A tutorial on an iterative approach for generating Shewhart control limits

Standard statistical quality control text books (e.g., Montgomery 2015 ) discuss the differences between Phase I and Phase II control charts. In Phase I, control charts are more of an exploratory data analytical tool whose purpose is to generate the control limits for Phase II. Phase II is the true control procedure, which may be viewed as a series of hypothesis tests. The null hypothesis is that the process is in-control, and the alternative is that it is out-of-control. The typical presentation of Phase I is a preset number of rational subgroups. Such an approach fails to address the tension that exists between having enough information to generate reliable control limits and being able to start active control of the process. Vining ( 1998 ; 2009 ) outline an iterative approach that he developed in the early 1980s when he was employed by the Faber-Castell Corp. This article discusses the differences between Phase I and Phase II control charts and the impact of the number of rational subgroups in the Phase I study upon the quality of the resulting control limits. It then presents two brief case studies that illustrate the iterative approach for the basic Shewhart and R charts.