A Multivariate Change Point Model for Statistical Process Control

• Activity Number: 234
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Quality and Productivity
• Author(s): Kokou Zamba*+
• Companies: The University of Iowa
• Keywords: Change point ; Phase I and II ; Likelihood ratio ; Control Chart ; ARL

Abstract

Multivariate statistical process control requires ongoing checks to ensure process readings have not changed. These checks traditionally are done by T-square, multivariate cusum, and MEWMA control charts. Traditional SPC charts have assumed the in-control true parameters were known exactly and used these assumed true values to set the control limits. The reality, however, is that true parameter values are seldom, if ever, known exactly; rather, they are commonly estimated from a Phase I sample. Phase I study is more demanding in multivariate setting than in univariate since multivariate processes involve more parameters to be estimated, and so require more data in order to satisfy their calibration needs. Some industrial settings, however, have a paucity of relevant data to estimate the process parameters. An attractive alternative to traditional charting methods when monitoring step change in the mean vector is to use an unknown-parameter likelihood ratio test for a change in mean of p-variate normal data. The benefit we have found from this description is to be able to control the run behavior despite the lack of a large Phase I sample.