Contributions to Profile Monitoring and Multivariate Statistical Process Control

Simple item page
dc.contributor.authorWilliams, James Dicksonen
dc.contributor.committeecochairBirch, Jeffrey B.en
dc.contributor.committeecochairWoodall, William H.en
dc.contributor.committeememberSpitzner, Dan J.en
dc.contributor.committeememberAnderson-Cook, Christine M.en
dc.contributor.committeememberVining, G. Geoffreyen
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T20:20:07Zen
dc.date.adate2004-12-14en
dc.date.available2014-03-14T20:20:07Zen
dc.date.issued2004-12-01en
dc.date.rdate2005-12-14en
dc.date.sdate2004-12-10en
dc.description.abstractThe content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring 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: Approximate Distribution of T² Although the T² 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 T² 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-12102004-150057en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-12102004-150057/en
dc.identifier.urihttp://hdl.handle.net/10919/30032en
dc.publisherVirginia Techen
dc.relation.haspartFinalDissertation_finalversion.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectheteroscedasticityen
dc.subjectHotelling's T² statisticen
dc.subjectlack-of-fiten
dc.subjectminimum volume ellipsoiden
dc.subjectnonlinear regressionen
dc.subjectsample sizeen
dc.subjectsuccessive differencesen
dc.subjectvertical density profileen
dc.subjectbioassayen
dc.subjectfalse alarm rateen
dc.subjectfunctional dataen
dc.titleContributions to Profile Monitoring and Multivariate Statistical Process Controlen
dc.typeDissertationen
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
FinalDissertation_finalversion.pdf
Size:
3.7 MB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations