A study of cumulative sum (x̄, s) control charts

The cumulative sum (CUSUM) control chart is known to be sensitive to a slight change of the process quality characteristics. The design of this control chart is based on a series of cumulative sums of the statistic derived from the data. For normally distributed characteristics, it is necessary to monitor both changes of the mean and variance simultaneously. However, it is difficult to design a joint CUSUM x̄ - R or x̄ - s control chart using the statistics x̄ and s or R jointly. Kanagawa et al. proposed a (x̄, s) control chart which enables the user to monitor both changes of the mean and variance simultaneously based on one statistic for normally distributed characteristics. When the CUSUM control chart is considered based on the (x̄, s) control chart, it is possible to design and use the CUSUM control chart more easily than the joint CUSUM x̄ and either the R or s control charts. We consider a CUSUM (x̄, s) control chart in order to improve the performance for a slight change of the process quality characteristics. The economical operation of the CUSUM (x̄, s) control chart is also considered.