[ $\overline{X}$ ] Chart with Geometrically Adjusted Control Limits under Continually Improving Processes

An adjusted control limit of the chart is proposed for monitoring the continually improving processes. The continual improvement of the process implies the decrease of the process variance, which is represented by a logistic curve. The process standard deviation is estimated by the exponentially weighted moving average of the sample standard deviations from the past to the current times. The control limits are adjusted by the estimated standard deviation at every sampling time. The performance of the adjusted control limit is compared with that of the standard control limits for various cases of the decreasing speed and size of the variance. The results show that the chart with the adjusted control limits provides better performances for monitoring the small and moderate shifts in continually improving processes.