 437-447.

[038] Vining, G. G. and Myers, R. H., (1990). Combining Taguchi and response surface philosophies: A dual response approach, Journal of Quality Technology 22(1): 38-45.

[039] Welch, W. J., Yu, T. K., Kang, S. M. and Sacks, J., (1990). Computer experiments for quality control by parameter design, Journal of Quality Technology 22(1): 15-22.