Power guidelines for process monitoring

We present a process for designing monitoring procedures that includes practical power guidelines. These guidelines are based upon the average run length (ARL). The specific guideline metric is the ratio of the in-control ARL (ARL ic ) to the out-of-control ARL (ARL oc ). Our recommended design process uses that ARL Ratio, in combination with the ARL ic , ARL oc , and ARL curve, to design effective process monitoring procedures. For adequate power, we generally recommend an ARL Ratio of 20 or more and argue that monitoring procedures with ARL Ratios less than 10 should usually be avoided. An area of caution lies between ARL Ratios of 10 and 20, allowing us to propose a stoplight type model for use in monitoring procedure design. We also discuss exceptions to these guidelines as well as a methodology to incorporate power considerations in other approaches to control chart design.