A general fuzzy-statistical clustering approach for estimating the time of change in variable sampling control charts

Despite their capability in monitoring the variability of the processes, control charts are not effective tools for identifying the real time of such changes. Identifying the real time of the change in a process is recognized as change-point estimation problem. Most of the change-point models in the literature are limited to fixed sampling control charts which are only a special case of more effective charts known as variable sampling charts. In this paper, we develop a general fuzzy-statistical clustering approach for estimating change-points in different types of control charts with either fixed or variable sampling strategy. For this purpose, we devise and evaluate a new similarity measure based on the definition of operation characteristics and power functions. We also develop and examine a new objective function and discuss its relation with maximum-likelihood estimator. Finally, we conduct extensive simulation studies to evaluate the performance of the proposed approach for different types of control charts with different sampling strategies.