Estimation of population generalized variance: Application in service industry

In statistical process control, monitoring process target is as important as process variability. In multivariate setting, the latter is still in development due to the complexity of multivariate variability measure. That is why the former is more popular than the latter. The most widely used measure of multivariate variability is the so called generalized variance (GV). In order to monitor GV, we need to estimate the population generalized variance and its square. In the literature, those estimates are given based on single sample. Only recently, it has been developed for the case of m independent samples with equal sample size. This motivates us to further develop in this paper for the case of m independent samples with unequal sample sizes which is usually encountered in service industry. An example of GV control charting for unequal sample sizes will be presented to illustrate the advantages of this method of estimation in monitoring the quality of service.