# zbMATH — the first resource for mathematics

Augmenting supersaturated designs with Bayesian $$D$$-optimality. (English) Zbl 06975453
Summary: A methodology is developed to add runs to existing supersaturated designs. The technique uses information from the analysis of the initial experiment to choose the best possible follow-up runs. After analysis of the initial data, factors are classified into one of three groups: primary, secondary, and potential. Runs are added to maximize a Bayesian $$D$$-optimality criterion to increase the information gained about those factors. Simulation results show the method can outperform existing supersaturated design augmentation strategies that add runs without analyzing the initial response variables.

##### MSC:
 62 Statistics
Full Text:
##### References:
 [1] Abraham, B.; Chipman, H.; Vijayan, K., Some risks in the construction and analysis of supersaturated designs, Technometrics, 41, 2, 135-141, (1999) [2] Atkinson, A. C.; Donev, A. N.; Tobias, R. D., Optimum experimental designs, with SAS. (vol. 34), (2007), Oxford University Press Oxford [3] Booth, K.; Cox, D. R., Some systematic supersaturated designs, Technometrics, 4, 4, 489-495, (1962) · Zbl 0109.12201 [4] Box, G. E.P., George’s column, Quality Engineering, 5, 2, 321-330, (1992) [5] Box, G. E.P.; Hunter, J. S.; Hunter, W. G., Statistics for experimenters: design, innovation, and discovery, (2005), John Wiley & Sons Hoboken, NJ · Zbl 1082.62063 [6] Box, G. E.P.; Meyer, R. D., An analysis for unreplicated fractional factorials, Technometrics, 28, 1, 11-18, (1986) · Zbl 0586.62168 [7] Box, G. E.P.; Meyer, R. D., Finding the active factors in fractionated screening experiments, Journal of Quality Technology, 25, 2, 94-105, (1993) [8] Bulutoglu, D. A.; Cheng, C. S., Construction of $$E(s^2)$$-optimal supersaturated designs, The Annals of Statistics, 32, 4, 1662-1678, (2004) · Zbl 1105.62362 [9] Chaloner, K.; Verdinelli, I., Bayesian experimental design: a review, Statistical Science, 10, 3, 273-304, (1995) · Zbl 0955.62617 [10] Daniel, C., Use of half-normal plots in interpreting factorial two-level experiments, Technometrics, 1, 4, 311-341, (1959) [11] DuMouchel, W.; Jones, B., A simple Bayesian modification of $$D$$-optimal designs to reduce dependence on an assumed model, Technometrics, 36, 1, 37-47, (1994) · Zbl 0800.62472 [12] Edwards, D. J.; Mee, R. W., Supersaturated designs: are our results significant?, Computational Statistics & Data Analysis, 55, 9, 2652-2664, (2011) · Zbl 06917722 [13] Georgiou, S., Supersaturated designs: a review of their construction and analysis, Journal of Statistical Planning and Inference, (2012) [14] Georgiou, S. D., Modelling by supersaturated designs, Computational Statistics & Data Analysis, 53, 2, 428-435, (2008) · Zbl 1231.62146 [15] Goos, P.; Jones, B., Optimal design of experiments, (2011), John Wiley & Sons New York, NY [16] Gupta, V. K.; Chatterjee, K.; Das, A.; Kole, B., Addition of runs to an $$s$$-level supersaturated design, Journal of Statistical Planning and Inference, 142, 8, 2402-2408, (2012) · Zbl 1244.62109 [17] Gupta, S.; Kohli, P., Analysis of supersaturated designs: a review, Journal of the Indian Society of Agricultural Statistics, 62, 2, 156-168, (2008) · Zbl 1188.62254 [18] Gupta, V. K.; Singh, P.; Kole, B.; Parsad, R., Addition of runs to a two-level supersaturated design, Journal of Statistical Planning and Inference, 140, 9, 2531-2535, (2010) · Zbl 1188.62218 [19] Jones, B.; Dumouchel, W., Follow-up designs to resolve confounding in multifactor experiments: discussion, Technometrics, 38, 4, 323-326, (1996) [20] Jones, B.; Lin, D. K.J.; Nachtsheim, C. J., Bayesian $$D$$-optimal supersaturated designs, Journal of Statistical Planning and Inference, 138, 1, 86-92, (2008) · Zbl 1144.62058 [21] Kiefer, J.; Wolfowitz, J., Optimum designs in regression problems, The Annals of Mathematical Statistics, 30, 2, 271-304, (1959), (with discussion) · Zbl 0090.11404 [22] Lin, D. K.J., A new class of supersaturated designs, Technometrics, 35, 1, 28-31, (1993) [23] Lin, D. K.J., Industrial experimentation for screening, (Rao, C. R; Khattree, R., Handbook of Statistics, Vol. 22, (2003), North Holland New York), (Chapter 2) [24] Lin, D. K.J., Generating systematic supersaturated designs, Technometrics, 37, 2, 213-225, (1995) · Zbl 0822.62062 [25] Li, P.; Zhao, S.; Zhang, R., A cluster analysis selection strategy for supersaturated designs, Computational Statistics & Data Analysis, 54, 6, 1605-1612, (2010) · Zbl 1284.62381 [26] Marley, C. J.; Woods, D. C., A comparison of design and model selection methods for supersaturated experiments, Computational Statistics & Data Analysis, 54, 12, 3158-3167, (2010) · Zbl 1284.62477 [27] Meyer, R. K.; Nachtsheim, C. J., The coordinate-exchange algorithm for constructing exact optimal experimental designs, Technometrics, 37, 1, 60-69, (1995) · Zbl 0825.62652 [28] Meyer, R. D.; Steinberg, D. M.; Box, G., Follow-up designs to resolve confounding in multifactor experiments, Technometrics, 38, 4, 303-313, (1996) · Zbl 0902.62088 [29] Montgomery, D. C., Design and analysis of experiments, (2009), John Wiley & Sons New York, NY [30] Neff, A.R., 1996. Bayesian two stage design under model uncertainty. Ph.D. Dissertation. Virginia Polytechnic Institute and State University. [31] Nguyen, N. K., An algorithmic approach to constructing supersaturated designs, Technometrics, 38, 1, 69-73, (1996) · Zbl 0900.62416 [32] Plackett, R. L.; Burman, J. P., The design of optimum multifactorial experiments, Biometrika, 33, 4, 305-325, (1946) · Zbl 0063.06274 [33] Pukelsheim, F., Optimal design of experiments, (1993), John Wiley & Sons New York, NY · Zbl 0834.62068 [34] Ruggoo, A.; Vandebroek, M., Bayesian sequential $$D D$$-optimal model-robust designs, Computational Statistics & Data Analysis, 47, 4, 655-673, (2004) · Zbl 1429.62343 [35] Satterthwaite, F. E., Random balanced experimentation, Technometrics, 1, 2, 111-137, (1959), (with discussion) [36] Suen, C.; Das, A., $$E(s^2)$$-optimal supersaturated designs with odd number of runs, Journal of Statistical Planning and Inference, 140, 6, 1398-1409, (2010) · Zbl 1185.62135 [37] Wu, C. F.J., Construction of supersaturated designs through partially aliased interactions, Biometrika, 80, 3, 661-669, (1993) · Zbl 0800.62483 [38] Wu, C. F.J.; Hamada, M., Experiments: planning, analysis, and parameter design optimization, (2000), Wiley New York, NY · Zbl 0964.62065
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.