Monitoring reduction in variability with the range

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Abstract
When monitoring a process it is important to quickly detect increases and decreases in its variability. In addition to preventing any increase in the variability of the process and any deterioration in the quality of the output, it is also important to search for special causes that may result in a smaller process dispersion. Considering this, users should always try to monitor for both increases and decreases in the variability. The process variability is commonly monitored by means of a Shewhart range chart. For small subgroup sizes this control chart has a lower control limit equal to zero. To help monitor for both increases and decreases in variability, Shewhart charts with probability limits or runs rules can be used. CUSUM and EWMA charts based on the range or a function of the subgroup variance can also be used. In this paper a CUSUM chart based on the subgroup range is proposed. Its performance is compared with that of other charts proposed in the literature. It is found that for small subgroup sizes, it has an excellent performance and it thus represents a powerful alternative to currently utilized strategies.