11 Multivariate Process Monitoring and Control

CHAPTER OUTLINE

11.1   THE MULTIVARIATE QUALITY-CONTROL PROBLEM

11.2   DESCRIPTION OF MULTIVARIATE DATA

11.2.1   The Multivariate Normal Distribution

11.2.2   The Sample Mean Vector and Covariance Matrix

11.3   THE HOTELLING T2 CONTROL CHART

11.3.1   Subgrouped Data

11.3.2   Individual Observations

11.4   THE MULTIVARIATE EWMA CONTROL CHART

11.5   REGRESSION ADJUSTMENT

11.6   CONTROL CHARTS FOR MONITORING VARIABILITY

11.7   LATENT STRUCTURE METHODS

11.7.1   Principal Components

11.7.2   Partial Least Squares

Supplemental Material for Chapter 11

S11.1   Multivariate CUSUM Control Charts.

The supplemental material is on the textbook Website www.wiley.com/college/montgomery.

CHAPTER OVERVIEW AND LEARNING OBJECTIVES

In previous chapters we have addressed process monitoring and control primarily from the univariate perspective; that is, we have assumed that there is only one process output variable or quality characteristic of interest. In practice, however, many if not most process monitoring and control scenarios involve several related variables. Although applying univariate control charts to each individual variable is a possible solution, we will see that this is inefficient and can lead to erroneous conclusions. Multivariate methods that consider the variables jointly are required.

This chapter presents control charts that can be regarded as the multivariate extensions of some of the univariate charts of previous chapters. The Hotelling ...

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