The most commonly used model of ‘statistical’ control' for industrial production processes is that observations taken over time are independent and identically distributed. Thus, for example, the estimate of variability used to establish Shewhart X¯-chart control limits is almost always based on within-subgroup variability. We review and present generalizations of this in-control model to include multiple components of common cause variability, such as batch-to-batch variability. An example involving integrated circuit processing, with three components of variability, is given to illustrate the proposed techniques. The usefulness of the multi-vari chart is emphasized.