직교성에 가까운 트레이스 최적 2-수준 Resolution-V 균형 일부실험법의 실험크기 결정에 관한 연구
A Study on the Determination of Experimental Size of Near-orthogonal Two-level Balanced Trace Optimal Resolution-V Fractional Factorial Designs
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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 2t fractional factorial designs for 4 ≤ t ≤ 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 2t fractional factorial designs for 4 ≤ t ≤ 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.
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 2t fractional factorial designs for 4 ≤ t ≤ 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 2t fractional factorial designs for 4 ≤ t ≤ 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.
참고문헌 (9)
- Chakravartie, I. M, "Fractional Replications in Asymmetrical Factorial Design and Partially Balanced Arrays", Sankhya, 17, pp.143~164 (1956)
- Chopra, D. V., "Optimal Balanced 27 Fractional Factorial Designs of Resolution V with N ≦ 42", Annals of Institute of Statistical Mathematics, 25, pp.587~604 (1973)
- Fang, K. T., "Optimal Mixed-level Supersaturated Design", Metrika, 58, pp.279~291 (2003)
- Jang, D. H, "Measures for Evaluating Non-orthogonality of Experimental Designs", Communications in Statistics-Theory and Methods, 31, pp.249~260 (2002)
- Kim, S. I, "Minimal Balanced 2t Fractional Factorial Designs of Resolution V and Taguchi Method", The Korean Journal of Applied Statistics, 5, pp.19~28 (1992)
- 김상익, "Evaluation of the Degree of the Orthogonality of 2-level Resolution-V Designs Constructed by Balanced Arrays", Communications for Statistical Applications and Methods, 15(2), pp.235~244 (2008), 한국통계학회
- Ma, C., "A New Approach in Constructing Orthogonal and Nearly Orthogonal Arrays", Metrica, 50, pp.255~268 (2000)
- Srivastava, J. N., "Optimal Balanced 2m Fractional Factorial Designs. S.N. Roy Memorial Volume", pp.1965
- Srivastava, J. N., "Balanced Optimal 2m Fractional Factorial Designs of Resolution V, m ≦ 6", Technometrics, 13, pp.257~269 (1971)