Some 3-Level Spherical Designs for Response Surface Experiments: Designs Constructed for the Radius of the Spherical Experimental Region to Vary with the Number of Factors

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Journal of Korean Society for Quality Management > Volume 29(1); 2001 > Article

Journal of Korean Society for Quality Management 2001;29(1): 24-.

반응표면실험을 위한 3-수준 구형(球形) 실험설계: 구형 실험지역의 반경이 요인 수에 따라 변화하도록 구축된 설계

이우선¹, 임성수²

¹성신여자대학교 통계학과
²고려대학교 정보통계학과

Some 3-Level Spherical Designs for Response Surface Experiments: Designs Constructed for the Radius of the Spherical Experimental Region to Vary with the Number of Factors

ABSTRACT

Response surface designs can be classified, according to the shape of the experimental region, into spherical designs and cuboidal designs. Among the central composite design(CCD)s and the Box-Behnken design(BBD)s that are popular in practice, when the number of factors is k, spherical designs are tile CCDs with the axial value being $sqrt{ extit{k}}$ and the BBDs, and cuboidal designs are the CCDs with the axial value being 1. With the CCDs having $sqrt{ extit{k}}$ as the axial value, the radius of the experimental region varies with number of factors, but these designs are the 5-level designs. With the BBDs that are 3-level designs, the radius of the experimental region does not vary with the number of factors. In this article, we propose tile 3-level spherical designs which are constructed so that tile radius of the experimental region varies with the number of factors.