Simultaneous Use of X and R Charts for Positively Correlated Data for Medium Sample Size

摘要

The X chart is used to monitor the process mean while range (R) and S charts are used to monitor the process standard deviation. But when it is required to monitor the changes in both mean and standard deviation of the process, the joint X and R charts should be used simultaneously for better results. The design of modified joint X and R chart is based upon the sum of Chi-squares theory and it may be used for medium sample sizes. The performance of modified joint chart is compared with joint Shewhart chart for sample sizes of five. It is found that the joint modified X and R chart outperforms the joint Shewhart X and R chart at all the levels of correlation and process shifts in the mean and standard deviation. It is observed that the performance of joint chart deteriorates as the level of correlation increases. The simplicity in the design of the modified joint X and R chart makes it suitable for the industries where the data are positively correlated.