Keywords
simultaneous optimization
global optima
ccontours
optimización
optimización simultánea
óptimos
óptimo global
contornos
How to Cite
Abstract
The simultaneous optimization problem may not to have a complete satisfactory solution from the point of view of the individual responses, in the sense that individual optimums are different respect to global optimum; but always it is possible to say that it exists the process operation conditions (point in the factors space) where the responses fit “in the best way” to their specification limits and target values. It is always possible to obtain a compromise solution, which look for the best balance between the responses. This paper discusses several methods that have been proposed for analyzing multi-response data, and it is shown that the graphical method can raise the best solution compared with the analytical methods. The performance of the methods is compared in the context of one example. Finally, in two of the methods we suggest alternative weighting of the responses in order to improve the results.
References
Ames, A. E.; Mattucci, M.; Stephen, M.; Szony, G.; Hawkins, D. M. (1997) “Quality loss functions for optimization across multiple response surfaces”, Journal of Quality Technology 29: 339–346.
Box, G. E. P.; Hunter, J. S.; Hunter, W. G. (1988) Estadística para Investigadores. Editorial Reverté, Barcelona.
Copeland, K. A. F.; Nelson, P. R. (1996) “Dual response optimization via direct function minimization”, Journal of Quality Technology 28: 331–336.
Cornell, J. A. (1990) How to Apply Response Surface Methodology. ASQC Press, Milwaukee WS.
Del Castillo, E. (1996) “Multiresponse process optimization via constrained confidence regions”, Journal of Quality Technology 28: 61–70.
Del Castillo, E.; Montgomery, D. C.; McCarville, D.R. (1996) “Modified desirability functions for multiple response optimization”, Journal of Quality Technology 28: 337–345.
Derringer, G.; Suich, R. (1980) “Simultaneous optimization of several response variables”, Journal of Quality Technology 12: 214–219.
Derringer, G. (1994) “A balancing act: optimizing a product’s properties”, Quality Progress : 51–58.
Desig-expert (1991) Stat-Ease, Version 2.02. Minneapolis, MN.
Harrington, E. C. Jr. (1965) “The desirability function”, Industrial Quality Control 21: 494–498.
Khuri, A.; Conlon, M. (1981) “Simultaneous optimization of multiple responses represented by polynomial regression functions”, Technometrics 23: 363–375.
Khuri, A.; Cornell, J. A. (1997) Response Surfaces: Designs and Analyses. Second Edition. Marcel Dekker, New York.
Lin, D. K. J.; Tu, W. (1995) “Dual response surface optimization”, Journal of Quality Technology 27: 34–39.
Myers, R. H.; Montgomery, D. C. (1995) Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons, New York.
Nelder, J. A.; Mead, R. (1965) “A simplex method for function minimization”, The Computer Journal 7: 308–313.
SAS Institute (1990) SAS Versión 6.0. SAS Institute, Cary NC.
Spiring, F. A. (1997) “A unifying approach to process capability indices”, Journal of Quality Technology 29: 49–58.