Multivariate Quality Control Using Loss-Scaled Principal Components

We consider a principal components based decomposition of the expected value of the multivariate quadratic loss function, i.e., MQL. The principal components are formed by scaling the original data by the contents of the loss constant matrix, which defines the economic penalty associated with specif...

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Main Author: Murphy, Terrence Edward
Format: Others
Language:en_US
Published: Georgia Institute of Technology 2005
Subjects:
Online Access:http://hdl.handle.net/1853/4916
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spelling ndltd-GATECH-oai-smartech.gatech.edu-1853-49162013-01-07T20:10:53ZMultivariate Quality Control Using Loss-Scaled Principal ComponentsMurphy, Terrence EdwardMultivariate statistical process controlRobust designLoss functionPrincipal componentsQuality control Statistical methodsMultivariate analysisPrincipal components analysisProcess control Statistical methodsWe consider a principal components based decomposition of the expected value of the multivariate quadratic loss function, i.e., MQL. The principal components are formed by scaling the original data by the contents of the loss constant matrix, which defines the economic penalty associated with specific variables being off their desired target values. We demonstrate the extent to which a subset of these ``loss-scaled principal components", i.e., LSPC, accounts for the two components of expected MQL, namely the trace-covariance term and the off-target vector product. We employ the LSPC to solve a robust design problem of full and reduced dimensionality with deterministic models that approximate the true solution and demonstrate comparable results in less computational time. We also employ the LSPC to construct a test statistic called loss-scaled T^2 for multivariate statistical process control. We show for one case how the proposed test statistic has faster detection than Hotelling's T^2 of shifts in location for variables with high weighting in the MQL. In addition we introduce a principal component based decomposition of Hotelling's T^2 to diagnose the variables responsible for driving the location and/or dispersion of a subgroup of multivariate observations out of statistical control. We demonstrate the accuracy of this diagnostic technique on a data set from the literature and show its potential for diagnosing the loss-scaled T^2 statistic as well.Georgia Institute of Technology2005-03-01T19:43:14Z2005-03-01T19:43:14Z2004-11-24Dissertation983161 bytesapplication/pdfhttp://hdl.handle.net/1853/4916en_US
collection NDLTD
language en_US
format Others
sources NDLTD
topic Multivariate statistical process control
Robust design
Loss function
Principal components
Quality control Statistical methods
Multivariate analysis
Principal components analysis
Process control Statistical methods
spellingShingle Multivariate statistical process control
Robust design
Loss function
Principal components
Quality control Statistical methods
Multivariate analysis
Principal components analysis
Process control Statistical methods
Murphy, Terrence Edward
Multivariate Quality Control Using Loss-Scaled Principal Components
description We consider a principal components based decomposition of the expected value of the multivariate quadratic loss function, i.e., MQL. The principal components are formed by scaling the original data by the contents of the loss constant matrix, which defines the economic penalty associated with specific variables being off their desired target values. We demonstrate the extent to which a subset of these ``loss-scaled principal components", i.e., LSPC, accounts for the two components of expected MQL, namely the trace-covariance term and the off-target vector product. We employ the LSPC to solve a robust design problem of full and reduced dimensionality with deterministic models that approximate the true solution and demonstrate comparable results in less computational time. We also employ the LSPC to construct a test statistic called loss-scaled T^2 for multivariate statistical process control. We show for one case how the proposed test statistic has faster detection than Hotelling's T^2 of shifts in location for variables with high weighting in the MQL. In addition we introduce a principal component based decomposition of Hotelling's T^2 to diagnose the variables responsible for driving the location and/or dispersion of a subgroup of multivariate observations out of statistical control. We demonstrate the accuracy of this diagnostic technique on a data set from the literature and show its potential for diagnosing the loss-scaled T^2 statistic as well.
author Murphy, Terrence Edward
author_facet Murphy, Terrence Edward
author_sort Murphy, Terrence Edward
title Multivariate Quality Control Using Loss-Scaled Principal Components
title_short Multivariate Quality Control Using Loss-Scaled Principal Components
title_full Multivariate Quality Control Using Loss-Scaled Principal Components
title_fullStr Multivariate Quality Control Using Loss-Scaled Principal Components
title_full_unstemmed Multivariate Quality Control Using Loss-Scaled Principal Components
title_sort multivariate quality control using loss-scaled principal components
publisher Georgia Institute of Technology
publishDate 2005
url http://hdl.handle.net/1853/4916
work_keys_str_mv AT murphyterrenceedward multivariatequalitycontrolusinglossscaledprincipalcomponents
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