Improved <italic>R</italic> and <italic>s</italic> control charts for monitoring the process variance

The Shewhart <italic>R</italic> control chart and <italic>s</italic> control chart are widely used to monitor shifts in the process spread. One fact is that the distributions of the range and sample standard deviation are highly skewed. Therefore, the <italic>R</italic> chart and <italic>s</italic> chart neither provide an in-control average run length (ARL) of approximately 370 nor guarantee the desired type I error of 0.0027. Another disadvantage of these two charts is their failure in detecting an improvement in the process variability. In order to overcome these shortcomings, we propose the improved <italic>R</italic> chart (IRC) and <italic>s</italic> chart (ISC) with accurate approximation of the control limits by using cumulative distribution functions of the sample range and standard deviation. Simulation studies show that the IRC and ISC perform very well. We also compare the type II error risks and ARLs of the IRC and ISC and found that the <italic>s</italic> chart is generally more efficient than the <italic>R</italic> chart. Examples are given to illustrate the use of the developed charts.