A Multivariate Change-Point Model for Statistical Process Control

Abstract

Multivariate statistical process control (SPC) carries out ongoing checks to ensure that a process is in control. These checks on the process are traditionally done by T², multivariate cusum, and multivariate exponentially weighted moving average control charts. These traditional SPC charts assume that the in-control true parameters are known exactly and use 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. It is increasingly recognized that this Phase I study needs to involve large samples if the parameter estimates are to provide run behavior matching that of the known-parameter situation. But, apart from the general undesirability of large and thus expensive studies preliminary to actual charting, some industrial settings have a paucity of relevant data for estimating the process parameters. An attractive alternative to traditional charting methods when monitoring for a step change in the mean vector is an unknown-parameter likelihood ratio test for a change in mean of p-variate normal data. We have found that this approach description is able to control the run behavior despite the lack of a large Phase I sample.

KEY WORDS :

• Average run length
• Change point
• Likelihood ratio
• Multivariate statistical process control
• Phases I and II
• T² statistic