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Journal of Quality Technology
A Quarterly Journal of Methods, Applications and Related Topics
Volume 24, 1992 - Issue 1
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Articles

Variance Dispersion Properties of Second-Order Response Surface Designs

Raymond H. MyersVirginia Polytechnic Institute and State University, Blacksburg, VA24061View further author information
,
G. Geoffrey ViningUniversity of Florida, Gainesville, FL32611View further author information
,
Ann Giovannitti-JensenBF Goodrich Chemical Group, Avon Lake, OH44012View further author information
&
Sharon L. MyersRadford University, Radford, VA24141View further author information
Pages 1-11 | Published online: 21 Feb 2018

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Bharat Tarapara & Jyoti Divecha. (2023) Practical efficient alpha: Encompassing all alphas of central composite design. Communications in Statistics - Simulation and Computation 52:4, pages 1621-1629.
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John J. Borkowski, Wanida Limmun & Boonorm Chomtee. (2022) Factorwise variance dispersion graphs. Communications in Statistics - Theory and Methods 51:23, pages 8427-8445.
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M. Hemavathi, Shashi Shekhar, Eldho Varghese, Seema Jaggi, Bikas Sinha & Nripes Kumar Mandal. (2022) Theoretical developments in response surface designs: an informative review and further thoughts. Communications in Statistics - Theory and Methods 51:7, pages 2009-2033.
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Charity Uchenna Onwuamaeze. (2021) Optimal prediction variance properties of some central composite designs in the hypercube. Communications in Statistics - Theory and Methods 50:8, pages 1911-1924.
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Juntao Fang, Zhen He & Linxi Song. (2015) Evaluation of Response Surface Designs in Presence of Errors in Factor Levels. Communications in Statistics - Theory and Methods 44:18, pages 3769-3781.
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DouglasC. Montgomery. (2014) Stu Hunter's Contributions to Experimental Design and Quality Engineering. Quality Engineering 26:1, pages 5-15.
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Myrta Rodríguez, Bradley Jones, Connie M. Borror & Douglas C. Montgomery. (2010) Generating and Assessing Exact G-Optimal Designs. Journal of Quality Technology 42:1, pages 3-20.
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WayneR. Wesley, JamesR. Simpson, PeterA. Parker & JosephJ. Pignatiello$suffix/text()$suffix/text(). (2009) Maximum and Minimum Prediction Variance for Spherical and Cuboidal Split Plot Designs. Communications in Statistics - Theory and Methods 38:13, pages 2251-2266.
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Wayne R. Wesley, James R. Simpson, Peter A. Parker & Joseph J. Pignatiello$suffix/text()$suffix/text(). (2009) Exact Calculation of Integrated Prediction Variance for Response Surface Designs on Cuboidal and Spherical Regions. Journal of Quality Technology 41:2, pages 165-180.
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WayneR. Wesley, JamesR. Simpson, PeterA. Parker & JosephR. Pignatiello$suffix/text()$suffix/text(). (2008) Analytical Characterization of the Information Matrix for Split-Plot Designs. Communications in Statistics - Theory and Methods 38:1, pages 90-102.
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Robert W. Mee. (2007) Optimal Three-Level Designs for Response Surfaces in Spherical Experimental Regions. Journal of Quality Technology 39:4, pages 340-354.
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Li Liang, Christine M Anderson-Cook, Timothy J Robinson & Raymond H Myers. (2006) Three-Dimensional Variance Dispersion Graphs for Split-Plot Designs. Journal of Computational and Graphical Statistics 15:4, pages 757-778.
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You-Jin Park, Diane E. Richardson, Douglas C. Montgomery, Ayca Ozol-Godfrey, Connie M. Borror & Christine M. Anderson-Cook. (2005) Prediction Variance Properties of Second-Order Designs for Cuboidal Regions. Journal of Quality Technology 37:4, pages 253-266.
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Heidi B. Goldfarb, Connie M. Borror, Douglas C. Montgomery & Christine M. Anderson-Cook. (2004) Evaluating Mixture-Process Designs with Control and Noise Variables. Journal of Quality Technology 36:3, pages 245-262.
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Heidi B. Goldfarb, Christine M. Anderson-Cook, Connie M. Borror & Douglas C. Montgomery. (2004) Fraction of Design Space Plots for Assessing Mixture and Mixture-Process Designs. Journal of Quality Technology 36:2, pages 169-179.
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Guillermo Miró-Quesada & Enrique Del Castillo. (2004) Two Approaches for Improving the Dual Response Method in Robust Parameter Design. Journal of Quality Technology 36:2, pages 154-168.
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Heidi B. Goldfarb, Connie M. Borror, Douglas C. Montgomery & Christine M. Anderson-Cook. (2004) Three-Dimensional Variance Dispersion Graphs for Mixture-Process Experiments. Journal of Quality Technology 36:1, pages 109-124.
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Raymond H. Myers, Douglas C. Montgomery, G. Geoffrey Vining, Connie M. Borror & Scott M. Kowalski. (2004) Response Surface Methodology: A Retrospective and Literature Survey. Journal of Quality Technology 36:1, pages 53-77.
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Alyaa Zahran, Christine M. Anderson-Cook & Raymond H. Myers. (2003) Fraction of Design Space to Assess Prediction Capability of Response Surface Designs. Journal of Quality Technology 35:4, pages 377-386.
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Connie M. Borror, Douglas C. Montgomery & Raymond H. Myers. (2002) Evaluation of Statistical Designs for Experiments Involving Noise Variables. Journal of Quality Technology 34:1, pages 54-70.
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John J Borkowski & Elsie S Valeroso. (2001) Comparison of Design Optimality Criteria of Reduced Models for Response Surface Designs in the Hypercube. Technometrics 43:4, pages 468-477.
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Shu-Kai S. Fan. (2000) A Generalized Global Optimization Algorithm for Dual Response Systems. Journal of Quality Technology 32:4, pages 444-456.
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André I. Khuri. (1999) Discussion. Journal of Quality Technology 31:1, pages 58-60.
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Luzia A. Trinca & Steven G. Gilmour. (1998) Variance Dispersion Graphs for Comparing Blocked Response Surface Designs. Journal of Quality Technology 30:4, pages 314-327.
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Enrique Del Castillo, Shu-Kai Fan & John Semple. (1997) The Computation of Global Optima in Dual Response Systems. Journal of Quality Technology 29:3, pages 347-353.
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JohnJ. Borkowski. (1995) Spherical Prediction-Variance Properties of Central Composite and Box—Behnken Designs. Technometrics 37:4, pages 399-410.
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D. R. Jensen. (1995) C432. Efficiency comparisons of central composite designs. Journal of Statistical Computation and Simulation 52:2, pages 177-183.
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John J. Borkowski. (1995) Minimum, maximum, and average spherical prediction variances for central composite and box-behnken designs. Communications in Statistics - Theory and Methods 24:10, pages 2581-2600.
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John J. Borkowski. (1995) Finding maximum G-criterion values for central composite designs on the hypercube. Communications in Statistics - Theory and Methods 24:8, pages 2041-2058.
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G. Geoffrey Vining. (1993) A Computer Program for Generating Variance Dispersion Graphs. Journal of Quality Technology 25:1, pages 45-58.
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Jun Zhang & Fan Guo. (2015) Statistical modification analysis of helical planetary gears based on response surface method and Monte Carlo simulation. Chinese Journal of Mechanical Engineering 28:6, pages 1194-1203.
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Norman R. Draper. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
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André I. Khuri & Siuli Mukhopadhyay. (2010) Response surface methodology. WIREs Computational Statistics 2:2, pages 128-149.
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Wayne R. Wesley, James R. Simpson, Peter A. Parker & Joseph J. PignatielloJrJr. (2008) Prediction variance and G‐criterion location for split‐plot designs. Quality and Reliability Engineering International 25:4, pages 381-395.
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Christine M. Anderson-Cook, Connie M. Borror & Douglas C. Montgomery. (2009) Response surface design evaluation and comparison. Journal of Statistical Planning and Inference 139:2, pages 629-641.
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Norman R. Draper. 2007. Encyclopedia of Statistics in Quality and Reliability. Encyclopedia of Statistics in Quality and Reliability.
John J. Borkowski. 2007. Encyclopedia of Statistics in Quality and Reliability. Encyclopedia of Statistics in Quality and Reliability.
Shu‐Kai S. Fan & Kuo‐Nan Huang. (2007) AMSE optimal design using generalized estimation for multi‐factor response surfaces. Journal of Chemometrics 21:3-4, pages 126-132.
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İnci Batmaz & Semra Tunali. (2003) Small response surface designs for metamodel estimation. European Journal of Operational Research 145:2, pages 455-470.
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C. M. Borror & D. C. Montgomery. (2000) Mixed resolution designs as alternatives to Taguchi inner/outer array designs for robust design problems. Quality and Reliability Engineering International 16:2, pages 117-127.
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M. Farooq Anjum, Imran Tasadduq & Khaled Al-Sultan. (1997) Response surface methodology: A neural network approach. European Journal of Operational Research 101:1, pages 65-73.
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AndréI. Khuri, Hyuk Joo Kim & Yonghwan Um. (1996) Quantile plots of the prediction variance for response surface designs. Computational Statistics & Data Analysis 22:4, pages 395-407.
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D. R. Jensen. (2007) Efficiency Indices for Second‐Order Designs. Biometrical Journal 37:1, pages 65-80.
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D.R. Jensen. (1994) Efficiencies of some small second-order designs. Statistics & Probability Letters 21:4, pages 255-261.
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