• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.235-244
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• 2008

Balanced arrays which are generalized orthogonal arrays, introduced by Chakravarti (1956) can be used to construct the fractional factorial designs. Especially for 2-level factorials, balanced arrays with strength 4 are identical to the resolution-V fractional designs. In this paper criteria for evaluation the degree of the orthogonality of balanced arrays of 2-levels with strength 4 are developed and some application methods of the suggested criteria are discussed. As a result, in this paper, we introduce the constructing methods of near orthogonal saturated balanced resolution-V fractional 2-level factorial designs.

• Journal of Korean Society for Quality Management
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• v.45 no.4
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• pp.889-902
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• 2017

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.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.167-175
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• 2006

Effective and quick methods that are easy to carry out even by hand, or easy to be programmed by hand-held calculators are needed for assessing the sizes of contrasts of unreplicated $2^P$ factorial designs. Moreover, they have the advantage to use the original numerical measurements which makes the analysis easier to explain. Basically, Lenth (1989) is one of the most familiar of such quick and powerful methods. Later on, Aboukalam (2001) proposes under constant effects an alternative sophisticated method to Lenth's method. The proposed method is the supreme from two considerable powers. The first utmost indicates less inflation deficiency while the other utmost indicates less shrinkage deficiency. Also under constant effects, Al-Shiha (2006) introduces an alternative quick method which is less shrinkage deficiency while the inflation deficiency is the same. If effects are random, Aboukalam (2005) introduces an alternative quick method in which the first power is favored as long as the second power is within a small margin. In the spirit of quickness and fixed effects, this article adds another method which is supreme from the two considerable powers. The method is based on a one step of the scale-part of a suggested M-estimate for location. Explicitly, we suggest adapting the skipped median (ASKM) estimate. Critical values of ASKM-method, for several sample sizes often used, are empirically computed.