Multivariate Quality Control Using Loss-Scaled Principal Components

Multivariate statistical process control;Robust design;Loss function;Principal components

Murphy, Terrence Edward ; Industrial and Systems Engineering

University:Georgia Institute of Technology

Department:Industrial and Systems Engineering

关键词: Multivariate statistical process control;    Robust design;    Loss function;    Principal components;   

Others  :  https://smartech.gatech.edu/bitstream/1853/4916/1/murphy_terrence_e_200412_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We consider a principal components based decomposition of theexpected value of the multivariate quadratic loss function, i.e.,MQL. The principal components are formed by scaling the originaldata by the contents of the loss constant matrix, which definesthe economic penalty associated with specific variables being offtheir desired target values. We demonstrate the extent to which asubset of these ``loss-scaled principal components", i.e., LSPC,accounts for the two components of expected MQL, namely thetrace-covariance term and the off-target vector product. We employthe LSPC to solve a robust design problem of fulland reduceddimensionality with deterministic models that approximate the truesolution and demonstrate comparable results in less computationaltime. We also employ the LSPC to construct a test statistic calledloss-scaled T^2for multivariate statistical process control.We show for one case how the proposed test statistic has fasterdetection than Hotelling's T^2of shifts in location forvariables with high weighting in the MQL. In addition weintroduce a principal component based decomposition of Hotelling'sT^2 to diagnose the variables responsible for driving thelocation and/or dispersion of a subgroup of multivariateobservations out of statistical control. We demonstrate theaccuracy of this diagnostic technique on a data set from theliterature and show its potential for diagnosing the loss-scaledT^2 statistic as well.