- Main

## Robust and Optimum Fractional Factorial Designs

- Author(s): Huang, fu ze
- Advisor(s): Ghosh, Subir
- et al.

## Abstract

This thesis is devoted to the study of robust and optimum fractional factorial designs. We consider models that contain the general mean, main effects, and * k * two-factor interactions for 2^{m} fractional factorial experiments. We define S_{i} to be the set of all (1 × m) vectors, with elements 1 and -1 of weight i, where the weight of a vector is the number of nonzero elements in it. We present the robustness property of two classes of designs D={S_{0}, S_{1}, S_{m-1}, S_{m}} and D_{1}={S_{0}, S_{1}, S_{2}, S_{m}} with respect to any t runs as well as a specific set of t runs in the sense that the full estimation capacity of the designs remain when we delete any t runs as well as specific t runs from the designs D and D_{1}. The number of runs are (2+m) and [2+m+.5(m)(m-1)] in D and D_{1} respectively.

We introduce a general structure **M** for the information matrices of a class of models possibly describing the data from a fractional factorial experiment with m factors each at two levels and n runs. We characterize all the eigenvalues and eigenvectors for such matrices **M**. For m=4 we establish the robustness property of the design D_{7}={S_{0}, S_{1}, S_{3}}. The runs of D_{7} are contained in design D when m=4. We show all the information matrices from design D_{7} and designs obtained from D_{7} by deleting some runs are special cases of **M**.

Let D_{T} be the class of designs with n runs for estimating the main effects only and let F_{T} be the class of foldover designs with 2n runs, n runs from T in D_{T} and another n runs from -T, having full estimation capacity for k=1. We prove that if T* in D_{T} is E-optimum, the foldover design [T*, -T*] is optimum design with respect to AMCR and GMCR in F_{T}. Furthermore, if T* is D- and A- optimum with a special structure for **X' _{1T*}X_{1T*}** we prove [T*, -T*] is GD, AD, GT, and AT optimal in F

_{T}.