The Use of Simulation in Fuzzy Control Charts

Abstract

Fuzzy Control Charts are modern tools in statistical process analysis and control, representing an advancement over traditional models by incorporating Fuzzy Logic. These charts are designed to address issues arising from uncertainty or imprecision in data encountered in industrial systems or administrative processes. In this study, four types of fuzzy control charts were utilized: the fuzzy () chart, the fuzzy () chart, the fuzzy exponentially weighted moving average (FEWMA) chart with three weighting factors (λ = 0.3, 0.6, 0.9), and the fuzzy cumulative sum (FCUSUM) chart. A triangular membership function was used, and a simulation approach was applied with three sample sizes (n = 3, 4, 6), three batch sizes (m = 40, 80, 100), and three cutoff levels (α = 0.3, 0.5, 0.7). Three comparison criteria were adopted: the capability index (C_P), the process performance index (C_PK), and the average run length (ARL). The results showed that the ARL increases as sample sizes and batch sizes grow, while the CP and CPK indices were equal in some charts. Moreover, the performance of the charts improved when smaller sample sizes were used, indicating the flexibility of nonparametric control charts.