Projection Properties of Blocked Non-regular Two-level Designs

Minimum resolution IV (MinResIV) and Plackett and Burman (PB) designs are popular screening designs because of their run size efficiency and good projection properties. The purpose of this investigation is to find out which projection properties that can be maintained when these designs are blocked and also the efficiency by which the effects of interest can be estimated. MinResIV designs with 10–20 runs and PB designs with 12 and 20 are investigated. For the PB designs, design factor columns were used as blocking columns, while for the MinResIV designs, the main rule consisted of finding good arrangements for allocating mirror‐image pair runs to the same blocks, a method inspired from Jacroux. As a criterion for a good blocking arrangements, we used maximum Ds ‐ efficiency, which we found to be more generally applicable and provide better projection properties than previous suggested methods. It came out that for most of these designs, it was possible to find blocking schemes satisfying that for any three factors, either all main effects and their interactions or all main effects and their two‐factor interactions could be estimated with a reasonable high efficiency when blocked.