Screening design with categorical factor: construction and evaluation

Alhelali, Marwan Hussain 2019, Screening design with categorical factor: construction and evaluation, Doctor of Philosophy (PhD), Science, RMIT University.

Document type: Thesis
Collection: Theses

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Title Screening design with categorical factor: construction and evaluation
Author(s) Alhelali, Marwan Hussain
Year 2019
Abstract Screening designs are used widely by industrial experimentation. They are used to identify the most potential factors among a large number of factors. This thesis seeks to put into focus the construction of experimental designs and their analysis. In a recent paper, (Jones and Nachtsheim, 2011a) proposed a new class of designs called definitive screening designs DSDs. (Xiao et al., 2012) have used Conference matrices (C-matrix) to construct definitive screening designs DSDs with good properties. (Georgiou et al., 2013) introduced a method for constructing efficient three-level screening designs based on weighing matrices and their complete fold over. (Jones and Nachtsheim, 2013) have shown how a few categorical factors could be introduced in those designs.

The study seeks to concentrate into Definitive Screening Designs DSDs and their generalizations: construction, properties and analysis. The consideration will be on the construction of new DSDs and study their properties and analysis. The various DSDs and their properties, including how they are constructed with respect to the situation under consideration, will be of interest in this study. In this research, we provide a new general method that can use weighing matrices to construct screening designs with some two level qualitative factors. The methodology is illustrated through a number of small examples in the thesis. The generated designs are compared to the designs in the literature and their advantages and disadvantages are discussed.Also, we provide a new analysis structure for designs (SDW1), (SDW2) and (SDW3).

The construction of DSDs poses a great challenge in how to efficiently perform the experiment. Effective Design-Based Model Selection for Definitive Screening Designs is an approach that introduced by (Jones and Nachtsheim, 2017) for the analysis of DSDs that makes effective use of their special structure. The power of this approach is to detect the active main effects as well as the active second-order effects that far exceeds the capabilities of generic model selection tools, which do not take into account the structure of the data (see (Jones and Nachtsheim,2017)). In this thesis, we use the Effective Design-Based Model Selection procedure, that was introduced in (Jones and Nachtsheim, 2017) on Screening (SDWs) designs for s = (1, 2, 3) that constructed by (Alhelali et al., 2019). The method was applied to these designs for the first time and simulation studies with a number of different models has been applied. These models include main effects and second order terms and the procedure was evaluated by calculating the type I and type II error rates. A comparison between the performances of the screening designs (SDWs) for s = (1, 2, 3) is also provided with respect to the applied models and the resulted type I and type II errors
Degree Doctor of Philosophy (PhD)
Institution RMIT University
School, Department or Centre Science
Subjects Statistical Theory
Applied Statistics
Keyword(s) screening
definitive screening designs
categorical factors
conference matrices
weighing matrices
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Created: Tue, 12 May 2020, 14:14:30 EST by Keely Chapman
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