Summary

Statistical Process Monitoring (SPM) provides statistical tools and techniques to understand process variation. Process variation is divided into common cause and special cause variation. A process operating under common cause variation is said to be in-control, while a process operating under both common cause and special cause variation is said to be out-of-control. An in-control process is stable and can be improved, while an out-of-control process is unstable and should be brought in-control. Control charts are used to determine whether a process is in-control or out-of-control. The performance of control charts can be evaluated by the so-called average runlength (ARL). The in-control ARL is the average number of samples that must be taken before a control chart gives an out-of-control signal when the process is in-control. When process parameters are estimated, the in-control ARL is a random variable with high variability. In this context, the expected value of the in-control ARL has been used to evaluate and design Phase II control charts. However, this ignores the individual chart performance. Hence, control charts are now evaluated and designed to provide a minimum in-control ARL performance with a specified probability. In this thesis I propose better methods of evaluating the in-control ARL and deriving sample size requirements and charting constants to design control charts.