Efficient three-level screening designs
Creators: name: ALOMAIR, Mohammed
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 490501
subject: Applied statistics
classificationCode: 490509
subject: Statistical theory

description: In general, screening designs are effective ways to study many controllable factors in industrial experiments when the number of experimental runs is limited. Traditionally, screening designs use two-level designs. However, to assess quantitative factors, certain experimenters favour three-level rather than two-level designs because three levels allow the capture of curvature in the response. For this purpose, Jones and Nachtsheim (2011) developed new three-level screening designs known as definitive screening designs (DSDs). In this dissertation, we seek to study the projection properties of new screening designs, notably DSDs and designs constructed from weighing matrices, and compare them based on several criteria. These criteria can be used for a range of models that include main effects, interactions and quadratic terms.

Chapter 1 briefly introduces experimental designs, the principles of experimental designs and factorial designs. Attention is given to types of factorial designs and the use of fractional factorial designs. In addition, the chapter defines and outlines the advantages of two-level screening designs, DSDs and designs constructed from weighing matrices.

Chapter 2, provides a comprehensive review of two- and three-level screening designs, including a discussion of their projection properties. It contains a literature review of the criteria used for comparing and ranking designs.

Chapter 3, studies the projection properties of three-level screening designs. The comparison is based on several alphabetical optimality criteria over a range of models that include main effects, interaction and quadratic terms. New designs are generated as projections of the full designs into a smaller-factor dimensional space. The best projections and their properties are presented in a tabular form.

The aim of Chapter 4 is to complement the work of Deng and Tang (1999), who used generalised resolution and minimum aberration criteria to rank different two-level designs, particularly Plackett-Burman and other non-regular factorial designs. An advantage of generalised resolution, extended here to work on three-level designs, is that it offers a useful criterion for ranking three-level screening designs. In addition, we applied a projection estimation capacity (PEC) criterion to select three-level screening designs with desirable properties. Practical examples and the best projections of the designs are presented in tables.

In Chapter 5, we use two criteria introduced by Tsai et al. (2000, 2007) to study the projection properties of three-level screening designs. Then, we compare these designs with the orthogonal designs using 13, 14, 15, 16, 17 and 18 run forms (Tsai et al., 2000, 2004). Where possible, we generated new designs with four, five and six factors by taking the corresponding projections. Designs with a smaller number of runs were generated and tested in a similar manner.

Chapter 6, contains a review the contents of this dissertation and recommendations for possible future research.