| When a qualitative factor is included in an experiment,the traditional approach is to quantify it and represent it as one or more virtual variables.This method is valid but not applicable in all cases.This article has the following innovations.When dealing with the above issues,we take into account the various cases of the regression model impacted by qualitative factors.We prove equivalent theorem of the general regression model with a qualitative factor.We give the special block form and determinant of the information matrix and the D-optimal analytic solutions and apply it to a specific industrial experiment.Finally three kinds of D-optimal designs with qualitative factors are given.Chapter 1 has four sections.Section 1.1 introduces the experiment with qualitative factors.Section 1.2 describes the definition of the information matrix.Section 1.3 intro-duces the relevant optimal criteria and efficiency.Section 1.4 describes the relevant research background and current status.Chapter 2 has three sections.Section 2.1 introduces the general regression model.Section 2.2 describes the information matrix and its determinant.Section 2.3 introduces the equivalent theorem with a qualitative factor,which helps to test the D-optimality of the D-optimal design given by us.Chapter 3 has two sections.Section 3.1 gives a D-optimal method of regression model with qualitative factors.Section 3.2 gives the D-optimal design in three cases for the regres-sion model of specific examples in industrial experiment:firstly,the qualitative factor only affects the constant items in the model.We call it the D-optimal design with the qualitative factor interacts with the constant item in the model.Secondly,the qualitative factors not only have an effect on the constant items in the above model,but also have an effect on the linear item,which we call the qualitative factor and the constant and linear item in the model have the interaction effect.Thirdly,the qualitative factors have an effect on the constant items,the linear and quadratic item,we call it qualitative factors and constant items,the linear item,the quadratic item in the model have an interactive effect.Some concluding remarks and some questions worthy of further investigation are given in Chapter 4. |
