In this paper we consider experimental situations in which m 2-level factors are to be studied using a 2-level main effects plan where n runs are to be partitioned into b blocks of different sizes. For these experimental situations, methods of constructing type I optimal designs are given.

In this paper we consider experimental situations in which m 2-level factors are to be studied using a main effects plan where n runs are partitioned into b block of size k. For the case n≡3 (mod 4), we establish some sufficient conditions for a design to be E-optimal and then give a method...

In this paper we consider experimental situations where a 2-level main effects plan is to be used to study m-factors using n runs which are partitioned into b blocks of size k=n/b and where k is an odd integer. For odd k≥3 and certain cases where b is a multiple of k, we show how to construct...

In this paper, we consider experimental situations where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks of equal size k=n/b. For the case and k2 where k is even, sufficient conditions are derived for certain designs having all main...

In this paper we consider the problem of constructing two-level fractional factorial designs in blocks of size two that allow for the orthogonal estimation of all main effects and two-factor interactions (after adjusting for blocks). This problem has been considered in the literature,...

In this paper we consider experimental situations in which n factors are to be studied in N runs arranged in N/2 blocks of size two. A simple method for constructing optimal designs in many such situations is given and examples are used to illustrate the technique.