Minimum cost linear and quadratic trend free 2n–(n–k) designs. (1st January 2013) - Hilow, Hisham
This paper extends the degree of protection of factor effects in systematic 2 n–(n–k) designs from the linear time trend into the quadratic and minimises the total number of factor level changes between runs (i.e., the cost) by constructing a catalogue of (2 k–1 – k) minimum cost linear and quadratic trend free 2 n–(n–k) designs (of resolution at least III) from the full 2 k factorial experiment using the interactions-main effects assignment technique, where (2 k–1 – (k – 1) – (k – 1)(k – 2) / 2) ≤ n ≤ (2 k – 1 – k – k(k – 1) / 2) and k ≥ 4. All k main effects and their k(k – 1) / 2 two-factor interactions are excluded from the selection assignment process due to their non-quadratic time trend resistance. The paper provides for each design in the catalogue the following: 1) the independent interaction effects of the defining relation so that the alias structure can easily be identified; 2) the two-factor interactions that are linear/quadratic trend free besides the linear and quadratic trend freeness of all n main effects; 3) the k independent generators needed for the generalised fold-over scheme of Coster and Cheng (1988) to sequence the 2 n–(n–k) runs; 4) the total number of factor level changes between the 2 n–(n–k) successive runs (i.e., the experimental cost).