การเปรียบเทียบประสิทธิภาพของแผนภูมิควบคุมคุณภาพสำหรับตัวแปรลักษณะทางคุณภาพ 2 ตัวแปร ที่มีการแจกแจงแบบทวิคูณปกติ / พงษ์ศักดิ์ อภิเรืองธรรม = A comparison on efficiency of quality control charts for bivariate normal distributed characteristics / Pongsak Apirungtum
The purpose of this study is to compare the efficiency of control chars for2 variables when there are shifts in the process means. The control chars under consideration include 1) Univariate x̄ Control Chart, 2) Hotelling Control Char and 3) Mulivariate Shewhar x̄ - Char. The comparison employs the average run length (ARL) as the performance measure. The control variables assume time series constant time model. The study is made under the following situation. The distribution of X1 and X2 is assumed to be the bivariate normal distribution with population means and variances al and a? =I and correlation coefficient The shift in the process mean is assumed to be of the form The study of the mean shif is divided into 2 cases. Case and case , where the levels of he shift are and . The sample sizes (n) is fixedat 10. The data in this study is obtained via the Mote Carlo simulation technique and the experiment is done under 10,000 iterations in each case. The results of the study are as follows. Case 1: the experiment shows that Univariate X Control Chart and Multivariate Shewhart X - Chart are the most efficient. the experiment shows that Hotelling Control Char is the most ellicient control char, but, when Univariatc X Control Char and Mullivariate Shewha X - Chart are the most cfficicnt control charts. If there exist mean shifts in both variables, the experiment shows no pattem. This lack of pattern can be explained by the diflerence berween Mahalanobis distance( DM )and Euclidean distance( DE ).
