Optimal Semifoldover Plans for Two-Level Orthogonal Designs

Foldover is a widely used procedure for selecting follow-up experimental runs. As foldover designs require twice as many runs as the initial design, they can be inefficient if the number of effects to be dealiased is smaller than the size of the original experiment. Semifolding refers to adding half of a foldover fraction and is a technique that has been investigated in recent literature for regular two-level fractional factorial designs as an alternative to foldover. In this paper, a criterion for determining optimal semifoldover plans for two-level orthogonal factorial designs is proposed. Optimal plans are developed for selected 12, 16, 20, and 32-run designs and displayed for practical use. A hidden projection property of optimal semifoldovers of 12 and 20-run orthogonal arrays is also uncovered. General properties of semifoldover designs are obtained using indicator functions.