×

Supersaturated designs: a review of their construction and analysis. (English) Zbl 1278.62125

Summary: Supersaturated designs are fractional factorial designs in which the run size \((n)\) is too small to estimate all the main effects. Under the effect sparsity assumption, the use of supersaturated designs can provide the low-cost identification of the few, possibly dominating factors (screening). Several methods for constructing and analyzing two-, multi-, or mixed-level supersaturated designs have been proposed in the recent literature. A brief review of the construction and analysis of supersaturated designs is given in this paper.

MSC:

62K15 Factorial statistical designs
62K05 Optimal statistical designs

Software:

CodingTheory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Abraham, B.; Chipman, H.; Vijayan, K., Some risks in the construction and analysis of supersaturated designs, Technometrics, 41, 135-141, (1999)
[2] Aggarwal, M. L.; Gupta, S., A new method of construction of multi-level supersaturated designs, Journal of Statistical Planning and Inference, 121, 127-134, (2004) · Zbl 1038.62068
[3] Ai, M.; Fang, K.-T.; He, S., \(E(\chi^2) \operatorname{-} \operatorname{optimal}\) multi-level supersaturated designs, Journal of Statistical Planning and Inference, 137, 306-316, (2007) · Zbl 1098.62097
[4] Allen, T. T.; Bernshteyn, M., Supersaturated designs, that maximize the probability of identifying active factors, Technometrics, 45, 90-97, (2003)
[5] Beattie, S. D.; Fong, D. K.H.; Lin, D. K.J., A two-stage Bayesian model selection strategy for supersaturated designs, Technometrics, 44, 55-63, (2002)
[6] Booth, K. H.V.; Cox, D. R., Some systematic supersaturated designs, Technometrics, 4, 489-495, (1962) · Zbl 0109.12201
[7] Box, G. E.P.; Meyer, R. D., An analysis for unreplicated fractional factorials, Technometrics, 28, 11-18, (1986) · Zbl 0586.62168
[8] Bulutoglu, D. A.; Cheng, C. S., Construction of \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Annals of Statistics, 32, 1662-1678, (2004) · Zbl 1105.62362
[9] Bulutoglu, D. A., Cyclicly constructed \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Journal of Statistical Planning and Inference, 137, 2413-2428, (2007) · Zbl 1125.62081
[10] Bulutoglu, D. A.; Ryan, K. J., \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs with good minmax properties when N is odd, Journal of Statistical Planning and Inference, 138, 1754-1762, (2008) · Zbl 1131.62069
[11] Butler, N.; Mead, R.; Eskridge, K. M.; Gilmour, S. G., A general method of constructing \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Journal of the Royal Statistical Society, 63, 621-632, (2001) · Zbl 1040.62064
[12] Butler, N., Minimax 16-run supersaturated designs, Statistics and Probability Letters, 73, 139-145, (2005) · Zbl 1065.62132
[13] Butler, N., Supersaturated Latin hypercube designs, Communications in Statistics—Theory and Methods, 34, 417-428, (2005) · Zbl 1062.62144
[14] Butler, N., Two-level supersaturated designs for 2^{k} runs and other cases, Journal of Statistical Planning and Inference, 139, 23-29, (2009) · Zbl 1154.62057
[15] Chai, F.-S.; Chatterjee, K.; Gupta, S., Generalized \(E(s^2)\) criterion for multilevel supersaturated designs, Communications in Statistics—Theory and Methods, 38, 3725-3735, (2009) · Zbl 1177.62091
[16] Chatterjee, K.; Gupta, S., Construction of supersaturated designs involving s-level factors, Journal of Statistical Planning and Inference, 113, 589-595, (2003) · Zbl 1014.62093
[17] Chatterjee, K.; Koukouvinos, C.; Mylona, K., A new lower bound to A_{2}-optimality measure for multi-level and mixed level column balanced designs and its applications, Journal of Statistical Planning and Inference, 141, 877-888, (2011) · Zbl 1353.62087
[18] Chen, J.; Lin, D. K.J., On the identifiability of a supersaturated designs, Journal of Statistical Planning and Inference, 72, 99-107, (1998) · Zbl 1055.62541
[19] Chen, J.; Liu, M.-Q., Optimal mixed-level supersaturated designs with general number of runs, Statistics and Probability Letters, 78, 2496-2502, (2008) · Zbl 1456.62164
[20] Chen, J.; Liu, M.-Q., Optimal mixed-level k-circulant supersaturated designs, Journal of Statistical Planning and Inference, 138, 4151-4157, (2008) · Zbl 1146.62055
[21] Cheng, C. S., \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Statistica Sinica, 7, 929-939, (1997) · Zbl 1067.62560
[22] Cheng, C. S.; Tang, B., Upper bounds on the number of columns in supersaturated designs, Biometrika, 88, 1169-1174, (2001) · Zbl 0986.62064
[23] Chipman, H.; Hamada, H.; Wu, C. F.J., A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing, Technometrics, 39, 372-381, (1997) · Zbl 1063.62528
[24] Cossari, A., Applying box-Meyer method for analyzing supersaturated designs, Quality Technology and Quantitative Management, 5, 393-401, (2008)
[25] Das, A.; Dey, A.; Chan, L. Y.; Chatterjee, K., \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Journal of Statistical Planning and Inference, 138, 3749-3757, (2008) · Zbl 1394.62101
[26] Deng, L.-Y.; Lin, D. J.K.; Wang, J., A measurement of multi-factor orthogonality, Statistics and Probability Letters, 28, 203-209, (1996) · Zbl 0854.62065
[27] Deng, L.-Y.; Lin, D. J.K.; Wang, J., Marginally oversaturated designs, Communications in Statistics—Theory and Methods, 25, 2557-2573, (1996) · Zbl 0870.62061
[28] Deng, L.-Y.; Lin, D. J.K.; Wang, J., A resolution rank criterion for supersaturated designs, Statistica Sinica, 9, 605-610, (1999) · Zbl 0921.62097
[29] Edwards, D. J.; Mee, R. W., Supersaturated designsare our results significant?, Computational Statistics and Data Analysis, 55, 2652-2664, (2011) · Zbl 1464.62063
[30] Eskridge, K. M.; Gilmour, S. G.; Mead, R.; Butler, N. A.; Travnicek, D. A., Large supersaturated designs, Journal of Statistical Computation and Simulation, 74, 525-542, (2004) · Zbl 1061.62112
[31] Fang, K. T.; Lin, D. K.J.; Ma, C. X., On the construction of multi-level supersaturated designs, Journal of Statistical Planning and Inference, 86, 239-252, (2000) · Zbl 0964.62078
[32] Fang, L. T.; Ge, G.; Liu, M.-Q., Uniform supersaturated designs and its construction, Science in China, Series A, 45, 1080-1088, (2002) · Zbl 1098.62104
[33] Fang, L. T.; Lin, D. J.K.; Liu, M.-Q., Optimal mixed-level supersaturated designs, Metrika, 58, 279-291, (2003) · Zbl 1042.62073
[34] Fang, L. T.; Ge, G.; Liu, M.-Q., Construction of optimal supersaturated designs by the packing method, Science in China, Series A, 47, 128-143, (2004) · Zbl 1217.62105
[35] Fang, L. T.; Ge, G.; Liu, M.-Q.; Qin, H., Combinatorial construction for optimal supersaturated designs, Discrete Mathematics, 279, 191-202, (2004) · Zbl 1035.62076
[36] George, E. I.; McCulloch, R. E., Variable selection via Gibbs sampling, Journal of the American Statistical Association, 88, 881-889, (1993)
[37] Georgiou, S.; Koukouvinos, C.; Mantas, P., Construction methods for three-level supersaturated designs based on weighing matrices, Statistics and Probability Letters, 63, 339-352, (2003) · Zbl 1116.62382
[38] Georgiou, S.; Koukouvinos, C., Multi-level k-circulant supersaturated designs, Metrika, 64, 209-220, (2006) · Zbl 1100.62076
[39] Georgiou, S.; Koukouvinos, C.; Mantas, P., Multi-level supersaturated designs based on error correcting codes, Utilitas Mathematica, 71, 65-82, (2006) · Zbl 1104.62088
[40] Georgiou, S.; Koukouvinos, C.; Mantas, P., A new method for the construction of two-level \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Journal of Statistical Theory and Applications, 5, 403-415, (2006)
[41] Georgiou, S.; Koukouvinos, C.; Mantas, P., On multi-level supersaturated designs, Journal of Statistical Planning and Inference, 136, 2805-2819, (2006) · Zbl 1090.62075
[42] Georgiou, S. D., On the construction of \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs, Metrika, 69, 189-198, (2008) · Zbl 1433.62233
[43] Georgiou, S. D., Modelling by supersaturated designs, Computational Statistics and Data Analysis, 53, 428-435, (2008) · Zbl 1231.62146
[44] Georgiou, S. D.; Draguljić, D.; Dean, A., An overview of two-level supersaturated designs with cyclic structure, Journal of Statistical Theory and Practice, 3, 489-504, (2009) · Zbl 1211.62135
[45] Gilmour, S. G., Supersaturated designs in factor screening, (Lewis, S. M.; Dean, A. M., Screening, (2006), Springer New York), 169-190
[46] Gupta, S.; Kohli, P., Analysis of supersaturated designsa review, Journal of Indian Society of Agricultural Statistics, 62, 156-168, (2008) · Zbl 1188.62254
[47] Gupta, V. K.; Parsad, R.; Kole, B.; Bhar, L., Computer-generated efficient two-level supersaturated designs, Journal of Indian Society of Agricultural Statistics, 62, 183-194, (2008) · Zbl 1188.62256
[48] 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, 2531-2535, (2010) · Zbl 1188.62218
[49] Gupta, S.; Hisano, K.; Morales, L. B., Optimal k-circulant supersaturated designs, Journal of Statistical Planning and Inference, 141, 782-786, (2011) · Zbl 1353.62088
[50] Gupta, S.; Morales, L. B., Constructing \(E(s^2) \operatorname{-} \operatorname{optimal}\) and minimax-optimal k-circulant supersaturated designs via multi-objective tabu search, Journal of Statistical Planning and Inference, 142, 1415-1420, (2012) · Zbl 1242.62081
[51] 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, 2402-2408, (2012) · Zbl 1244.62109
[52] Holcomb, D. R.; Montgomery, D. C.; Carlyle, W. M., Analysis of supersaturated designs, Journal of Quality Technology, 35, 13-27, (2003)
[53] Holcomb, D. R.; Montgomery, D. C.; Carlyle, W. M., The use of supersaturated experiments in turbine engine development, Quality Engineering, 19, 17-27, (2007)
[54] Jones, B. A.; Li, W.; Nachtheim, C. J.; Ye, K. Q., Model-robust supersaturated and partially supersaturated designs, Journal of Statistical Planning and Inference, 139, 45-53, (2009) · Zbl 1154.62058
[55] Kole, B.; Gangwani, J.; Gupta, V. K.; Parsad, R., Two level supersaturated designsa review, Journal of Statistical Theory and Practice, 4, 598-608, (2010)
[56] Koukouvinos, C.; Stylianou, S., Optimal multi-level supersaturated designs constructed from linear and quadratic functions, Statistics and Probability Letters, 69, 199-211, (2004) · Zbl 1075.62060
[57] Koukouvinos, C.; Stylianou, S., A method for analyzing supersaturated designs, Communications in Statistics—Simulation, 34, 929-937, (2005) · Zbl 1089.62094
[58] Koukouvinos, C.; Mantas, P., Construction of some \(E(f_{\mathit{NOD}}) \operatorname{-} \operatorname{optimal}\) mixed-level supersaturated designs, Statistics and Probability Letters, 74, 312-321, (2005) · Zbl 1116.62079
[59] Koukouvinos, C.; Mantas, P.; Mylona, K., A general construction of \(E(f_{\mathit{NOD}}) \operatorname{-} \operatorname{optimal}\) mixed-level supersaturated designs, Sankhya, 69, 358-372, (2007) · Zbl 1193.62133
[60] Koukouvinos, C.; Mylona, K.; Simos, D. E., Exploring k-circulant supersaturated designs via genetic algorithms, Computational Statistics and Data Analysis, 51, 2958-2968, (2007) · Zbl 1161.62391
[61] Koukouvinos, C.; Mantas, P.; Mylona, K., A general construction of \(E(s^2) \operatorname{-} \operatorname{optimal}\) large supersaturated designs, Metrika, 68, 99-110, (2008) · Zbl 1433.62214
[62] Koukouvinos, C.; Mylona, K.; Simos, D. E., \(E(s^2) \operatorname{-} \operatorname{optimal}\) and minimax-optimal supersaturated designs via multi-objective simulated annealing, Journal of Statistical Planning and Inference, 138, 1639-1646, (2008) · Zbl 1131.62071
[63] Koukouvinos, C.; Mylona, K., A method for analyzing supersaturated designs with a block orthogonal structure, Communications in Statistics—Simulation, 37, 290-300, (2008) · Zbl 1132.62058
[64] Koukouvinos, C.; Mylona, K.; Simos, D. E., A hybrid SAGA algorithm for the construction of \(E(s^2) \operatorname{-} \operatorname{optimal}\) cyclic supersaturated designs, Journal of Statistical Planning and Inference, 139, 478-485, (2009) · Zbl 1149.62065
[65] Koukouvinos, C.; Mylona, K., Group screening method for the statistical analysis of \(E(f_{\mathit{NOD}}) \operatorname{-} \operatorname{optimal}\) mixed-level supersaturated designs, Statistical Methodology, 6, 380-388, (2009)
[66] Koukouvinos, C.; Mylona, K., A general construction of \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs via supplementary difference sets, Metrika, 70, 257-265, (2009) · Zbl 1433.62215
[67] Koukouvinos, C.; Massou, E.; Mylona, K.; Parpoula, C., Analyzing supersaturated designs with entropic measures, Journal of Statistical Planning and Inference, 141, 1307-1312, (2011) · Zbl 1274.62503
[68] Li, R.; Lin, D. K.J., Data analysis in supersaturated designs, Statistics and Probability Letters, 59, 135-144, (2002) · Zbl 1092.62570
[69] Li, R.; Lin, D. K.J., Analysis methods for supersaturated designssome comparisons, Journal of Data Science, 1, 249-260, (2003)
[70] Li, W. W.; Wu, C. F.J., Columnwise-pairwise algorithms with applications to the construction of supersaturated designs, Technometrics, 39, 171-179, (1997) · Zbl 0889.62066
[71] Li, P.-F.; Liu, M.-Q.; Zhang, R.-C., Some theory and the construction of mixed-level supersaturated designs, Statistics and Probability Letters, 69, 105-116, (2004) · Zbl 1116.62383
[72] Li, P.; Zao, S.; Zhang, Z., A cluster analysis selection strategy for supersaturated designs, Computational Statistics and Data Analysis, 54, 1605-1612, (2010) · Zbl 1284.62381
[73] Lin, D. K.J., A new class of supersaturated designs, Technometrics, 35, 28-31, (1993)
[74] Lin, D. K.J., Generating systematic supersaturated designs, Technometrics, 37, 213-225, (1995) · Zbl 0822.62062
[75] Liu, M.-Q.; Zhang, R., Construction of \(E(s^2)\) optimal supersaturated designs using cyclic bibds, Journal of Statistical Planning and Inference, 91, 139-150, (2000) · Zbl 0958.62066
[76] Liu, M.-Q.; Hickernell, F. J., \(E(s^2) \operatorname{-} \operatorname{optimality}\) and minimum discrepancy in 2-level supersaturated designs, Statistica Sinica, 12, 931-939, (2002) · Zbl 1002.62059
[77] Liu, Y. F.; Dean, A. M., K-circulant supersaturated designs, Technometrics, 46, 32-43, (2004)
[78] Liu, Y.; Liu, M.-Q.; Zhang, R., Construction of multi-level supersaturated designs via Kronecker product, Journal of Statistical Planning and Inference, 137, 2984-2992, (2007) · Zbl 1115.62077
[79] Liu, Y. F.; Ruan, S.; Dean, A. M., Construction and analysis of Es^{2} efficient supersaturated designs, Journal of Statistical Planning and Inference, 137, 1516-1529, (2007) · Zbl 1110.62101
[80] Liu, M.-Q.; Kai, Z.-Y., Construction of mixed-level supersaturated designs by the substitution method, Statistica Sinica, 19, 1705-1719, (2009) · Zbl 1191.62137
[81] Liu, M.-Q.; Lin, D. K.J., Construction of optimal mixed-level supersaturated designs, Statistica Sinica, 19, 197-211, (2009) · Zbl 1153.62057
[82] Liu, Y.; Liu, M.-Q., Construction of optimal supersaturated designs with large number of levels, Journal of Statistical Planning and Inference, 141, 2035-2043, (2011) · Zbl 1419.62196
[83] Liu, Y.; Liu, M.-Q., Construction of equidistant and weak equidistant supersaturated designs, Metrika, 75, 33-53, (2012) · Zbl 1241.62111
[84] Lu, X.; Wu, X., A strategy of searching active factors in supersaturated screening experiments, Journal of Quality Technology, 36, 392-399, (2004)
[85] Mandal, B. N.; Gupta, V. K.; Parsad, R., Construction of efficient mixed-level k-circulant supersaturated designs, Journal of Statistical Theory and Practice, 5, 627-648, (2011)
[86] Marley, C. J.; Woods, D. C., A comparison of design and model selection methods for supersaturated experiments, Computational Statistics and Data Analysis, 54, 3158-3167, (2010) · Zbl 1284.62477
[87] Nguyen, N. K., An algorithmic approach to constructing supersaturated designs, Technometrics, 38, 69-73, (1996) · Zbl 0900.62416
[88] Nguyen, N. K.; Cheng, C.-S., New \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs constructed from incomplete block designs, Technometrics, 50, 26-31, (2008)
[89] Niki, N.; Iwata, M.; Hashiguchi, H.; Yamata, S., Optimal selection and ordering of columns in supersaturated designs, Journal of Statistical Planning and Inference, 141, 2449-2462, (2011) · Zbl 1214.62081
[90] Phoa, F. K.H.; Pan, Y.-H.; Xu, H., Analysis of supersaturated designs via the Dantzig selector, Journal of Statistical Planning and Inference, 139, 2362-2372, (2009) · Zbl 1160.62071
[91] Ryan, K. J.; Bulutoglu, D. A., \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs with good minmax properties, Journal of Statistical Planning and Inference, 137, 2250-2262, (2007) · Zbl 1120.62059
[92] Sakar, A.; Lin, D. K.J.; Chatterjee, K., Probability of correct model identification in supersaturated designs, Statistics and Probability Letters, 79, 1224-1230, (2009) · Zbl 1160.62342
[93] Satterthwaite, F. E., Random balance experimentation (with discussions), Technometrics, 1, 111-137, (1959)
[94] Srivastava, N.J., 1975. Designs for searching for non-negligible effects. In: A Survey of Statistical Designs and Linear Models, North-Holland, Amsterdam, pp. 507-519.
[95] Suen, C. S.; Das, A., \(E(s^2) \operatorname{-} \operatorname{optimal}\) supersaturated designs with odd number of runs, Journal of Statistical Planning and Inference, 140, 1398-1409, (2010) · Zbl 1185.62135
[96] Sun, F.; Lin, D. K.J.; Liu, M.-Q., On construction of optimal mixed-level supersaturated designs, Annals of Statistics, 39, 1310-1333, (2011) · Zbl 1215.62073
[97] Tang, B.; Wu, C. F.J., A method for constructing supersaturated designs and its Es^{2} optimality, Canadian Journal of Statistics, 25, 191-201, (1997) · Zbl 0891.62054
[98] Tang, Y.; Ai, M.; Ge, G.; Fang, K.-T., Optimal mixed-level supersaturated designs and a new class of combinatorial designs, Journal of Statistical Planning and Inference, 137, 2294-2301, (2007) · Zbl 1120.62060
[99] Westfall, P. H.; Young, S. S.; Lin, D. K.J., Forward selection error control in the analysis of supersaturated designs, Statistica Sinica, 8, 101-117, (1998) · Zbl 0886.62077
[100] Wu, C. F.J., Construction of supersaturated designs through partially aliased interactions, Biometrika, 80, 661-669, (1993) · Zbl 0800.62483
[101] Xu, H., Minimum moment aberration for nonregular designs and supersaturated designs, Statistica Sinica, 13, 691-708, (2003) · Zbl 1028.62063
[102] Xu, H.; Wu, C. F.J., Construction of optimal multi-level supersaturated designs, Annals of Statistics, 33, 2811-2836, (2005) · Zbl 1084.62070
[103] Yamada, S.; Lin, D. K.J., Supersaturated designs including an orthogonal base, Canadian Journal of Statistics, 25, 203-213, (1997) · Zbl 0891.62056
[104] Yamada, S.; Lin, D. K.J., Three-level supersaturated designs, Statistics and Probability Letters, 45, 31-39, (1999) · Zbl 0958.62071
[105] Yamada, S.; Ikebe, Y. T.; Hashiguchi, H.; Niki, N., Construction of three-level supersaturated designs, Journal of Statistical Planning and Inference, 81, 183-193, (1999) · Zbl 0939.62083
[106] Yamada, S.; Matsui, T., Optimality of mixed-level supersaturated designs, Journal of Statistical Planning and Inference, 104, 459-468, (2002) · Zbl 0992.62069
[107] Yamata, S., Selection of active factors by stepwise regression in the data analysis of supersaturated design, Quality Engineering, 16, 501-513, (2004)
[108] Yamata, S.; Matsui, M.; Matsui, T.; Lin, D. K.J.; Takahashi, T., A general construction method for mixed-level supersaturated design, Computational Statistics and Data analysis, 50, 254-265, (2006) · Zbl 1429.62352
[109] Zhang, Q. Z.; Zhang, R. C.; Liu, M. Q., A method for screening active effects in supersaturated designs, Journal of Statistical Planning and Inference, 137, 235-248, (2006)
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.