Article: Comparison among algorithms for sequencing runs of the full 2n factorial experiment Journal: International Journal of Experimental Design and Process Optimisation (IJEDPO) 2013 Vol.3 No.4 pp.410 - 434 Abstract: The complete 2n factorial experiment has 2n different experimental runs among which there are 2n! permutations for carrying out this experiment sequentially one run at a time, but not all of these permutations produce runs sequences with desirable properties. There are four algorithms for sequencing runs of the 2n factorial experiment such that: 1) main effects and/or two-factor interactions are orthogonal to the linear/quadratic time trend and/or such that; 2) the total number of factor level changes between the 2n runs (i.e., the cost) is minimal. These algorithms are: Correa et al. (2009), Cui and John (1998), Cheng and Jacroux (1988) and Coster and Cheng (1988), referred to here as Algorithms 1, 2, 3(a) and 3(b) and 4, respectively. This paper conducts a comparison among these algorithms and documents their differences according to the three criteria: 1) which algorithm produces runs sequences in a less number of factor level changes (i.e., less costly); 2) which algorithm produces runs sequences with more linear/quadratic time trend free main effects and/or two-factor interactions; 3) which runs sequence of an algorithm can be generated by another algorithm using the generalised fold-over scheme or the interactions-main effects assignment. Results of this comparison are summarised in Section 4. Inderscience Publishers - linking academia, business and industry through research

Title: Comparison among algorithms for sequencing runs of the full 2ⁿ factorial experiment

Authors: Hisham Hilow

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

Abstract: The complete 2ⁿ factorial experiment has 2ⁿ different experimental runs among which there are 2ⁿ! permutations for carrying out this experiment sequentially one run at a time, but not all of these permutations produce runs sequences with desirable properties. There are four algorithms for sequencing runs of the 2ⁿ factorial experiment such that: 1) main effects and/or two-factor interactions are orthogonal to the linear/quadratic time trend and/or such that; 2) the total number of factor level changes between the 2ⁿ runs (i.e., the cost) is minimal. These algorithms are: Correa et al. (2009), Cui and John (1998), Cheng and Jacroux (1988) and Coster and Cheng (1988), referred to here as Algorithms 1, 2, 3(a) and 3(b) and 4, respectively. This paper conducts a comparison among these algorithms and documents their differences according to the three criteria: 1) which algorithm produces runs sequences in a less number of factor level changes (i.e., less costly); 2) which algorithm produces runs sequences with more linear/quadratic time trend free main effects and/or two-factor interactions; 3) which runs sequence of an algorithm can be generated by another algorithm using the generalised fold-over scheme or the interactions-main effects assignment. Results of this comparison are summarised in Section 4.

Keywords: sequential factorial experimentation; time trend free runs orders; factor level changes; experimental cost; run sequencing algorithms; interactions-main effects assignment; generalised fold-over scheme; experimental runs.

DOI: 10.1504/IJEDPO.2013.059664

International Journal of Experimental Design and Process Optimisation, 2013 Vol.3 No.4, pp.410 - 434

Received: 21 Aug 2013
Accepted: 04 Dec 2013
Published online: 02 Jul 2014 *

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Title: Comparison among algorithms for sequencing runs of the full 2ⁿ factorial experiment