Blocked two-level semifoldover designs

Foldover design is a commonly used technique that is obtained by adding another fraction to an initial fractional factorial design. Because such added designs require the same run size as the initial design, semifoldover designs that consist of half of a foldover fraction have been investigated in the recent literature for regular two-level fractional factorial designs. As the initial design and the follow-up semifoldover design are usually conducted at different stages, it is important to consider a block factor reflecting this effect. This paper studies the impact of the block factor on the semifoldover of 2 k − p designs. We first propose a method for obtaining the equivalent semifoldover plans. Then the properties and the structures of blocked semifoldover designs are explored. The optimal blocked semifoldover designs for 16 and 32 runs are obtained and tabulated for practical use.