A Novel Fuzzy Cumulative Sum Control Chart with an α-Level Cut Based on Trapezoidal Fuzzy Numbers for a Real Case Application

Statistical process control (SPC) is widely used to monitor production processes in many industries under certain conditions. When dealing with a quality characteristic for uncertainty, fuzzy numbers are used in the context of the statistical process control (SPC) to monitor a fuzzy production process. The aim of this paper is fourfold. One, a fuzzy X¯-R control chart with an α-level cut is used based on trapezoidal fuzzy numbers (TFNs) for detecting the large shifts in the fuzzy process mean. Second, a fuzzy cumulative sum (FCUSUM) control with an α-level cut based on TFNs is firstly developed for detecting the small shifts in the fuzzy process mean. Third, the fuzzy process capability indices (FPCIs) are presented to measure the fuzzy process performance. Finally, an ultra-fine calcite production process is controlled with both the fuzzy X¯-R control chart and the proposed FCUSUM control chart. The results of the fuzzy X¯-R control charts show that the fuzzy production process is in control, and large shifts in the fuzzy process mean were detected. On the other hand, the results of the FCUSUM charts show that the fuzzy production process is out of control, and small shifts in the fuzzy process mean were detected. FPCIs are also conducted, and the results of fuzzy Cpk indices show that the ultra-fine calcite production process is not capable of meeting specification limits.