Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix with Variable Sampling Intervals

Abstract

Traditional control charts for process monitoring are fixed sampling rate (FSR) control charts based on taking samples of fixed size with a fixed sampling interval between samples. Variable sampling rate (VSR) control charts vary the sampling rate as a function of the data from the process, and can detect most process changes significantly faster than traditional FSR control charts. The main focus of this article is on a type of VSR control chart called a variable sampling interval (VSI) control chart, but another type of VSR control chart based on sequential sampling is also considered. We consider the problem of detecting sustained or transient shifts in the mean or variability of a process. We investigate Shewhart control charts and multivariate exponentially weighted moving average (MEWMA) control charts based on sample means and on the sum of the squared deviations from target. We show that the combination of the standard MEWMA chart and an MEWMA-type chart based on squared deviations from target gives excellent overall performance. When the VSI feature is used with this combination, the performance is dramatically better than the performance of the standard FSR multivariate control charts that have traditionally been used.

Keywords:

• Average time to signal
• Exponentially weighted moving average control chart
• Multivariate exponentially weighted moving average control chart
• Regression adjustment of variables
• Sequential sampling
• Squared deviations from target
• Statistical process control
• Steady-state average time to signal

2000 Mathematics Subject Classification:

• 62D99
• 62L10
• 62P30

Notes

Recommended by Hock Peng Chan