Multivariate control charts for the mean vector and variance-covariance matrix with variable sampling intervals

When using control charts to monitor a process it is frequently necessary to simultaneously monitor more than one parameter of the process. Multivariate control charts for monitoring the mean vector, for monitoring variance-covariance matrix and for simultaneously monitoring the mean vector and the variance-covariance matrix of a process with a multivariate normal distribution are investigated. A variable sampling interval (VSI) feature is considered in these charts.

Two basic approaches for using past sample information in the development of multivariate control charts are considered. The first approach, which is called the combine-accumulate approach, reduces each multivariate observation to a univariate statistic and then accumulates over past samples. The second approach, which is called the accumulate-combine approach, accumulates past sample information for each parameter and then forms a univariate statistic from the multivariate accumulations.

Multivariate control charts are compared on the basis of their average time to signal (ATS) performance. The numerical results show that the multivariate control charts based on the accumulate-combine approach are more efficient than the corresponding multivariate control charts based on the combine-accumulate approach in terms of ATS. Also VSI charts are more efficient than corresponding FSI charts.