Approximating the Distribution of the T-Square Statistic for Multivariate Non-Normal Distributions

• Activity Number: 321
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 12:00 PM to 1:50 PM
• Sponsor: Section on Quality & Productivity*
• Author(s): John Young*+ and Robert Mason
• Affiliation(s): McNeese State University and Southwest Research Institute
• Keywords: Multivariate Statistical Process Control ; Multivariate Kurtosis ; Sampling Distribution

Abstract

The probability distribution of the statistic used in monitoring a multivariate process plays an important role in determining the control limits used in the corresponding control chart. The distribution of a T-Square statistic for a single observation, when based on a sample taken from a multivariate normal population, is well-known. When purging outliers in a Phase I operation with unknown parameters, some form of a beta distribution is used to describe the T-Square statistic. When monitoring future observations in a Phase II operation with unknown parameters, the F distribution is appropriate. With known parameters, a chi-square distribution is used in both a Phase I and Phase II operation. These distributions all require the assumption of sampling from a multivariate normal population. In this paper, we show that these results are also adequate in describing the behavior of a T-Square statistic when sampling from many multivariate non-normal populations.