Identification of Dispersion Effects from Partially Replicated Two-Level Factorial Designs

Variation reduction in industrial quality improvement is always a primary objective to reach. Thus, well-designed experiments are needed to identify both location and dispersion effects to control the quality characteristic of interest around a target value with a minimal variation. Analysis of dispersion effects typically requires duplicates on treatment combinations. This can lead to a costly experiment due to a large number of experimental runs. An unreplicated design with relatively fewer runs seems to be an attractive alternative for users. However, the use of an unreplicated design can be inherently difficult in the identification of the truly active effects because location and dispersion effects are possibly confounded. In this article, we promote a class of regular two-level factorial designs with partial replications, which could be considered as compromise designs in terms of cost and efficiency. Also, based on the concepts of generalized p-values, we develop a statistical testing procedure to identify significant dispersion effects from the partially replicated designs. In addition, a catalogue of such designs with practical run sizes is provided for applications.