A Type-2 Fuzzy u-Control Chart Considering Probability-Based Average Run Length

Fuzzy sets are an emerging trend in shaping the development of control charts for statistical process control. The sets are germane to vague data that comes from incomplete or inaccurate measurements. Nevertheless, fuzzy sets are inadequate in some areas of industry since their membership functions are crisp numbers. The fuzzy sets are not fully able to compute higher levels of uncertainty, which might degrade the performance of the analysis. Therefore, type-2 fuzzy sets are proposed to be merged with control charts since these sets are hypothesized to be more capable of detecting a defect in process control. This paper aims to develop interval type-2 fuzzy u (IT2Fu) charts as a new approach to detecting defects. In addition, this paper presents a comparative analysis of performances between traditional u-control charts, type-1 fuzzy u-control charts, and type-2 fuzzy u-control charts. 23 samples of lubricant data with 48 subgroups were examined to identify the defects. The output showed that all of the control charts produced almost similar results except for data 14, which is “out of control” in IT2Fu-control charts but “in control” in traditional u-control charts and “rather in control” in type-1 fuzzy u-control charts. Furthermore, the performances of the charts were compared using a probability-based average run length (ARL), where probability type 1 error is computed. It was found that the ARL value of the IT2Fu-control chart showed the lowest value among the three types of charts. The analysis indicated that the IT2Fu-control chart outperformed the traditional u-control chart and the type-1 fuzzy u-control chart. The results obtained seem to support the idea that IT2Fu-control charts are more sensitive compared to type 1 fuzzy u-control charts and traditional u-control charts, so that IT2Fu-control charts are able to adequately support incomplete and vague data on process control.