Balancing Location and Dispersion Effects for Multiple Responses

In robust design studies, location and dispersion effects play different roles, and balancing them when there are multiple responses is an important and challenging task. We propose to use desirability function to simultaneously optimize multiple responses after assigning weights to reflect the relative importance of location and dispersion effects. Our analytical strategy is to plot the solutions obtained from different weights versus the weights and/or some aspects of the solutions versus the weights. These plots provide valuable information that can be useful in choosing one or more compromise solutions to balance the multiple location and dispersion effects. The proposed approach is illustrated using two real problems. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  C. Anderson‐Cook.  Response Surfaces, Mixtures, and Ridge Analyses , 2008 .

[2]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[3]  R. H. Myers,et al.  Response Surface Techniques for Dual Response Systems , 1973 .

[4]  Dennis K. J. Lin,et al.  Optimization of multiple responses considering both location and dispersion effects , 2006, Eur. J. Oper. Res..

[5]  S. Gilmour,et al.  Characterisation of colloidal gas aphrons for subsequent use for protein recovery , 1997 .

[6]  John J. Peterson.  A Posterior Predictive Approach to Multiple Response Surface Optimization , 2004 .

[7]  M. Deaton,et al.  Response Surfaces: Designs and Analyses , 1989 .

[8]  Anthony C. Atkinson,et al.  Multiresponse optimization with consideration of probabilistic covariates , 2011, Qual. Reliab. Eng. Int..

[9]  Robert D. Plante,et al.  Process capability: a criterion for optimizing multiple response product and process design , 2001 .

[10]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[11]  Wen Wan,et al.  A semiparametric technique for the multi‐response optimization problem , 2011, Qual. Reliab. Eng. Int..

[12]  Mostafa K. Ardakani,et al.  An Overview of Optimization Formulations for Multiresponse Surface Problems , 2013, Qual. Reliab. Eng. Int..

[13]  William T. Scherer,et al.  "The desirability function: underlying assumptions and application implications" , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[14]  Zhuoyan Hu,et al.  Desirability function approach for the optimization of microwave-assisted extraction of saikosaponins from Radix Bupleuri , 2008 .

[15]  L. Tang,et al.  A Unified Approach for Dual Response Surface Optimization , 2002 .

[16]  Kwang-Jae Kim,et al.  Expected Desirability Function: Consideration of Both Location and Dispersion Effects in Desirability Function Approach , 2007 .

[17]  M. Hamada,et al.  Analyzing Experiments with Correlated Multiple Responses , 2001 .