@article{2978789,
    title = "On the optimality of orthogonal and balanced arrays with N≡ 0 (mod 9) runs",
    author = "Chasiotis, V. and Chatzopoulos, S.A. and Kounias, S. and Farmakis, N.",
    journal = "Statistical Papers",
    year = "2021",
    volume = "62",
    number = "4",
    pages = "1965-1980",
    publisher = "Springer Science and Business Media Deutschland GmbH",
    issn = "0932-5026",
    doi = "10.1007/s00362-020-01167-3",
    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 runs and 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≡ 0 (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 , 18, 27, 36 runs and m= 2 three-level factors under the second-order model. Furthermore, it is shown that the BA(18, m, 3, 2)s, m= 3 , 4 and a BA(27, 3, 3, 2) perform better than the OA(18, m, 3, 2)s, 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. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature."
}