For optimal assignment of factors to columns of a 4m2n, design, we consider extensions of the minimum aberration criterion for the 2 level designs Minimum aberration 412n and 422n designs in t6 and 32 runs are obtained and tabulated Some results on the wordlength pattens and design classification are obtained.

In this paper, we introduce a class of generalized Browaian sheets and extend the OUP; in [1]. By studying some fundamental properties of the former process, we first derive some of simple relaxed past Markov properties of the rwo processes. Next, utilizing the relation between the two processes, we successively prove that, for two kinds of general sets, they possess the general relaxed past Markov properties and the Levy Markoy properties re-spectively. As a result, we conclude that the OUP; in [1] also has general Markov properties for the corresponding sets.

This paper introduces minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) criteria for discriminating among rival nonisomorphic regular multistratum fractional factorial split-plot (FFSP) designs. Some general rules for identifying MSA or MSEC multistratum FFSP designs through their consulting designs are also established. It is an improvement and eneralization of the related results in (Statist. Sinica 12 (2002) 885). The comparison between the MSEC criterion and that of Mukerjee and Fang (2002) is briefly given.

We extend the grouping scheme introduced by Wu (1989) and construct a class of saturated asymmetrical orthogonal arrays of the type OA(sk, sm (sr)n), where s is a prime power and r is any positive integer. The method is generalized to construct OA(sk, sm(sr1)m1... (sr1)ni) for any prime power s, any positive integer ri, and some combinations of m and ni.

Based on the work of Wang and Fang (1990a, b), this paper extends the def-inition of discrepancy of a set of points with respect to a distribution. To construct multivariate uniform designs, two transformations, discrepancy-preserving transfor-mation and density-preserving transformation, and a method of separating variables are introduced. Also, for some special domains useful in statistics, some related transformations are given. In particular, as an application of the method of sepa-rating variables, we give an approach of constructing a uniform design in the Stiefel manifold and outline its applications in projection pursuit methods.