The productivity of an industrial processing unit often depends on equipment that changes over time. These changes may not be consistent, and, in many cases, may appear to occur in stages. Although changes in the process levels within each stage may appear insignificant, they can be substantial when monitored across the various stages. Standard process control procedures do not perform well in the presence of these step-like changes, especially when the observations from stage to stage are correlated. This paper presents an alternative multivariate control procedure for monitoring a process under these conditions. The methodology is based on a double decomposition of Hotelling'sT2statistic.