Title: Minimum cost linear and quadratic trend free 2^n−(n−k) designs

Authors: Hisham Hilow

Addresses: Mathematics Department, The University of Jordan, Amman, 11942, Jordan

Abstract: 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).

Keywords: sequential factorial experimentation; trend robust run orders; minimum factor level changes; experimental cost; interactions-main effects assignment; generalised foldover scheme; aliasing; defining relations; experimental design.

DOI: 10.1504/IJEDPO.2013.055753

International Journal of Experimental Design and Process Optimisation, 2013 Vol.3 No.3, pp.311 - 326

Received: 16 Feb 2013
Accepted: 30 Apr 2013
Published online: 02 Jul 2014 *

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