Screening Experiments for Dispersion Effects

Reduction of the variability in performance of products and manufacturing processes is crucial to the achievement of high levels of quality. Designed experiments can play an important role in this effort by identifying factors with dispersion effects, that is, factors that affect performance variability. Methods are presented for the design and analysis of experiments whose goal is the rapid screening of a list of candidate factors to find those with large dispersion effects. Several types of experiments are considered, including “robust design experiments” with noise factors, and both replicated and unreplicated fractional factorial experiments. We conclude that the effective use of noise factors is the most successful way to screen for dispersion effects. Problems are identified that arise in the various analyses proposed for unreplicated factorial experiments. Although these methods can be successful in screening for dispersion effects, they should be used with caution.

[1]  P. Rosenbaum.  DISPERSION EFFECTS FROM FRACTIONAL FACTORIALS IN TAGUCHI'S METHOD OF QUALITY DESIGN , 1994 .

[2]  R. Wolfinger,et al.  Joint estimation of location, dispersion, and random effects in robust design , 1998 .

[3]  G. Pan.  The Impact of Unidentified Location Effects on Dispersion-Effects Identification From Unreplicated Factorial Designs , 1999, Technometrics.

[4]  Douglas C. Montgomery,et al.  Experimental Design for Product and Process Design and Development , 1999 .

[5]  Vijayan N. Nair,et al.  EXPLOITING THE INHERENT STRUCTURE IN ROBUST PARAMETER DESIGN EXPERIMENTS , 1998 .

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

[7]  P. C. Wang.  Testing dispersion effects from general unreplicated fractional factorial designs , 2001 .

[8]  Dennis K. J. Lin,et al.  Testing Multiple Dispersion Effects in Unreplicated Fractional Factorial Designs , 2001, Technometrics.

[9]  William A. Brenneman.  Inference for location and dispersion effects in unreplicated factorial experiments. , 2000 .

[10]  A. Ferrer,et al.  Small samples estimation of dispersion effects from unreplicated data , 1993 .

[11]  David M. Steinberg,et al.  Dispersion Effects in Robust-Design Experiments with Noise Factors , 1994 .

[12]  John A. Nelder,et al.  Generalized linear models for the analysis of quality‐improvement experiments , 1998 .

[13]  Vijayan N. Nair,et al.  Methods for Identifying Dispersion Effects in Unreplicated Factorial Experiments , 2001, Technometrics.

[14]  David M. Steinberg,et al.  7 Robust design: Experiments for improving quality , 1996, Design and analysis of experiments.

[15]  R. Lenth.  Quick and easy analysis of unreplicated factorials , 1989 .

[16]  James M. Lucas,et al.  Designs of mixed resolution for process robustness studies , 1997 .

[17]  G. Pan,et al.  On Generalized Linear Model Method for Detecting Dispersion Effects in Unreplicated Factorial Designs , 2002 .

[18]  B. Bergman,et al.  Identification of factors influencing dispersion in split-plot experiments , 2001 .

[19]  Madhan Shridhar Phadke,et al.  Quality Engineering Using Robust Design , 1989 .

[20]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[21]  R. H. Myers,et al.  Response Surface Alternatives to the Taguchi Robust Parameter Design Approach , 1992 .

[22]  Ola Blomkvist,et al.  A METHOD TO IDENTIFY DISPERSION EFFECTS FROM UNREPLICATED MULTILEVEL EXPERIMENTS , 1997 .

[23]  John A. Nelder,et al.  Generalized linear models for the analysis of Taguchi-type experiments , 1991 .

[24]  S. Weisberg,et al.  Diagnostics for heteroscedasticity in regression , 1983 .

[25]  A. Verbyla,et al.  Modelling Variance Heterogeneity: Residual Maximum Likelihood and Diagnostics , 1993 .

[26]  C. F. Jeff Wu,et al.  Experiments: Planning, Analysis, and Parameter Design Optimization , 2000 .

[27]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[28]  M. S. Bartlett,et al.  Some examples of statistical methods of research in agriculture and applied biology , 1937 .

[29]  Neil R. Ullman,et al.  Signal-to-noise ratios, performance criteria, and transformations , 1988 .

[30]  D. Pregibon,et al.  Analyzing dispersion effects from replicated factorial experiments , 1988 .

[31]  G. Geoffrey Vining,et al.  Combining Taguchi and Response Surface Philosophies: A Dual Response Approach , 1990 .

[32]  D. Montgomery.  USING FRACTIONAL FACTORIAL DESIGNS FOR ROBUST PROCESS DEVELOPMENT , 1990 .

[33]  M. Aitkin.  Modelling variance heterogeneity in normal regression using GLIM , 1987 .

[34]  R. H. Myers.  Generalized Linear Models: With Applications in Engineering and the Sciences , 2001 .

[35]  A. S. Hedayat,et al.  Compound Orthogonal Arrays , 1999, Technometrics.

[36]  B. Bergman,et al.  Dispersion Effects From 7 Unreplicated Designs in the 2 k—p Series , 1997 .

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

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

[39]  C. Liao.  Identification of dispersion effects from unreplicated 2 n- K fractional factorial designs , 2000 .

[40]  Dennis K. J. Lin,et al.  A nonparametric dispersion test for unreplicated two-level fractional factorial designs , 2002 .

[41]  J. Nelder,et al.  JOINT MODELING OF MEAN AND DISPERSION , 1998 .

[42]  Simultaneous estimation of location and dispersion in two-level fractional factorial designs , 1999 .

[43]  Nasser Fard,et al.  Estimation of dispersion effects from robust design experiments with censored response data , 2001 .

[44]  Rafael Romero,et al.  A SIMPLE METHOD TO STUDY DISPERSION EFFECTS FROM NON- NECESSARILY REPLICATED DATA IN INDUSTRIAL CONTEXTS , 1995 .

[45]  P. C. Wang.  Tests for dispersion effects from orthogonal arrays , 1989 .

[46]  Bruce E. Ankenman,et al.  Ch. 8. Quality improvement and robustness via design of experiments , 2003 .

[47]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[48]  George E. P. Box,et al.  Dispersion Effects From Fractional Designs , 1986 .

[49]  P. Rosenbaum.  Some useful compound dispersion experiments in quality design , 1996 .

[50]  J. Engel,et al.  A generalized linear modeling approach to robust design , 1996 .

[51]  B. Bergman,et al.  Dispersion effects from unreplicated designs in the 2 k-p series , 1997 .

[52]  David M. Steinberg,et al.  NOISE FACTORS, DISPERSION EFFECTS, AND ROBUST DESIGN , 1993 .