Study on state transition tracking method in process fraction nonconforming

When a control chart signals that an assignable cause is present, process engineers are required to identify a time point of process changes and then search for the assignable cause of the process disturbance. In the statistical process control literature, there is a research area called change point detection. As one of change point detection problems, it has been considered how to identify the time of a step-change in the process fraction nonconforming using the maximum likelihood theory. However, the process fraction nonconforming may be changed multiple times until a chart signals. Such a multiple change-points model for the process fraction nonconforming has not been considered yet. In this study, we consider a multiple change-points model of the process fraction nonconforming under a p chart. Then, a method of tracking the transition of process fraction nonconforming is proposed using the maximum likelihood theory and information criterion.