Design Considerations and Tradeoffs for Shewhart Control Charts

When in-control parameters are unknown, they have to be estimated using a reference sample. The control chart performance in Phase II, which is generally measured in terms of the Average Run Length (ARL) or False Alarm Rate (FAR), will vary across practitioners due to the use of different reference samples in Phase I. This variation is especially large for small sample sizes. Although increasing the amount of Phase I data improves the control chart performance, others have shown that the amount required to achieve a desired in-control performance is often infeasibly high. This holds even when the actual distribution of the data is known. When the distribution of the data is unknown, it has to be estimated as well, along with its parameters. This yields even more uncertainty in control chart performance when parametric models are applied. With these issues in mind, choices have to be made in order to control the performance of control charts. We discuss several of these choices and their corresponding implications.