On the optimality of orthogonal and balanced arrays with $$N\equiv 0$$ N ≡ 0 $$(\text {mod}$$ ( mod 9) runs

Vasilis Chasiotis (), Stavros A. Chatzopoulos, Stratis Kounias and Nikos Farmakis
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Vasilis Chasiotis: Aristotle University of Thessaloniki
Stavros A. Chatzopoulos: Aristotle University of Thessaloniki
Stratis Kounias: National and Kapodistrian University of Athens
Nikos Farmakis: Aristotle University of Thessaloniki

Statistical Papers, 2021, vol. 62, issue 4, No 16, 1965-1980

Abstract: Abstract We investigate the role of orthogonal arrays (OAs) and balanced arrays (BAs) in both full and fractional factorial designs with N runs and m three-level quantitative factors. Firstly, due to the non-existence of the OA(18, 8, 3, 2), we find and construct a BA(18, 8, 3, 2) that represents the E-, A-, D-optimal design with $$N=18$$ N = 18 runs and $$m=8$$ m = 8 three-level factors under the main-effect model. Also, we are interested in comparing the OA(N, m, 3, 2)s with the BA(N, m, 3, 2)s, when they represent designs with $$N\equiv 0$$ N ≡ 0 $$(\text {mod}$$ ( mod 9) runs and m three-level factors with respect to the E-, A-, D-criteria under the second-order model. We provide a generalized definition of balanced arrays. Moreover, we find and construct the OA(N, m, 3, 2)s and the BA(N, m, 3, 2)s that represent the E-, A-, D-optimal designs with $$N=9$$ N = 9 , 18, 27, 36 runs and $$m=2$$ m = 2 three-level factors under the second-order model. Furthermore, it is shown that the BA(18, m, 3, 2)s, $$m=3$$ m = 3 , 4 and a BA(27, 3, 3, 2) perform better than the OA(18, m, 3, 2)s, $$m=3$$ m = 3 , 4 and the OA(27, 3, 3, 3), respectively, when they represent the corresponding designs with respect to the E-, A-, D-criteria under the second-order model.

Keywords: E-; A-; D-optimal designs; Universal optimality; Resolution; Main effects; Interactions; 62K05; 62K15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01167-3

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