Sixteen run designs of high projectivity for factor screening

A two level orthogonal array design for n observations with k factors and of projectivity P provides an (n, k, P) factor screen for which every projection into P space produces a complete 2(P) factorial, possibly with certain points replicated. Box and Tyssedal (1) rigorously investigated the screening properties of such designs derived from fractional factorials and Plackett Burman orthogonal arrays (OA's). For example, they showed that these always provided (12, 11, 3) and (20, 19, 3) screens, but for 16 runs only a(16, 8, 3) screen could be generated. In this paper it is shown that designs derived from a different class of OA's due to Hall (2) can produce sixteen run designs that can screen a larger number of factors and that in particular (16, 12, 3) screens and also a (16, 14, 3) screen can be obtained.