Determining Robust Control Limits hor Hotelling's T^2 Control Chart

• Activity Number: 599
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Quality and Productivity Section
• Author(s): Gary R Mercado*+ and Marcus Perry
• Companies: The University of Alabama and The University of Alabama
• Keywords: kernel density estimation ; bandwidth ; average run length ; multivariate statistical process control

Abstract

Hotelling's T^2 seems to be a reasonable charting statistic to implement when multivariate data can not be grouped into rational subgroups, i.e. n = 1. In many applications the underlying process distribution is not known sufficiently to assume multivariate normality. Accordingly, statistical properties of the Hotelling's control chart could be potentially affected. In this paper, the T^2 control chart based on the successive differences covariance matrix estimator is analyzed by applying the kernel quantile function estimator. The focus is to investigate the effect of Phase I sample size on the run length performance of the suggested multivariate control chart for monitoring the changes in the mean of a process when the normality assumption may be violated. Results indicate that the suggested control chart is insensitive to departures from normality.