Design of control charts for statistical process monitoring

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.