A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

Control charts are the most popular Statistical Process Control (SPC) tools used to monitor process changes. When a control chart produces an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of the process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifying the real time of the process change is known as change-point estimation problem. Most of the traditional change-point methods are based on maximum likelihood estimators (MLE) which need strict statistical assumptions. In this paper, first, we introduce clustering as a potential tool for change-point estimation. Next, we discuss the challenges of employing clustering methods for change-point estimation. Afterwards, based on the concepts of fuzzy clustering and statistical methods, we develop a novel hybrid approach which is able to effectively estimate change-points in processes with either fixed or variable sample size. Using extensive simulation studies, we also show that the proposed approach performs considerably well in all considered conditions in comparison to powerful statistical methods and popular fuzzy clustering techniques. The proposed approach can be employed for processes with either normal or non-normal distributions. It is also applicable to both phase-I and phase-II. Finally, it can estimate the true values of both in- and out-of-control states’ parameters.