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Activity Number: 345
Type: Contributed
Date/Time: Tuesday, August 8, 2006 : 2:00 PM to 3:50 PM
Sponsor: Section on Quality and Productivity
Abstract - #305877
Title: The Relationship between the T-Square Statistics of a Phase I and Phase II Operation
Author(s): John Young*+ and Robert L. Mason and Youn-Min Chou
Companies: McNeese State University and Southwest Research Institute and The University of Texas at San Antonio
Address: 1750 Bilbo Street, Lake Charles, LA, 70601,
Keywords: multivariate statistical process control ; generalized variance ; scatter matrices
Abstract:

A T2 statistic serves two major functions when implementing a MVSPC. When used in the construction stage, or a Phase I operation, the statistic helps locate special events in a preliminary data set, such as potential outliers or atypical points. When used in the monitoring stage, or a Phase II operation, the statistic helps detect signals, which are observations that do not conform to the baseline conditions established in the Phase I operation. For the unknown parameter case, the T2 statistics used in Phase I and Phase II have different distributions. This difference has been attributed to the specialized functions performed by the separate T2 statistics. However, in this paper, we show mathematically that the T2 statistic used in Phase I is actually a function of the T2 statistic used in Phase II, and either statistic can be used as a substitute for the other.

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