การเปรียบเทียบแผนภูมิควบคุมสำหรับกระบวนการที่มีการเปลี่ยนแปลงในค่าเฉลี่ย / นิยม เจริญสุขโสภณ = A comparison on control charts for shifted process mean / Niyom Charoensuksophon
The objectives of this research was to investigate the efficiency of four Control Chart types, specifying the mean shift process. Four Control Chart types consisted of [Mean] Control Chart, Exponentially Weighted Moving Average Control Chart, Synthetic Control Chart and Run Sum Control Chart. The efficiency of these Control Charts was compared and measured by the use of Average Run Length method (ARL). The sample mean average was examined until the process was beyond control, as the micro and sigma were yet unknown, therefore, the unbiased estimates value x substituted micro and s/c(n[superscript *]) substituted sigma, which x and s/c(n[superscript *]) values were applied to establish the control chart. The data simulations were micro[subscript 0] = 10, sigma[superscript 2] = 1, and the mean shift level was tested at gamma = 0.5sigma,0.6sigma,0.7sigma,0.8sigma,0.9sigma,1.0sigma,1.1sigma,1.2sigma,1.3sigma,1.4sigma,1.5sigma,2.0sigma,2.5sigma,3.0sigma,3.5sigma,4.0sigma,4.5sigma,5.0sigma and sigma = s/c(n[superscript *]) at n sample (n = 4,5,6,7,8, 9,10,15,20,25,30,35,40,45,50); the mean level of the in-control process micro[subscript 0] = x and the ARL starting point of Synthetic Control Chart was ARL[subscript 0] = 300,370,500. Data, applied to this research, was derived by the use of simulated Monte Carlo method (1000 times) under each examination. The findings showed as follows: - Run Sum Control Chart showed the least ARL, at the slight mean shift [0.5, 0.8], at the 4-6 sample size. With the 7-8 sample size, Run Sum Control Chart and Synthetic 300 worked the best. Also, Synthetic 300 showed the least ARL with the 9 or more sample size. - Synthetic 300 and Synthetic 370 Control Chart showed the least ARL at the moderate mean shift [0.9, 2.0], with the 4-6 sample size, Synthetic Control Chart worked the best at the sample size of 7-10, and all Control Chart types showed the least ARL 15 or more sample size. - At the extreme mean shift [2.1, 5.0], all Control Chart types demonstrated the least ARL with all sample sizes. - The higher mean shift level, and the more sample size, the less ARL would be for all Control Chart types. Under this research, the result of the Power of Test, measured from the probability of the out-control sample mean shift, was the same as the Average Run Length. That is, the research had completely supported the most efficient control chart at the different mean shifts.
