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

Abstract

This paper discusses how to run 2^k 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 2^k 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 2^k 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.

• Block Size
• Cost Function
• Expensive-to-Change Factors
• G-Efficiency
• Prediction Variance

Additional information

Notes on contributors

Frank T. Anbari

Dr. Anbari is an Assistant Professor in the Department of Decision Sciences. He is a Senior Member of the ASQ and an ASQ Certified Six Sigma Black Belt. His e-mail address is [email protected].

James M. Lucas

Dr. Lucas is the Principal at J. M. Lucas and Associates. He is a Fellow of the ASQ and the ASA. His e-mail address is [email protected].