Identifying time of a monotonic change in the fraction nonconforming of a high-quality process

When a signal is detected by control charts, a search begins to identify and eliminate the sources of this signal. Knowing when a process has changed is very helpful for this purpose. The unknown special point that the process changed for the first time is referred to as change point. In this paper, we propose a maximum-likelihood estimator for the behavior model of the process fraction nonconforming in a high-quality process monitored with a cumulative count of conforming (CCC) control chart. We estimate the time of change without requiring the prior knowledge of the change type rather than we assume the type of change present belongs to a family of monotonic changes. Then, we compare the performance of the proposed change point estimator relative to estimators for the process fraction nonconforming change point derived under a single step and a linear trend change assumption. We do this for a number of monotonic change types following a signal from a CCC control chart. Finally, the application of the proposed change point estimator is shown through a real case.