Experimentation with Randomization Restrictions: Targeting Practical Implementation

Abstract

Abstract Randomization, one of the fundamental principles of statistically designed experiments, is not always easy to implement in practice. In fact, many industrial settings involve factors of interest that are difficult to change, requiring some modification to a completely randomized test sequence. Practical issues associated with restricted randomization commonly arise regarding design efficiencies, design requirements for error estimation, overall ease of software‐assisted analysis, required replication, tests for nonlinearity, and sequential testing plans. The purpose of this paper is to deal directly with these roadblocks to efficient and effective experimentation under randomization restrictions. The general approach involves modifying standard split‐plot designs with appropriate augmentation followed by a two‐stage model building method using a standard general linear model framework. An alternative procedure for analyzing two‐level factorial split‐plot designs is provided for commonly occurring situations involving more than one hard‐to‐change factor. The proposed methods were developed and implemented in conducting experiments for wind tunnel applications. These tests serve as case studies for the paper. We also suggest possible methods for limiting the replication required for estimating whole plot error. Copyright © 2004 John Wiley & Sons, Ltd.