Interval type-2 fuzzy moving average control charts considering explicit formula of average run length and their application

Abstract

Abstract Previous literature suggest that fuzzy control charts are more sensitive than conventional one hence, it provides better quality and conformance of products. However, it is known that much of the data used in manufacturing sector cannot be expressed by type-1 fuzzy numbers and some of it more suitable to be expressed in type-2 fuzzy numbers. This paper aims to develop type-2 fuzzy moving average (MA) control charts by considering interval type 2 fuzzy numbers, and the case of known and unknown standard deviations. This new control chart combines the advantages of lower bound and upper bound of interval type-2 fuzzy numbers and a modified Best Nonfuzzy Performance as defuzzification method instead of typical centroid method, which can find the upper and lower control limits. In order to verify the performance of the proposed control chart, average run length (ARL) is computed and compared to other charts which are type-1 fuzzy MA chart and conventional MA chart. Twenty samples with sample size of six of fertilizers’ production is examined to identify the defects. Based on the result of the conventional MA chart, 8 out of 20 samples are “out of control”. On the other hand, type-1 fuzzy MA chart founds 10 samples are “out of control”, whereas interval type-2 fuzzy MA chart found 15 samples are “out of control”. Thus, we can conclude that, interval type-2 fuzzy chart is more sensitive and takes lesser number of observations to identify the shift in the process. In addition, the ARL test shows that interval type-2 fuzzy MA outperforms the other control charts under the comparison of ARL. Thanks to the introduction of interval type-2 fuzzy numbers to the MA and the explicit formula of ARL where the quality of fertilizers production can be improved.