Three Categories of Minimum Cost Systematic Full 2n Factorial Designs
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 is minimal (i.e., (2n − 1)) or less than that of existing algorithms. These three categories are called (i) minimal-cost full 2n factorial designs, (ii) minimum-cost linear-trend-free full 2n factorial designs, and (iii) minimum-cost linear and quadratic-trend-free full 2n factorial designs. A comparison with existing systematic full 2n factorial designs reveals that the proposed systematic 2n designs compete well regarding minimization of the number of factor level changes (i.e., cost) or regarding protection of main effects and/or two-factor interactions against the linear/quadratic time trend.
KeywordsSequential factorial experimentation Time-trend-free run orders Number of factor level changes and the experimental cost Runs sequencing algorithms Interactions-main effects assignment Generalized foldover scheme
AMS Subject Classification62K15
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