D- and A-Optimal Screening Designs

References

• Ahipaşaoğlu, S. D. (2021), “A Branch-and-Bound Algorithm for the Exact Optimal Experimental Design Problem,” Statistics and Computing, 31, 65. DOI: 10.1007/s11222-021-10043-5.
   Web of Science ®Google Scholar
• Allen-Moyer, K., and Stallrich, J. (2022), “Incorporating Minimum Variances into Weighted Optimality Criteria,” The American Statistician, 76, 262–269. DOI: 10.1080/00031305.2021.1947375.
   Web of Science ®Google Scholar
• Atkinson, A. C., Donev, A. N., and Tobias, R. D. (2007), Optimum Experimental Design, with SAS, Oxford: Oxford University Press.
   Google Scholar
• Bingham, D. R., and Chipman, H. A. (2007), “Incorporating Prior Information in Optimal Design for Model Selection,” Technometrics, 49, 155–163. DOI: 10.1198/004017007000000038.
   Web of Science ®Google Scholar
• Bisgaard, S. (1994), “A Note on the Definition of Resolution for Blocked 2k−p Designs,” Technometrics, 36, 308–311.
   Web of Science ®Google Scholar
• Box, M., and Draper, N. R. (1971), “Factorial Designs, the |XTX| Criterion, and some Related Matters,” Technometrics, 13, 731–742.
   Web of Science ®Google Scholar
• Byrd, R. H., Lu, P., Nocedal, J., and Zhu, C. (1995), “A Limited Memory Algorithm for Bound Constrained Optimization,” SIAM Journal on Scientific Computing, 16, 1190–1208. DOI: 10.1137/0916069.
   Web of Science ®Google Scholar
• Chen, H., and Cheng, C.-S. (1999), “Theory of Optimal Blocking of 2n−m Designs,” Annals of Statistics, 27, 1948–1973.
   Web of Science ®Google Scholar
• Chen, H. H., and Cheng, C.-S. (2004), “Aberration, Estimation Capacity and Estimation Index,” Statistica Sinica, 14, 203–215.
   Web of Science ®Google Scholar
• Cheng, C.-S. (1980), “Optimality of Some Weighing and 2n Fractional Factorial Designs,” The Annals of Statistics, 8, 436–446.
   Web of Science ®Google Scholar
• Cheng, C.-S. (2014a), “Optimal Biased Weighing Designs and Two-Level Main-Effect Plans,” Journal of Statistical Theory and Practice, 8, 83–99.
   Google Scholar
• Cheng, C.-S. (2014b), Theory of Factorial Design: Single- and Multi-Stratum Experiments (1st ed), Boca Raton: Taylor and Francis.
   Google Scholar
• Cheng, C.-S., and Mukerjee, R. (2001), “Blocked Regular Fractional Factorial Designs with Maximum Estimation Capacity,” Annals of Statistics, 29, 530–548.
   Web of Science ®Google Scholar
• Cheng, S.-W., Li, W., and Ye, K. Q. (2004), “Blocked Nonregular Two-Level Factorial Designs,” Technometrics, 46, 269–279. DOI: 10.1198/004017004000000301.
   Web of Science ®Google Scholar
• Cheng, S.-W., and Wu, C. F. J. (2002), “Choice of Optimal Blocking Schemes in Two-Level and Three-Level Designs,” Technometrics, 44, 269–277. DOI: 10.1198/004017002188618455.
   Web of Science ®Google Scholar
• Cook, R. D., and Nachtsheim, C. J. (1989), “Computer-Aided Blocking of Factorial and Response-Surface Designs,” Technometrics, 31, 339–346. DOI: 10.1080/00401706.1989.10488556.
   Web of Science ®Google Scholar
• Dean, A., and Lewis, S. (2006), Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics, New York: Springer.
   Google Scholar
• Dinkelbach, W. (1967), “On Nonlinear Fractional Programming,” Management Science, 13, 492–498. DOI: 10.1287/mnsc.13.7.492.
   Google Scholar
• Duarte, B. P. M., Granjo, J. O., and Wong, W. K. (2020), “Optimal Exact Designs of Experiments via Mixed Integer Nonlinear Programming,” Statistics and Computing, 30, 93–112. DOI: 10.1007/s11222-019-09867-z.
   Web of Science ®Google Scholar
• DuMouchel, W., and Jones, B. (1994), “A Simple Bayesian Modification of D-Optimal Designs to Reduce Dependence on an Assumed Model,” Technometrics, 36, 37–47. DOI: 10.2307/1269197.
   Web of Science ®Google Scholar
• Esteban-Bravo, M., Leszkiewicz, A., and Vidal-Sanz, J. M. (2017), “Exact Optimal Experimental Designs with Constraints,” Statistics and Computing, 27, 845–863. DOI: 10.1007/s11222-016-9658-x.
   Web of Science ®Google Scholar
• Fang, K.-T., Zhang, A., and Li, R. (2007), “An Effective Algorithm for Generation of Factorial Designs with Generalized Minimum Aberration,” Journal of Complexity, 23, 740–751. DOI: 10.1016/j.jco.2007.03.010.
   PubMed Web of Science ®Google Scholar
• Galil, Z., and Kiefer, J. (1980), “D-Optimum Weighing Designs,” Annals of Statistics, 8, 1293–1306.
   Web of Science ®Google Scholar
• Gilmour, S. G., and Trinca, L. A. (2012), “Optimum Design of Experiments for Statistical Inference,” Journal of the Royal Statistical Society, Series C, 61, 345–401. DOI: 10.1111/j.1467-9876.2011.01000.x.
   Web of Science ®Google Scholar
• Goos, P., and Jones, B. (2011), A Screening Experiment in Blocks, chap. 8, pp. 163–185, West Sussex: Wiley.
   Google Scholar
• Jacroux, M., Wong, C., and Masaro, J. (1983), “On the Optimality of Chemical Balance Weighing Designs,” Journal of Statistical Planning and Inference, 8, 231–240. DOI: 10.1016/0378-3758(83)90041-1.
   Web of Science ®Google Scholar
• Jones, B., Allen-Moyer, K., and Goos, P. (2020), “A-Optimal versus D-Optimal Design of Screening Experiments,” Journal of Quality Technology, 53, 369–382. DOI: 10.1080/00224065.2020.1757391.
   Web of Science ®Google Scholar
• Jones, B., Lekivetz, R., Majumdar, D., Nachtsheim, C. J., and Stallrich, J. W. (2020), “Construction, Properties, and Analysis of Group-Orthogonal Supersaturated Designs,” Technometrics, 62, 403–414. DOI: 10.1080/00401706.2019.1654926.
   Web of Science ®Google Scholar
• Jones, B., and Nachtsheim, C. J. (2011a), “A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects,” Journal of Quality Technology, 43, 1–15. DOI: 10.1080/00224065.2011.11917841.
   Web of Science ®Google Scholar
• Jones, B., and Nachtsheim, C. J. (2011b), “Efficient Designs with Minimal Aliasing,” Technometrics, 53, 62–71.
   Web of Science ®Google Scholar
• Jones, B., and Nachtsheim, C. J. (2017), “Effective Design-Based Model Selection for Definitive Screening Designs,” Technometrics, 59, 319–329.
   Web of Science ®Google Scholar
• Joseph, V. R. (2006), “A Bayesian Approach to the Design and Analysis of Fractionated Experiments,” Technometrics, 48, 219–229. DOI: 10.1198/004017005000000652.
   Web of Science ®Google Scholar
• Li, W., and Nachtsheim, C. J. (2000), “Model-Robust Factorial Designs,” Technometrics, 42, 345–352. DOI: 10.1080/00401706.2000.10485707.
   Web of Science ®Google Scholar
• Li, X., Sudarsanam, N., and Frey, D. D. (2006), “Regularities in Data from Factorial Experiments,” Complexity, 11, 32–45. DOI: 10.1002/cplx.20123.
   Web of Science ®Google Scholar
• Masaro, J. C. (1983), “Optimality of Chemical Balance Weighing Designs,” Ph.D. thesis, University of Windsor.
   Google Scholar
• Meyer, R. K., and Nachtsheim, C. J. (1995), “The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs,” Technometrics, 37, 60–69. DOI: 10.1080/00401706.1995.10485889.
   Web of Science ®Google Scholar
• Mitchell, T. J. (1974), “An Algorithm for the Construction of D-Optimal Experimental Designs,” Technometrics, 16, 203–210. DOI: 10.2307/1267940.
   Web of Science ®Google Scholar
• Mukerjee, R., and Wu, C. F. J. (2006), A Modern Theory of Factorial Designs (1st ed.), New York: Springer.
   Google Scholar
• Schoen, E. D., Vo-Thanh, N., and Goos, P. (2017), “Two-Level Orthogonal Screening Designs With 24, 28, 32, and 36 Runs,” Journal of the American Statistical Association, 112, 1354–1369. DOI: 10.1080/01621459.2017.1279547.
   Web of Science ®Google Scholar
• Sherman, J., and Morrison, W. J. (1950), “Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix,” The Annals of Mathematical Statistics, 21, 124–127. DOI: 10.1214/aoms/1177729893.
   Google Scholar
• Smucker, B. J., del Castillo, E., and Rosenberger, J. L. (2012), “Model-Robust Two-Level Designs Using Coordinate Exchange Algorithms and a Maximin Criterion,” Technometrics, 54, 367–375. DOI: 10.1080/00401706.2012.694774.
   Web of Science ®Google Scholar
• Stallings, J. W., and Morgan, J. P. (2015), “General Weighted Optimality of Designed Experiments,” Biometrika, 102, 925–935. DOI: 10.1093/biomet/asv037.
   Web of Science ®Google Scholar
• Toman, B. (1994), “Bayes Optimal Designs for Two- and Three-Level Factorial Experiments,” Journal of the American Statistical Association, 89, 937–946. DOI: 10.1080/01621459.1994.10476827.
   Web of Science ®Google Scholar
• Tsai, P.-W., and Gilmour, S. G. (2010), “A General Criterion for Factorial Designs Under Model Uncertainty,” Technometrics, 52, 231–242. DOI: 10.1198/TECH.2010.08093.
   Web of Science ®Google Scholar
• Tsai, P.-W., Gilmour, S. G., and Mead, R. (2007), “Three-Level Main-Effects Designs Exploiting Prior Information About Model Uncertainty,” Journal of Statistical Planning and Inference, 137, 619–627. DOI: 10.1016/j.jspi.2006.01.003.
   Web of Science ®Google Scholar
• Vazquez, A. R., Schoen, E. D., and Goos, P. (2022), “Two-Level Orthogonal Screening Designs with 80, 96, and 112 Runs, and up to 29 Factors,” Journal of Quality Technology, 54, 338–358. DOI: 10.1080/00224065.2021.1916412.
   Web of Science ®Google Scholar
• Wong, C. S., and Masaro, J. C. (1984), “A-Optimal Design Matrices X=(xij)N×n with xij={−1,0,1},” Linear and Multilinear Algebra, 15, 23–46.
   Google Scholar
• Wu, C. F. J., and Hamada, M. (2009), Experiments: Planning, Analysis, Optimization, Hoboken, NJ: Wiley.
   Google Scholar