Supersaturated designs: A review of their construction and analysis

Journal of Statistical Planning and Inference

Volumn 144, Issue 1, 2014, Pages 92-109

  Georgiou, Stelios D ^a  

^a UNIVERSITY OF THE AEGEAN   (Greece)

Author keywords

Factorial design; Optimal designs; Orthogonal design; Saturated design; Screening designs

Indexed keywords

EID: 84888039819     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2012.09.014     Document Type: Article

References (109)

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