Title page for ETD etd-12102004-150057


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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