Statistical Process Control Charts

A control chart puts a process statistic in time order with a center line and control limits based on an in-control reference period. Control limits are statistical monitoring thresholds, not necessarily customer specification limits or legal acceptability thresholds. A point beyond a limit can reflect a process change, a measurement error or a poor baseline; it does not name the cause. A Shewhart chart often watches each subgroup mean or another statistic and signals when a point breaches a control rule. NIST's handbook describes limits for means and variability built from preliminary process data. Shewhart charts are intuitive for larger abrupt shifts, but a small sustained change may leave every individual point inside limits. A team should choose the sampling interval and subgroup definition to match the process rather than treating rows gathered at different times as interchangeable. CUSUM, or cumulative sum, adds departures from a target over successive observations. Small deviations in the same direction can accumulate into a signal. NIST describes CUSUM as more efficient than a simple Shewhart approach for detecting small changes in the mean under specified designs. EWMA, or exponentially weighted moving average, blends the latest observation with the prior smoothed value. Older observations receive diminishing weights, allowing a gradual shift to emerge. The smoothing weight and control limits determine sensitivity and false-alarm behavior; neither chart detects every change instantly. Choose the reference period and chart design before judging signals. Autocorrelation, seasonality, changes in measurement definitions and varying sample sizes can distort naive limits. Investigate alarms with process logs and domain knowledge, and record whether an alert led to a real finding. For AI systems, charting input statistics may reveal data-pipeline changes, but only outcome labels can show whether a model's task performance changed. If labels arrive late, report that monitoring gap. Recalculate limits deliberately after an understood, stable process change instead of silently moving them whenever the chart alarms.