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 Blocking is a good technique to reduce the variations in factorial experiments. The method of construction by Sun, Wu, and Chen (1997) is to use the fractional factorial designs by Chen, Sun, and Wu (1993) to generate blocking schemes. In this paper, we propose an algorithm for constructing blocking schemes. For example we want to construct a 2(n+k)-k fractional factorial design arranged in 2q blocks. The method of construction is to use 2n-0 full factorial to generate 2n-0 full factorial in 2q blocking designs, and then use the latter to generate 2(n+k)-(0+k) fractional factorial in 2q blocking designs. A collection of the blocking schemes with 16, 32, 64, 128 runs is given in the Appendix 6.2B. Our construction also finds some optimal blocking schemes by multiple criterions proposed by Sun, Wu, and Chen (1997). These schemes are marked "☆". This paper also provides two examples of semi-folding factorial designs, and the two designs can also be regarded as Taguchi's parameter designs.
 Blocking is a good technique to reduce the variations in factorial experiments. The method of construction by Sun, Wu, and Chen (1997) is to use the fractional factorial designs by Chen, Sun, and Wu (1993) to generate blocking schemes. In this paper, we propose an algorithm for constructing blocking schemes. For example we want to construct a 2(n+k)-k fractional factorial design arranged in 2q blocks. The method of construction is to use 2n-0 full factorial to generate 2n-0 full factorial in 2q blocking designs, and then use the latter to generate 2(n+k)-(0+k) fractional factorial in 2q blocking designs. A collection of the blocking schemes with 16, 32, 64, 128 runs is given in the Appendix 6.2B. Our construction also finds some optimal blocking schemes by multiple criterions proposed by Sun, Wu, and Chen (1997). These schemes are marked "☆". This paper also provides two examples of semi-folding factorial designs, and the two designs can also be regarded as Taguchi's parameter designs.
 1 Introduction 1 1.1 Preliminary 3 1.2 Notation and Definition 4 2 Construction of Blocking Schemes 13 2.1 Isomorphism of Blocking Schemes 13 2.2 Construction Method 19 3 Semi-Folding Design with Taguchi’s Design 39 4 Summary 47 5 Bibliography 49 6 Appendix 50 6.1 Appendix A 50 6.2 Appendix B 53
 [1] Bisgaard, S. (1994a), “Blocking Generators for Small 2k-p Designs,” Journal of Quality Technology, 26, 288-296.[2] Bisgaard, S. (1994b), “A Note on the Definition of Resolution for Blocked 2k-p Designs,” Journal of Quality Technology, 26, 288-296[3] Box, G.E.P, Hunter, W.G., and Hunter, J.S. (1978), Statistics for Experiments, New York: John Wiley & Sons.[4] Chen, J., Sun, D.X., and Wu, C.F.J. (1993), “ A Catalogue of Two-Level and Three-Level Fractional Factorial Designs with Small Runs,” International Statistical Review, 61, 131-145.[5] Douglas C. Montgomery (2001), Design and Analysis of Experiments, New York: John Wiley & Sons.[6] Fries, A. and Hunter, W.G. (1980), “Minimum Aberration 2k-p Designs,” Technometrics, 22, 601-608.[7] Sun, D.X., Wu, C.F.J., and Chen, Y. (1997), “Optimal Blocking Schemes for 2n and 2n-k Designs,” Technometrics, 39, 298-307.[8] Sitter, R.R., Chen, J., and Feder, M. (1997), “Fractional Resolution and Minimum Aberration in Blocked 2n-k Designs,” Technometrics, 39, 382-390.[9] Wu, C.F.J. and Hamada, M. (2000), Experiments Planning, Analysis, and Parameter Design Optimization, New York: John Wiley & Sons.
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