The Xbar-R chart is a statistical process control mechanism designed to monitor and maintain process stability by tracking variable data over time through subgroup means (X-bar) and subgroups ranges (R). This theory relies on the principle that for small sample sizes, the range provides a more reliable estimator of standard deviation than direct calculation due to its reduced sensitivity to individual value fluctuations. Formally defined using constants $A_2$, $D_3$, and $D_4$ which are functions of subgroup size $n$, these charts establish control limits at three standard deviations ($\pm 3\sigma$) from the center line based on the average range or mean, distinguishing between common cause variation inherent to a process and assignable causes indicating instability.
The Xbar-R chart is a statistical process control mechanism designed to monitor and maintain process stability by tracking variable data over time through subgroup means (X-bar) and subgroups ranges …