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http://dx.doi.org/10.7469/JKSQM.2017.45.4.889

A Study on the Determination of Experimental Size of Near-orthogonal Two-level Balanced Trace Optimal Resolution-V Fractional Factorial Designs  

Kim, Sang Ik (Department of Applied Statistics, Konkuk University)
Publication Information
Journal of Korean Society for Quality Management / v.45, no.4, 2017 , pp. 889-902 More about this Journal
Abstract
Purpose: The orthogonality and trace optimal properties are desirable for constructing designs of experiments. This article focuses on the determination of the sizes of experiments for the balanced trace optimal resolution-V fractional factorial designs for 2-level factorial designs, which have near-orthogonal properties. Methods: In this paper, first we introduce the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$, by exploiting the partially balanced array for various cases of experimental sizes. Moreover some orthogonality criteria are also suggested with which the degree of the orthogonality of the designs can be evaluated. And we appraise the orthogonal properties of the introduced designs from various aspects. Results: We evaluate the orthogonal properties for the various experimental sizes of the balanced trace optimal resolution-V fractional factorial designs of the 2-level factorials in which each factor has two levels. And the near-orthogonal 2-level balanced trace optimal resolution-V fractional factorial designs are suggested, which have adequate sizes of experiments. Conclusion: We can construct the trace optimal $2^t$ fractional factorial designs for $4{\leq}t{\leq}7$ by exploiting the results suggested in this paper, which have near-orthogonal property and appropriate experimental sizes. The suggested designs can be employed usefully especially when we intend to analyze both the main effects and two factor interactions of the 2-level factorial experiments.
Keywords
Fractional Factorial Design; Balanced Design; Resolution-V; Experimental Size; Partially Balanced Array; Orthogonality;
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1 Srivastava, J. N. and Chopra, D.V. 1971. "Balanced Optimal $2^m$ Fractional Factorial Designs of Resolution V, $m{\leqq}6$." Technometrics 13:257-269.
2 Srivastava, J. N. 1965. "Optimal Balanced $2^m$ Fractional Factorial Designs." S.N. Roy Memorial Volume, Univ. of North Carolina and Indian Statistical Institute.
3 Kim, S.I. 1992. "Minimal Balanced $2^t$ Fractional Factorial Designs of Resolution V and Taguchi Method." The Korean Journal of Applied Statistics 5:19-28.
4 Kim, S.I. 2008. "Evaluation of the Degree of Orthogonality of 2- level Resolution-V Designs of Constructed by Balanced Array." Comumunications of the Korean Statistical Society 15: 235-244.
5 Ma, C., Fang, K., and Liski, E. 2000. "A New Approach in Constructing Orthogonal and Nearly Orthogonal Arrays."Metrica 50:255-268.   DOI
6 Jang, D.H. 2002. "Measures for Evaluating Non-orthogonality of Experimental Designs." Communications in Statistics-Theory and Methods 31:249-260.   DOI
7 Chakravartie, I.M. 1956."Fractional Replications in Asymmetrical Factorial Design and Partially Balanced Arrays." Sankhya 17:143-164.
8 Chopra, D.V., and Srivastava, J.N. 1973. "Optimal Balanced $2^7$ Fractional Factorial Designs of Resolution V with $N{\leqq}42$." Annals of Institute of Statistical Mathematics 25:587-604.   DOI
9 Fang, K.T., Lin,D. K.J., and Liu, M. 2003. "Optimal Mixed-level Supersaturated Design." Metrika 58:279-291.   DOI