Interval type-2 X-S control charts for univariate processes

Abstract

Statistical Process Control (SPC) is fundamental to largescale manufacturing defect detection, being control charts the primary tool that promotes quality improvement. The x-s control charts monitor the mean and standard deviation of a continuous quality characteristic that can be measured and are influenced by human subjectivity, as well as to several other sources of uncertainty. Fuzzy set theory has advantages, but there are situations that it is not sufficient to model uncertainties present in the process, requiring the application of type-2 fuzzy sets. This work proposes an interval type-2 fuzzy and control charts using triangular fuzzy numbers. The x-s control limits are obtained through mathematical equations considering the defuzzification method under study. An illustrative example is developed, in order to demonstrate the usefulness of the proposed control chart. The proposed control model is called the IT2TFN x-s control chart, that is, the traditional x-s control charts combined with type-2 interval triangular fuzzy numbers. The IT2TFN x-s control chart can stabilize data very uncertain or vague in the fuzzification process, it is more flexible as it adds more information regarding uncertainties and expert opinion, which improves the assertiveness of the process decisions compared to the traditional x-s control charts.