Statistical process control is a method used for controlling processes in which causes of variations and correction actions can be observed. Control chart is one of the powerful tools of statistical process control that are used to control nonconforming products. Previous literature suggests that fuzzy charts are more sensitive than conventional control charts, and hence, they provide better quality and conformance of products. Nevertheless, some of the data used are more suitable to be presented in interval type-2 fuzzy numbers compared to type-1 fuzzy numbers as interval type-2 fuzzy numbers have more ability to capture uncertain and vague information. In this paper, we develop an interval type-2 fuzzy standardized cumulative sum (IT2F-SCUSUM) control chart and apply it to data of fertilizer production. This new approach combines the advantages of interval type-2 fuzzy numbers and standardized sample means which can control the variability. Twenty samples with a sample size of six were examined for testing the conformance. The proposed IT2F-SCUSUM control chart unveils that 15 samples are “out of control.” The results are also compared to the conventional CUSUM chart and type-1 fuzzy CUSUM chart. The conventional chart shows that 13 samples are “out of control.” In contrast, the type-1 fuzzy CUSUM chart shows that the process is “out of control” for 14 samples. In the analysis of average run length, the proposed IT2F-SCUSUM chart outperforms the other two CUSUM charts. Thus, we can conclude that the IT2F-SCUSUM chart is more sensitive and takes lesser number of observations to identify the shift in the process. The analyses suggest that the IT2F-SCUSUM chart is a promising tool in examining conformance of the quality of the fertilizer production.

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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.