On the monitoring of trended and regularly adjusted processes

Trended and regularly adjusted processes are common in manufacturing industries. Such processes are, for example, related to tool wear, material replenishment or some regular maintenance. When the process has a slow trend or is frequently adjusted, the Shewhart chart can be interpreted in the same way as for a stable process. To facilitate comparison between such a trended and adjusted process to a stable case, and to estimate further the loss of effectiveness when the traditional Shewhart chart is applied to trended and adjusted process, this paper provides a statistical interpretation of traditional Shewhart charts for this type of processes. Formulas are derived for the calculation of alarm rate and average run length (ARL). This study is useful when deciding if a traditional Shewhart chart is sufficient or if a more advanced Statistical Process Control method is necessary. Furthermore, given the in-control and out-of-control ARL, a combined decision with regard to the control limits setting and the adjustment interval can be made. The general formulation is described and a simple linear trend model with an actual data set is used as an illustration.