Fall Seminar Series - October 6, 2005
University of Minnesota
School of Statistics
College of Liberal Arts
Control Charts for Detecting Changes in a Covariance Matrix of a
Multivariate Normal Process
Arthur Yeh
Department of Applied Statistics and Operations Research
Bowling Green State University
Thursday, October 6, 2005
3:30 PM, 115
Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall
Abstract
The
problem under consideration is constructing statistical control charts
for detecting changes in a covariance matrix from a multivariate normal
process. I will discuss some of the developments in the last 15 years.
Detailed discussion will be given to three recent works which I have
been involved with.
There are three important considerations based on
which a control chart is constructed. The first consideration deals
with the methodology the control chart uses for combining sampled
information. Three such methodologies are Shewhart, CUSUM and EWMA
based statistics. The second consideration is the amount of data that
are available for constructing the control chart. Three such
possibilities exist: (1) the subgroup size (n) is larger than the total
number (p) of quality characteristics of interest; (ii) only individual
observations (n = 1) are available; and (iii) 1 < n < p. The
third consideration relates to the types of changes in the covariance
matrix the control chart is designed to detect. It could be changes in
the generalized variance (the determinant), or in the total variation
(the trace) of the covariance matrix, or in some of the p(p+1)/2
parameters of the covariance matrix. Examining existing works through
these considerations allows us to have a better understanding of what
has been accomplished so far and what future research may be needed.