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An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays

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  • Nguyen, Nam-Ky
  • Liu, Min-Qian

Abstract

Due to run size constraints, near-orthogonal arrays (near-OAs) and supersaturated designs, a special case of near-OA, are considered good alternatives to OAs. This paper shows (i) a combinatorial relationship between a mixed-level array and a non-resolvable incomplete block design (IBD) with varying replications (and its dual, a resolvable IBD with varying block sizes); (ii) the relationship between the criterion E(d2) proposed by Lu and Sun [Lu, X., Sun, Y., 2001. Supersaturated designs with more than two levels. Chinese Ann. Math. B 22, 183-194] or E(fNOD)E(fNOD) proposed by Fang et al. [Fang, K.T., Lin, D.K.J., Liu, M.Q., 2003b. Optimal mixed-level supersaturated design. Metrika 58, 279-291] used in the (near-) OA construction and the (M,S)-optimality criterion used in the IBD construction; (iii) the derivation of a tighter bound for E(d2); (iv) how to modify the IBD algorithm of Nguyen [Nguyen, N.-K., 1994. Construction of optimal incomplete block designs by computer. Technometrics 36, 300-307] to obtain efficient (near-) OA algorithms. Some new (near-) OAs are presented and some near-OAs are compared with arrays constructed by other authors. Examples showing the use of the constructed arrays are given.

Suggested Citation

  • Nguyen, Nam-Ky & Liu, Min-Qian, 2008. "An algorithmic approach to constructing mixed-level orthogonal and near-orthogonal arrays," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5269-5276, August.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5269-5276
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    References listed on IDEAS

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    1. Kai-Tai Fang & Dennis K. J. Lin & Min-Qian Liu, 2003. "Optimal mixed-level supersaturated design," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 279-291, December.
    2. Chen, Jie & Liu, Min-Qian, 2008. "Optimal mixed-level supersaturated design with general number of runs," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2496-2502, October.
    3. Nguyen, Nam-Ky & Miller, Alan J., 1992. "A review of some exchange algorithms for constructing discrete D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 489-498, November.
    4. Kai-Tai Fang & Gen-Nian Ge & Min-Qian Liu & Hong Qin, 2003. "Construction of minimum generalized aberration designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 37-50, February.
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    2. Liu, Min-Qian & Zhang, Li, 2009. "An algorithm for constructing mixed-level k-circulant supersaturated designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2465-2470, May.
    3. Gupta, V.K. & Singh, Poonam & Kole, Basudev & Parsad, Rajender, 2009. "Construction of efficient unbalanced mixed-level supersaturated designs," Statistics & Probability Letters, Elsevier, vol. 79(22), pages 2359-2366, November.

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