Type of Document	Dissertation
Author	Williams, James Dickson
Author's Email Address	jawill15@vt.edu
URN	etd-12102004-150057
Title	Contributions to Profile Monitoring and Multivariate Statistical Process Control
Degree	PhD
Department	Statistics
Advisory Committee	Advisor Name Title Birch, Jeffrey B. Committee Co-Chair Woodall, William H. Committee Co-Chair Anderson-Cook, Christine M. Committee Member Spitzner, Dan J. Committee Member Vining, G. Geoffrey Committee Member
Keywords	heteroscedasticity Hotelling's T^2 statistic lack-of-fit minimum volume ellipsoid nonlinear regression sample size successive differences vertical density profile bioassay false alarm rate functional data
Date of Defense	2004-12-01
Availability	unrestricted
Abstract The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T^2 statistic based on the successive differences covariance matrix estimator. (Part 1) In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. (Part 2) Although the T^2 statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T^2 chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use.
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