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.

Chen and Cheng (Ann. Statist. 27 (1999) 1948) got the relationships between a blocked symmetrical factorial design and its residual design. In this paper, we extend the study to the case of blocked mixed-level factorial designs. By introducing a concept of blocked consulting design and using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain combinatorial identities that govern the relationships between the partitioned wordlength patterns of a blocked regular mixed factorial design and that of its blocked consulting design. Based on these identities, we furthermore establish some general rules for identifying minimum aberration blocked mixed factorial designs in terms of their blocked consulting designs. As applications, some blocked 412n and 422n designs with 16 and 32 runs are tabulated.

In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain combinatorial identities that relate the wordlength pattern of a regular mixed factorial design to that of its consulting design. According to these identities, we further-more establish the general and unified rules for idejntifying mini-mum aberration mixed factorial designs through their consulting designs. It is an improvement and generalization of the results in Mukerjee and Wu (2001).

The authors introduce the notion of split generalized wordlength pattern (GWP), i.e., treatment GWP and block GWP, for a blocked nonregular factorial design. They generalize the minimum aberration criterion to suit this type of design. Connections between factorial design theory and coding theory allow them to obtain combinatorial identities that govern the relationship between the split GWP of a blocked factorial design and that of its blocked consulting design. These identities work for regular and nonregular designs. Furthermore, the authors establish general rules for identifying generalized minimum aberration (GMA) blocked designs through their blocked consulting designs. Finally they tabulate and compare some GMA blocked designs from Hall' s orthogonal array OA (16; 215; 2) of type III.