Abstract:
This research is inspired from monitoring the process covariance structure of q attributes
where samples are independent, having been collected from a multivariate normal distribution with
known mean vector and unknown covariance matrix. The focus is on two matrix random variables,
constructed from different Wishart ratios, that describe the process for the two consecutive time
periods before and immediately after the change in the covariance structure took place. The product
moments of these constructed random variables are highlighted and set the scene for a proposed
measure to enable the practitioner to calculate the run-length probability to detect a shift immediately
after a change in the covariance matrix occurs. Our results open a new approach and provides
insight for detecting the change in the parameter structure as soon as possible once the underlying
process, described by a multivariate normal process, encounters a permanent/sustained upward or
downward shift.
