x-bar chart

An x-bar chart is a control chart that plots the arithmetic means of successive subgroups (samples) collected from a process, with center line at the overall mean and control limits at ±3 standard errors of the mean. It detects shifts in the process average by comparing each subgroup mean against upper and lower control limits computed from within-subgroup variation (typically the average range or standard deviation). The parameters are subgroup size n, overall mean X-double-bar, and estimate of standard error sigma/sqrt(n); persistence is achieved through plotted points, control limit calculations, and Western Electric or Western Rules decision algorithms. [formal: x-bar chart | substrate: matter | horizon: hours | explicit: yes | epoch: 0.01]