Minimum Cost Linear Trend Free 2n-(n-k) Designs of Resolution IV

Abstract

This article extends the resolution of time trend free designs for sequential 2n-p experiments from III into IV and minimizes the number of factor level changes between runs (i.e., cost) by constructing a catalog of (2k−2 −1) minimum cost linear trend free resolution IV 2n−(n−k) designs (2k−2 ≤ n ≤ 2k−1−2) from the full 2k factorial experiment using the interactions-main effects assignment technique. Each systematic 2n−(n−k) design in the catalog is economic in minimum number of factor level changes and allows for the estimation of all n main effects unbiased by either the linear time trend (which may be present in the 2n−(n−k) sequentially generated responses) or the non negligible two-factor interactions. This article provides for each 2n−(n−k) design: (1) the defining relation or the alias structure; (2) the k independent generators for sequencing the 2n−(n−k) runs by the generalized foldover scheme; and (3) the minimum cost represented by the total number of factor level changes between the 2n−(n−k) runs. All k main effects of the 2k experiment are excluded from the selection assignment process due to their nonlinear time trend resistance as well as excluding a total of (2k−1 –k +1) interactions violating the resolution IV requirement.