DP-Optimality in Terms of Multiple Criteria and Its Application to the Split-Plot Design

References

• Atkinson, A. C.; Donev, A. N.; and Tobias, R. D. (2007). Optimum Experimental Designs, with SAS. New York, NY: Oxford University Press.
   Google Scholar
• Box, M. J. and Draper, N. P. (1971). “Factorial Designs, the |Y′Y| Criterion, and Some Related Matters”. Technometrics 13, pp. 731–742.
   Web of Science ®Google Scholar
• Box, G. and Jones, S. (1992). “Split-Plot Designs for Robust Product Experimentation”. Journal of Applied Statistics 19, pp. 3–26.
   Google Scholar
• Cao, Y.; Smucker, B. J.; and Robinson, T. J. (2016). “Hybrid Elitist Pareto-Based Coordinate Exchange Algorithm for Constructing Multi-Criteria Optimal Experimental Designs”. Statistics and Computing, DOI:10.1007/s11222-016-9630-9.
   Google Scholar
• Das, I. and Dennis, J. E. (1997). “Closer Look at Drawbacks of Minimizing Weighted Sums of Weighted Objectives for Pareto Set Generation in Multicriteria Optimization Problems”. Structural Optimization 14, pp. 63–69.
   Web of Science ®Google Scholar
• Gilmour, S. G. and Trinca, L. A. (2012). “Optimum Design of Experiments for Statistical Inference”. Applied Statistics 61, pp. 1–25.
   Web of Science ®Google Scholar
• Goos, P. (2002). The Optimal Design of Blocked and Split-Plot Experiments. New York, NY: Springer.
   Google Scholar
• Goos, P. (2006). “Optimal Versus Orthogonal and Equivalent-Estimation Design of Blocked and Split-Plot Experiments”. Statistica Neerlandica 60, pp. 361–378.
   Web of Science ®Google Scholar
• Goos, P.; Langhans, I.; and Vandebroek, M. (2006). “Practical Inference from Industrial Split-Plot Designs”. Journal of Quality Technology 38, pp. 162–179.
   Web of Science ®Google Scholar
• Goos, P. and Vandebroek, M. (2001). “Optimal Split-Plot Designs”. Journal of Quality Technology 33, pp. 436–450.
   Web of Science ®Google Scholar
• Goos, P. and Vandebroek, M. (2003). “D-Optimal Split-Plot Designs with Given Numbers and Sizes of Whole Plots”. Technometrics 45, pp. 235–245.
   Web of Science ®Google Scholar
• Harville, D. A. (1997). Matrix Algebra from A Statistician's Perspective. New York, NY: Springer.
   Google Scholar
• Jones, B. and Goos, P. (2007). “Candidate-Set-Free Algorithm for Generating D-Optimal Split-Plot Designs”. Journal of the Royal Statistical Society, Series C 56, pp. 347–364.
   Web of Science ®Google Scholar
• Jones, B. and Goos, P. (2011). Optimal Design of Experiments: A Case Study Approach. Hoboken, NJ: Wiley.
   Google Scholar
• Jones, B. and Goos, P. (2012). “An Algorithm for Finding D-Efficient Equivalent-Estimation Second-Order Split-Plot Designs”. Journal of Quality Technology 44, pp. 363–374.
   Web of Science ®Google Scholar
• Kowalski, S. M.; Parker, P. A.; and Vining, G. G. (2007). “Tutorial: Industrial Split-Plot Experiments”. Quality Engineering 19, pp. 1–15.
   Google Scholar
• Letsinger, J. D.; Myers, R. H.; and Lentner, M. (1996). “Response Surface Methods for Bi-Randomization Structures”. Journal of Quality Technology 28, pp. 381–397.
   Web of Science ®Google Scholar
• Lu, L.; Anderson-Cook, C. M.; and Robinson, T. J. (2011). “Optimization of Designed Experiments Based on Multiple Criteria Utilizing a Pareto Frontier”. Technometrics 61, pp. 353–365.
   Web of Science ®Google Scholar
• Macharia, H. and Goos, P. (2010). “D-Optimal and D-Efficient Equivalent-Estimation Second-Order Split-Plot Designs”. Journal of Quality Technology 42, pp. 358–372.
   Web of Science ®Google Scholar
• Meyer, R. K. and Nachtsheim, C. J. (1995). “The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs”. Technometrics 37, pp. 60–69.
   Web of Science ®Google Scholar
• Nguyen, N. K. and Miller, A. J. (1992). “A Review of Some Exchange Algorithms for Constructing Discrete D-Optimal Designs”. Computational Statistics and Data Analysis 14, pp. 489–498.
   Web of Science ®Google Scholar
• Parker, P. A.; Kowalski, S. M.; and Vining, G. G. (2007). “Construction of Balanced Equivalent Estimation Second-Order Split-Plot Designs”. Technometrics 49, pp. 56–65.
   Web of Science ®Google Scholar
• Robinson, T. J. and Anderson-Cook, C. M. (2011), “A Closer Look at D-Optimality for Screening Designs”. Quality Engineering 23, pp. 1–14.
   Web of Science ®Google Scholar
• Schott, J. R. (1997). Matrix Analysis for Statistics. New York, NY: John Wiley # Sons.
   Google Scholar
• Vining, G. G. and Kowalski, S. M. (2008). “Exact Inference for Response Surface Designs Within a Split-Plot Structure”. Journal of Quality Technology 40, pp. 394–406.
   Web of Science ®Google Scholar
• Vining, G. G.; Kowalski, S. M.; and Montgomery, D. C. (2005). “Response Surface Designs Within a Split-Plot Structure”. Journal of Quality Technology 37, pp. 115–129.
   Web of Science ®Google Scholar