On the Joint Use of the Foldover and Partial Confounding for the Construction of Follow-Up Two-Level Blocked Fractional Factorial Designs

Abstract

In this article, we consider experimental situations where a regular fractional factorial design is initially used to study m two-level factors using experimental units arranged in 2^p blocks of size but where a follow-up design is desired to further study main effects and two-factor interactions. A typical follow-up would consist of folding over some of the experimental factors but using the same blocking scheme for the foldover design. Here, we consider the joint use of the foldover and the use of a different blocking scheme in the follow-up design to generate alternative combined designs that outperform the combined designs obtained using previously given procedures in terms of estimability of two-factor interactions, estimation capacity, or both.

AMS Subject Classification:

• Primary 62K15
• Secondary 62K05

Keywords:

• Design matrix
• Estimable effect
• Estimation capacity