Minimum projection uniformity criterion and its application

Based on a so-called uniformity pattern, Fang and Qin [2005. Uniformity pattern and related criteria for two-level factorials. Sci. China Ser. A 48, 1–11] proposed the minimum projection uniformity criterion to assess and compare two-level factorials. In present paper, we study applications of minimum projection uniformity criterion in aberration designs, orthogonal arrays and supersaturated designs. Relationship among minimum projection uniformity, generalized minimum aberration [Ma, C. X., Fang, K. T., 2001. A note on generalized aberration factorial designs. Metrika 53, 85–93; Xu, H., Wu, C. F. J., 2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist. 29, 549–560], V-criterion [Tang, B., 2001. Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2G2-aberration. Biometrika 88, 401–407], nearest balance criterion [Fang, K. T., Lu, X., Winker, P., 2003. Lower bounds for centered and wrap-around L2L2-discrepancies and construction of uniform designs by threshold accepting. J. Complexity 19, 692–711] and E(s2)E(s2) criterion [Booth, K. H. V., Cox, D. R., 1962. Some systematic supersaturated designs. Technometrics 4, 489–495] is made explicit. Noting that minimum projection uniformity criterion is related to uniform designs, our results should raise the hope of improving the connection between uniform design theory and factorial design theory.