Change-point detection for shifts in control charts using fuzzy shift change-point algorithms

•A new fuzzy mechanism is proposed to detect the time of shifts in mean.•Knowledge of the distribution and the process parameters is not required.•The algorithm is applicable to normal and non-normal processes of phase I and II.•The method performs better than traditional methods in accuracy and precision.•Efficiency in small shifts detection is helpful for identifying causes fast.

Knowing the real time of changes, called change-point, in a process is essential for quickly identifying and removing special causes. Many change-point methods in statistical process control assume the distribution and the in-control parameters of the process known, however, they are rarely known accurately. Small errors accompanied with estimated parameters may lead to unfavorable change-point estimates. In this paper, a new method, called fuzzy shift change-point algorithm, which does not require the knowledge of the distribution nor the parameter of the process, is proposed to detect change-points for shifts in process mean. The fuzzy c-partition concept is embedded into change-point formulation in which any possible collection of change-points is considered as a partitioning of data with a fuzzy membership. These memberships are then transferred into the pseudo memberships of observations belonging to each individual cluster, so the fuzzy c-means clustering can be used to obtain the estimates for shifts. Subsequently, the fuzzy c-means algorithm is used again to obtain new iterates of change-point collection memberships by minimizing an objective function concerning the deviations between observations and the corresponding cluster means. The proposed algorithm is nonparametric and applicable to normal and non-normal processes in both phase I and II. The performance of the proposed fuzzy shift change-point algorithm is discussed in comparison with powerful statistical methods through extensive simulation studies. The results demonstrate the superiority and usefulness of our proposed method.