Space-Filling Designs for Robustness Experiments

ABSTRACT To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of accurately estimating the control-by-noise interactions. Moreover, the existing space-filling designs focus on uniformly distributing the points in the design space, which are not suitable for noise factors because they usually follow nonuniform distributions such as normal distribution. This would suggest placing more points in the regions with high probability mass. However, noise factors also tend to have a smooth relationship with the response and therefore, placing more points toward the tails of the distribution is also useful for accurately estimating the relationship. These two opposing effects make the experimental design methodology a challenging problem. We propose optimal and computationally efficient solutions to this problem and demonstrate their advantages using simulated examples and a real industry example involving a manufacturing packing line. Supplementary materials for the article are available online.

[1]  Shreyes N. Melkote,et al.  Analysis of Computer Experiments With Functional Response , 2012, Technometrics.

[2]  Holger Dette,et al.  Generalized Latin Hypercube Design for Computer Experiments , 2010, Technometrics.

[3]  V. Roshan Joseph,et al.  Space-filling designs for computer experiments: A review , 2016 .

[4]  V. R. Joseph,et al.  Maximum projection designs for computer experiments , 2015 .

[5]  Luc Pronzato,et al.  Efficient prediction designs for random fields , 2013, Applied stochastic models in business and industry.

[6]  R. Gunst.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[7]  Jeongbae Kim,et al.  A cautious approach to robust design with model parameter uncertainty , 2011 .

[8]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[9]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[10]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[11]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[12]  V. Roshan Joseph,et al.  Quality Loss Functions for Nonnegative Variables and Their Applications , 2004 .

[13]  Derek Bingham,et al.  Design and Analysis of Experiments on Non-Convex Regions , 2016 .

[14]  Ron S. Kenett,et al.  Achieving Robust Design from Computer Simulations , 2006 .

[15]  Derek Bingham,et al.  Design and Analysis of Experiments on Nonconvex Regions , 2017, Technometrics.

[16]  Gregory E. Fasshauer,et al.  Kernel-based Approximation Methods using MATLAB , 2015, Interdisciplinary Mathematical Sciences.

[17]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[18]  C. F. Jeff Wu,et al.  Experiments , 2021, Wiley Series in Probability and Statistics.

[19]  V. Roshan Joseph,et al.  Support points , 2016, The Annals of Statistics.

[20]  Thomas J. Santner,et al.  Sequential design of computer experiments to minimize integrated response functions , 2000 .

[21]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[22]  Laura Ilzarbe,et al.  A New Design Criterion for Robust Parameter Experiments , 2007 .

[23]  Lulu Kang,et al.  Bayesian Optimal Single Arrays for Robust Parameter Design , 2009, Technometrics.

[24]  Kwok-Leung Tsui,et al.  Economical experimentation methods for robust design , 1991 .

[25]  Ruichen Jin,et al.  Analytical Global Sensitivity Analysis and Uncertainty Propagation for Robust Design , 2006 .

[26]  Irad Ben-Gal,et al.  Designing experiments for robust-optimization problems: the V s-optimality criterion , 2006 .

[27]  Matthias Hwai Yong Tan,et al.  Robust Parameter Design With Computer Experiments Using Orthonormal Polynomials , 2015, Technometrics.

[28]  William I. Notz,et al.  DESIGNING COMPUTER EXPERIMENTS TO DETERMINE ROBUST CONTROL VARIABLES , 2004 .

[29]  V. Roshan Joseph,et al.  Minimax and Minimax Projection Designs Using Clustering , 2016, 1602.03938.

[30]  Luc Pronzato,et al.  Relations Between Designs for Prediction and Estimation in Random Fields: An Illustrative Case , 2012 .

[31]  Daniel W. Apley,et al.  Understanding the effects of model uncertainty in robust design with computer experiments , 2006, DAC 2006.

[32]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[33]  Randy R. Sitter,et al.  Fractional Factorial Split-Plot Designs for Robust Parameter Experiments , 2003, Technometrics.

[34]  Jerome Sacks,et al.  Computer Experiments for Quality Control by Parameter Design , 1990 .

[35]  A. Zhigljavsky,et al.  A New Approach to Optimal Design for Linear Models With Correlated Observations , 2010 .

[36]  Paul L. Zador,et al.  Asymptotic quantization error of continuous signals and the quantization dimension , 1982, IEEE Trans. Inf. Theory.

[37]  C. F. Jeff Wu,et al.  Robust Design Optimization With Quadratic Loss Derived From Gaussian Process Models , 2012, Technometrics.

[38]  Arnold J. Stromberg,et al.  Number-theoretic Methods in Statistics , 1996 .

[39]  James M. Calvin,et al.  Optimal random non-adaptive algorithm for global optimization of Brownian motion , 1996, J. Glob. Optim..

[40]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[41]  S. M. Handcock.  On cascading latin hypercube designs and additive models for experiments , 1991 .

[42]  Yu Zhu,et al.  OPTIMAL SELECTION OF SINGLE ARRAYS FOR PARAMETER DESIGN EXPERIMENTS , 2003 .