Student Seminar Series - June 16, 2006
University of Minnesota
School of Statistics
College of Liberal Arts

Self-Starting Multivariate Exponentially Weighted Moving Average


Edgard Maboudou


Friday, June 16, 2006
11:00 AM, 170 Ford Hall
Minneapolis, East Bank Campus

Refreshments at 10:30 AM
300 Ford Hall


Abstract


Multivariate control charts have been widely used in industry. They are a valuable tool for quality control. These charts are based on the assumption of the knowledge of the in-control process parameters. The reality is that practitioners have used parameter estimates from in-control preliminary observations (phase I sample) to establish charts. However, it is not known what the exact process parameters are, and it is not known whether there have been drifts from the conditions obtained at the process start-up. Also, no sample will establish the exact process parameters, and quite small random errors translate into serious distortions of the run behavior. Moreover, using estimated parameters instead of known process parameters degrades the performance of the charts.

On the other hand, the self-starting method begins the control of the process since start-up without preliminary step of a large phase I sample. Univariate self-starting methods have been available for some time now; this thesis develops a multivariate equivalent by providing a way to transform the process readings into a stream of vectors following an exact multivariate standard normal distribution.

Next, this thesis discusses an exponentially weighted moving covariance matrix (MEWMC) for monitoring the stability of the covariance matrix of a process. Used together with the location MEWMA, this chart provides a way to satisfy Shewhart's dictum that proper process control monitor both mean and variability.