A Comparison of the Efficiency of the HEWMA THWMA and DMEWMA Control Chart for 3 Parameter Gamma Distribution

Abstract

The purpose of this research was to compare the performance of the three control chart types: The Hybrid Exponentially Weighted Moving Average Control Chart (HEWMA), Triple Homogeneously Weighted Average Control Chart (THWMA) and Double Exponential Weighted Average Control Chart (DMEWMA) by detecting shift in size of the shape parameter of the process in which the data has a 3-parameter gamma distribution.simulating the data studied by the Monte Carlo Method in which each situation was repeated 10,000 cycles by specifying the shape parameter, scale parameter,location parameter amd the smoothing parameters of the HEWMA control chart were set to 0.05, 0.08 and 0.1, 0.3, 0.5 THWMA control chartis 0.03, 0.07, 0.09, 0.1, 0.2, 0.5 and DMEWMA control chart is 0.03, 0.05, 0.07, 0.09, 0.2, 0.5. Process variation shift size () is 0.01, 0.03, 0.05, 0.07, 0.09, 0.1, 0.3, 0.5, 0.7, 1.5, 2 and 2.5. The criteria for the control chart's performance is determined by its average run length (ARL), where the most efficient control chart gave the least average run length when the process was out of control. THWMA control charts the best monitor shift of parameter and as the size increases the THWMA control chart performs similarly to the DMEWMA1 and DMEWMA2 control charts if the shift is large. The HEWMA control chart will give you the best performance.