3-Level Response Surface Design by Using Expanded Spherical Experimental Region

확장된 구형설계를 이용한 반응표면설계

Kim, Ha-Yan;Lee, Woo-Sun

  • Received : 2011.12.13
  • Accepted : 2012.01.16
  • Published : 2012.02.29


Response surface methodology(RSM) is a very useful statistical techniques for improving and optimizing the product process. By this reason, RSM has been utilized extensively in the industrial world, particularly in the circumstances where several product variables potentially influence some quality characteristic of the product. In order to estimate the optimal condition of product variables, an experiment is being conducted defining appropriate experimental region. However, this experimental region can vary with the experimental circumstances and choice of a researcher. Response surface designs can be classified, according to the shape of the experimental region, into spherical and cuboidal. In the spherical case, the design is either rotatable or very near-rotatable. The central composite design(CCD)s widely used in RSM is an example of 5-level and spherical design. The cuboidal CCDs(CCDs with ${\alpha}=1$) is appropriate when an experimental region is cuboidal but this design dose not satisfy the rotatability as it is not spherical. Practically, a 3-level spherical design is often required in the industrial world where various level of experiments are not available. Box-Behnken design(BBD)s are a most popular 3-level spherical designs for fitting second-order response surfaces and satisfy the rotatability but the experimental region does not vary with the number of variables. The new experimental design with expanded experimental region can be considered if the predicting response at the extremes are interested. This paper proposes a new 3-level spherical RSM which are constructed to expand the experimental region together with number of product variables.


Spherical design;cuboidal design;3-level design;rotatability


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