Exponentially Weighted Moving Average Charts Based on Interval Type-2 Fuzzy Numbers: Analyses of Quality Control and Performance

Abstract

A control chart is one of the most important techniques used to monitor processes of variability in the manufacturing data. However, conventional charts are relatively not suitable to deal with crisp data. Fuzzy charts are inevitable to evaluate the process with fuzzy data. Nevertheless, much of the data used in daily life cannot be used as a type-1 fuzzy number due to the complexity and uncertainty of information. It is suggested that type-2 fuzzy numbers are more capable in detecting the meaning of process shifts. This paper aims to develop interval type-2 fuzzy (IT2F) Exponentially Weighted Moving Average (IT2F-EWMA) control charts as a new method where the advantages of lower membership and upper membership, which can capture sensitivity and variability in manufacturing data. In the proposed method, we also employed the Best Nonfuzzy Performance method as the defuzzification method instead of the typical centroid method. In order to confirm the performance of the proposed control chart, the average run length (ARL) is calculated and compared to the other three charts. To test the performance of the proposed EWMA, twenty samples were analysed to identify the defects in the fertilizers’ production. Based on the result of the conventional chart, 8 out of 20 samples are “uncontrolled”. In contrast, the type-1 chart found 16 samples are “uncontrolled”, whereas IT2F-EWMA found 18 samples are “out of control”. Consequently, it is proven that IT2F-EWMA is the best method to be used in dealing with vague and fuzzy data since it is more precise and vulnerable. Lastly, the ARL test shows that IT2F-EWMA charts outperform the other control charts.