Different methods to fuzzy $\overline{\mathbf{X}}$-R control charts used in production: Interval type-2 fuzzy set example

The control charts are used in many production areas because they give an idea about the quality characteristic(s) of a product. The control limits are calculated and the data are examined whether the quality characteristic(s) is/are within these limits. At this point, it may be confusing to comment, especially if it is slightly below or above the limit values. In order to overcome this situation, it is suitable to use fuzzy numbers instead of crisp numbers. The purpose of this paper is to demonstrate how to create control limits of X ¯ -R control charts for a specified data set of interval type-2 fuzzy sets.

There are methods in the literature, such as defuzzification, distance, ranking and likelihood, which may be applicable for interval type-2 fuzzy set. This study is the first that these methods are adapted to the X ¯ -R control charts. This methodology enables interval type-2 fuzzy sets to be used in X ¯ -R control charts.

It is demonstrated that the methods – such as defuzzification, distance, ranking and likelihood for interval type-2 fuzzy sets – could be applied to the X ¯ -R control charts. The fuzzy control charts created using the methods provide similar results in terms of in/out control situations. On the other hand, the sample points depicted on charts show similar pattern, even though the calculations are different based on their own structures. Finally, the control charts obtained with interval type-2 fuzzy sets and the control charts obtained with crisp numbers are compared.

Based on the related literature, research works on interval type-2 fuzzy control charts seem to be very limited. This study shows the applicability of different interval type-2 fuzzy methods on X ¯ -R control charts. For the future study, different interval type-2 fuzzy methods may be considered for X ¯ -R control charts.

The unique contribution of this research to the relevant literature is that interval type-2 fuzzy numbers for quantitative control charts, such as X ¯ -R control charts, is used for the first time in this context. Since the research is the first adaptation of interval type-2 fuzzy sets on X ¯ -R control charts, the authors believe that this study will lead and encourage the people who work on this topic.