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 ...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.展开更多
In two-level fractional factorial designs,conditional main effects can provide insights by which to analyze factorial effects and facilitate the de-aliasing of fully aliased two-factor interactions.Con-ditional main e...In two-level fractional factorial designs,conditional main effects can provide insights by which to analyze factorial effects and facilitate the de-aliasing of fully aliased two-factor interactions.Con-ditional main effects are of particular interest in situations where some factors are nested within others.Most of the relevant literature has focused on the development of data analysis tools that use conditional main effects,while the issue of optimal factorial design for a given linear model involving conditional main effects has been largely overlooked.Mukerjee,Wu and Chang[Statist.Sinica 27(2017)997-1016]established a framework by which to optimize designs under a con-ditional effect model.Although theoretically sound,their results were limited to a single pair of conditional and conditioning factors.In this paper,we extend the applicability of their frame-work to double pairs of conditional and conditioning factors by providing the corresponding parameterization and effect hierarchy.We propose a minimum contamination-based criterion by which to evaluate designs and develop a complementary set theory to facilitate the search of minimum contamination designs.The catalogues of 16-and 32-run minimum contamination designs are provided.For five to twelve factors,we show that all 16-run minimum contamination designs under the conditional effect model are also minimum aberration according to Fries and Hunter[Technometrics 22(1980)601-608].展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11871033,11971204,12101357,12131001 and 12271270National Ten Thousand Talents Program of China+2 种基金Natural Science Foundation of Tianjin under Grant No.20JCYBJC01050Natural Science Foundation of Shandong under Grant No.ZR2021QA080the 111 Project B20016。
文摘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We gratefully acknowledge funding from Academia Sinica[Grant Number AS-CDA-111-M05]from National Science and Technology Council[Grant Number 111-2118-M-001-001-MY3].
文摘In two-level fractional factorial designs,conditional main effects can provide insights by which to analyze factorial effects and facilitate the de-aliasing of fully aliased two-factor interactions.Con-ditional main effects are of particular interest in situations where some factors are nested within others.Most of the relevant literature has focused on the development of data analysis tools that use conditional main effects,while the issue of optimal factorial design for a given linear model involving conditional main effects has been largely overlooked.Mukerjee,Wu and Chang[Statist.Sinica 27(2017)997-1016]established a framework by which to optimize designs under a con-ditional effect model.Although theoretically sound,their results were limited to a single pair of conditional and conditioning factors.In this paper,we extend the applicability of their frame-work to double pairs of conditional and conditioning factors by providing the corresponding parameterization and effect hierarchy.We propose a minimum contamination-based criterion by which to evaluate designs and develop a complementary set theory to facilitate the search of minimum contamination designs.The catalogues of 16-and 32-run minimum contamination designs are provided.For five to twelve factors,we show that all 16-run minimum contamination designs under the conditional effect model are also minimum aberration according to Fries and Hunter[Technometrics 22(1980)601-608].
