Title page for ETD etd-04202006-134123


Type of Document Dissertation
Author Jensen, Willis Aaron
URN etd-04202006-134123
Title Profile Monitoring for Mixed Model Data
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Birch, Jeffrey B. Committee Chair
Reynolds, Marion R. Jr. Committee Member
Spitzner, Dan J. Committee Member
Vining, G. Geoffrey Committee Member
Woodall, William H. Committee Member
Keywords
  • High Breakdown Estimation
  • Multivariate Outliers
  • Nonlinear Mixed Models
  • Multivariate Statistical Process Control
  • Linear Mixed Models
Date of Defense 2006-04-10
Availability unrestricted
Abstract
The initial portion of this research focuses on appropriate parameter estimators within a general context of multivariate quality control. The goal of Phase I analysis of multivariate quality control data is to identify multivariate outliers and step changes so that the estimated control limits are sufficiently accurate for Phase II monitoring. High breakdown estimation methods based on the minimum volume ellipsoid (MVE) or the minimum covariance determinant (MCD) are well suited to detecting multivariate outliers in data. Because of the inherent difficulties in computation many algorithms have been proposed to

obtain them. We consider the subsampling algorithm to obtain the MVE estimators and the FAST-MCD algorithm to obtain the MCD estimators. Previous studies have not clearly determined which of these two estimation methods is best for control chart applications. The comprehensive simulation study here gives guidance for when to use which estimator. Control limits are provided. High breakdown estimation methods such as MCD and MVE can be applied to a wide variety of multivariate quality control data.

The final, lengthier portion of this research considers profile monitoring. Profile monitoring is a relatively new technique in quality control used when the product or process quality is best

represented by a profile (or a curve) at each time period. The essential idea is often to model the profile via some parametric method and then monitor the estimated parameters over time to

determine if there have been changes in the profiles. Because the estimated parameters may be correlated, it is convenient to monitor them using a multivariate control method such as the T-squared statistic. Previous modeling methods have not incorporated the correlation structure within the profiles. We propose the use of mixed models (both linear and nonlinear) to monitor linear and

nonlinear profiles in order to account for the correlation structure within a profile. We consider various data scenarios and show using simulation when the mixed model approach is preferable to an approach that ignores the correlation structure. Our focus is on Phase I control chart applications.

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  Appendices.pdf 81.57 Kb 00:00:22 00:00:11 00:00:10 00:00:05 < 00:00:01
  BackMatter.pdf 80.82 Kb 00:00:22 00:00:11 00:00:10 00:00:05 < 00:00:01
  Chapter1.pdf 51.12 Kb 00:00:14 00:00:07 00:00:06 00:00:03 < 00:00:01
  Chapter2.pdf 69.06 Kb 00:00:19 00:00:09 00:00:08 00:00:04 < 00:00:01
  Chapter3.pdf 325.27 Kb 00:01:30 00:00:46 00:00:40 00:00:20 00:00:01
  Chapter4.pdf 224.11 Kb 00:01:02 00:00:32 00:00:28 00:00:14 00:00:01
  Chapter5.pdf 812.87 Kb 00:03:45 00:01:56 00:01:41 00:00:50 00:00:04
  Chapter6.pdf 195.46 Kb 00:00:54 00:00:27 00:00:24 00:00:12 00:00:01
  Chapter7.pdf 1.05 Mb 00:04:52 00:02:30 00:02:11 00:01:05 00:00:05
  Chapter8.pdf 62.08 Kb 00:00:17 00:00:08 00:00:07 00:00:03 < 00:00:01
  FrontMatter.pdf 81.64 Kb 00:00:22 00:00:11 00:00:10 00:00:05 < 00:00:01

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