A control chart plots a process statistic over time together with limits representing the variation expected from a stable process.

For an individual measurement $x$, a simple conceptual form uses centre line $\mu$ and control limits

$$UCL=\mu+3\sigma,\qquad LCL=\mu-3\sigma,$$

where $\sigma$ describes stable process variation. Practical charts estimate these quantities from process data using chart-specific methods.

A point beyond a control limit is evidence that stable background variation may no longer explain the observation. Patterns such as sustained runs on one side of the centre line can also indicate a process shift even when every point remains inside the limits.

Control limits are not specification limits. Specification limits come from product requirements; control limits describe process behavior.

For example, a process may be statistically stable around 10.00 mm with $3\sigma=0.20$ mm while the drawing allows only $9.95$ to $10.05$ mm. The process is stable but incapable. Conversely, a process can produce measurements inside specifications while showing a clear unstable trend that predicts future failure.

Subgroup charts can separate movement of the process centre from within-subgroup variation. The exact chart depends on how data are collected, but the governing idea remains the same: estimate normal process variation and detect evidence that the generating process has changed.