Experimentation with Randomization Restrictions: Targeting Practical Implementation

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-tochange 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.

Practical Inference from Industrial Split-Plot Designs

“…The split-plot nature of the experiment comes from the fact that the levels of the hard-to-change variables are not reset independently for several sequences of runs. Simpson, Kowalski and Landman (2003), for example, describe a wind tunnel experiment to investigate how the total drag and the down force of a race car depend on the front ride height, the rear ride height, the yaw angle and the covering of the car's grille. To change the front and rear ride heights was extremely cumbersome.…”

Analysis of an Unreplicated Fractional-Factorial Design Using Nonparametric Tests

“…Hence, no repetition of the 8-run set was required. All runs were randomized such as design nuisances that may still hamper the evaluation will be downplayed (Simpson et al, 2004). In Table 2, the safety factor output values are presented along with the experimental schedule.…”

Computer experiments: application to the case of a recovery boiler

“…Other reasons like resistance to change, insufficient resources, and low commitment of the management have been reported in literature, for example, by Owen et al (2003), Thia et al (2005), and Tanco et al (2007). Fortunately, experimental design has enjoyed increased exposure in the industry over the past decade (Simpson et al, 2004a), and among their most often uses are the design and development of processes and products. These activities, and many other engineering activities, have been increasingly performed using computer models.…”