Some Advances in Experimental Designs

Abstract

In the talk, I will present some of my works in experimental designs. It will contain four different topics as follows. 1. Factor screening and response surface exploration 　A novel approach was proposed to achieve two objectives, factor screening and response surface exploration, on one design. The approach is based on a two-stage analysis that employs identification of important factors, projection, and second-order model fitting. We defined projection-efficiency criteria to evaluate the performance of designs under the two-stage analysis. To improve some shortcomings of the criteria, an alternative optimality criterion that is based on the generalized minimum aberration was given in a later work. 2. Indicator function 　A factorial design can be represented by a polynomial, called indicator function. Based on the indicator function approach, we had studied the geometric structure of designs, and defined geometric isomorphism, word length, and minimum aberration criterion for designs with quantitative factors. We also applied indicator function to the blocking schemes of non-regular two-level designs. For non-regular designs, indicator function plays a role which is similar to that of defining contrast subgroup in regular designs. 3. Optimal blocking schemes for factorial designs 　Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. We proposed some criteria that allow estimation of more lower-order effects. Tables of useful designs were given. The criteria were also generalized to non-regular designs in a later work. 4. Experiments with factor of sliding level 　Design of experiments with related factors can be implemented by using the technique of sliding levels. Factors are related when the desirable experimental range of one factor depends on the level of the other factors. We proposed an analysis method based on a response surface model, and demonstrated its superiority for prediction. When the desirable experimental region is unknown and has to be explored in the experiment, we proposed a two-stage design strategy. An innovative analysis method for the two-stage data was also suggested.