Design and Analysis of Partially Replicated Factorial Experiments
Date Issued
2011
Date
2011
Author(s)
Tsai, Shin-Fu
Abstract
Factorial design is a useful statistical tool for simultaneously investigating the relationship between the experimental response and multiple factors of interest. It has been successfully used in a wide range of applications, such as agricultural field experiments, biomedical trials,
social sciences, quality controls and industrial product/process improvements, etc. At the preliminary stage of a scientific investigation, an unreplicated two-level or three-level fractional factorial design is commonly used to identify important factorial effects, which have an impact on the experimental response. Under the effect sparsity principle, several statistical analysis methods are developed for analyzing the outcomes of unreplicated experiments. However, there are many experimental scenarios in which unreplicated experiments typically lead to unsatisfactory findings. This is due mainly to the lack of a replication-based estimate of the experimental error variance. Fully replicating all the treatment combinations
is a straightforward method to obtain the pure replicates. However, the experimental cost is rapidly outgrown.
In this dissertation, partially replicated factorials, which serve as a compromise between unreplicated and fully replicated experiments, are proposed for effectively and economically screening important effects. First, several practical examples are provided to demonstrate that the partially replicated factorials are competitive in practical applications. To meet the requirements of experimental designs raised by investigators, the following practical design issues regarding the selection of partial replication on fractional factorial designs are explored, respectively. (1) The optimality of partially replicated two-level main-effect plans. (2) The robustness of partially replicated two-level main-effect plans against non-negligible two-factor and higher order interactions. (3) The optimality of partially replicated two-level and three-level mixed factorials for a user pre-specified requirement set. For these important design issues, sufficient conditions and construction approaches to derive the desired designs are investigated. In addition, a series of designs are provided for practical uses.
Subjects
Factorial design
Hadamard matrix
Optimal design
Orthogonal array
Projection property
Robust design
Type
thesis
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