摘要
Fractional factorial(FF)designs are commonly used for factorial experiments in many fields.When some prior knowledge has shown that some factors are more likely to be significant than others,Li,et al.(2015)proposed a new pattern,called the individual word length pattern(IWLP),which,defined on a column of the design matrix,measures the aliasing of the effect assigned to this column and effects involving other factors.In this paper,the authors first investigate the relationships between the IWLP and other popular criteria for regular FF designs.As we know,fractional factorial split-plot(FFSP)designs are important both in theory and practice.So another contribution of this paper is extending the IWLP criterion from FF designs to FFSP designs.The authors propose the IWLP of a factor from the whole-plot(WP),or sub-plot(SP),denoted by the I_w WLP and Is WLP respectively,in the FFSP design.The authors further propose combined word length patterns C_(w) WLP and Cs WLP,in order to select good designs for different cases.The new criteria C_(w) WLP and Cs WLP apply to the situations that the potential important factors are in WP or SP,respectively.Some examples are presented to illustrate the selected designs based on the criteria established here.
基金
supported by the National Natural Science Foundation of China under Grant Nos.11871033,11971204,12101357,12131001 and 12271270
National Ten Thousand Talents Program of China
Natural Science Foundation of Tianjin under Grant No.20JCYBJC01050
Natural Science Foundation of Shandong under Grant No.ZR2021QA080
the 111 Project B20016。
