Research On Response Surface Design With Quantitative And Qualitative Factors

Central composite design (CCD) is widely applied in many fields to construct a second-order responsesurface model with quantitative factors to help to increase the precision of the estimated model.Most of research about response surface design is based on when there are only quantitative factorsin the experiment. Chun-Pin Lee and Mong-Na Lo Huang did some research on the occasion when singlequalitative factor is included with multiple quantitative factors. They discussed the occasion when thereis interaction between qualitative factor and linear effects,2-factor interactions or quadratic effects of theD optimal design under each qualitative level of the qualitative factor also consists of three portions asCCD, but with different weights.This paper expands Chun-Pin Lee and Mong-Na Lo Huang.s research to multiple qualitative factors,it mainly consists of three parts:Chapter2, first we introduced the second-order response surface models with multiple qualitativefactors. Then we induced the relation of information matrix and dispersion function between models withquantitative and qualitative factors and models with quantitative factors. Next we gave the expression ofdispersion function for models only with quantitative factors. Last we gave the weights calculation formula,which satisfy the D optimal request.Chapter3, we discussed the changing tendency and relations between ωs,ωcand ω0under the condi-tion r=2, m1=m2=2,2≤k≤20, we also discussed the relations between ωs,ωcand ω0under thecondition k∈{2,...,5}, m1, m2∈{2,...,4}.Chapter4, first we introduced the definition of D efficiency, then discussed these models.D efficiency, in the end compare the D optimal design of models with single qualitative factor and thatwith multiple qualitative factors.