Partially replicated two-level fractional factorial designs via semifoldover

Most fractional factorial designs have no replicated points and thus do not provide a reliable estimate for experimental error. The objective of this paper is to study the issue of partially replicated two-level fractional factorial (FF) designs, thereby allowing for the unbiased estimation of the experimental error while maintaining the orthogonality of the main effects. Through the tool of indicator function and the idea of semifoldover, we propose two simple and effective techniques to produce designs with partially replicated points in general two-level FF designs, whether they are regular or not. The related properties of constructed partially replicated designs are investigated. Our results indicate that partially replicated FF are competitive in practice.