Characterization of Six Categories of Systematic 2<sup><i>n</i>－(<i>n</i>－<i>k</i>)</sup> Fractional Factorial Designs

Abstract

Six categories of systematic designs. This paper characterizes these six categories and documents their differences with regard to either time trend resistance of factor effects and/or the number of factor level changes. The paper introduces the last category of systematic the defining relation or its alias structure and 3) the k independent generators needed for sequencing the ( ) 2 n n k − − runs by the generalized foldover scheme. A comparison among these six categories of designs reveals that when the polynomial degree of the time trend increases from linear into quadratic and/or when the design's resolution increases from III to IV, the number of factor level changes between the ( ) 2 n n k − − runs increases. Also as the number of factors (i.e. n) increases, the design's resolution decreases.