Design of and ewma charts in a variance components model

In statistical process control, the Shewhart model postulates that an individual observation consists of a constant plus a random variation about zero. In processes where group-to-group variability exists, the mean within a given group can be thought of a realization of the between-group variability. For such cases we consider a variance components model where individual observations have between-group variation plus within-group variation. The average run lengths of the standard X and exponentially weighted moving average charts designed for the Shewhart model are calculated in the variance components model. It is shown that the standard procedures are quite misleading. The standard procedures are modified to construct the control limits using the in-control variance of subgroup means in the variance components model. The modification of the procedures improves significantly the performance of the standard procedures. A method of estimating the in-control between-group variance is shown using the observed in-control run lengths from past experiences.