Designing and Running Super-Efficient Experiments: Optimum Blocking With One Hard-to-Change Factor

This paper discusses how to run 2k experiments for process improvement when there is one hard-to-change factor. The paper studies the different ways of running these experiments and gives practical recommendations. It shows how to block designs to get small prediction variance and low cost. It presents an algorithm to allow the selection of efficient blocking relations, in 2k designs, where there is one hard-to-change factor and tabulates the results for 23 to 27 designs, in various block sizes. It presents methods for calculating the prediction variance and G-efficiency when there are hard-to-change factors. The calculations are demonstrated by applying them to 2k designs, and results are tabulated for various block sizes. We show that optimally blocked split-plot designs dominate randomized designs. A blocked split-plot design is both less expensive to run, because it requires fewer resets of the hard-to-change factor, and more precise, as it gives a lower variance of prediction than a completely randomized design.