A Multivariate Process Variability Monitoring Based on Individual Observations

Abstract

In order to have a better understanding whether or not an additional observation has changed the covariance structure, a new statistic will be introduced. This statistic will be defined as the scatter matrix issued from augmented data set subtracted by that from historical data set. Under normality assumption, the distribution of its Frobenius norm will be derived and, for practical purpose, a chi-square approximation will be presented. This statistic and Wilks’ will be used to construct a new procedure for monitoring process variability based on individual observations. The performance of this procedure in providing information about the effect of an additional observation on covariance structure is promising. An industrial application will be presented to illustrate its advantage. .