Three Categories of Minimum Cost Systematic Full 2nFactorial Designs

Abstract

Full 2n factorial experiments are often conducted sequentially run after run. A full 2n factorial experiment has a total of 2n! permutations among its 2n runs but not all of these 2n! permutations produce runs sequences with good statistical properties. In fact, the standard runs order is not economic (requiring a large number of factor level changes between runs), and does not produce time-trend-resistant main effects. Four main algorithms exist for sequencing runs of the full 2n factorial experiment such that: (1) main effects and/or two-factor interactions are orthogonal to the linear/quadratic time trend and/or (2) the number of factor level changes between runs (i.e., cost) is minimal = (2n – 1) or minimum. This article proposes, through using the generalized foldover scheme and the interactions–main effects assignment, three categories of systematic full 2n factorial designs where main effects and/or two-factor interactions are linear/quadratic trend free and where the number of factor level changes...