CUSUM and EWMA: catching small, sustained shifts
Follow how CUSUM and EWMA accumulate small process shifts, work through a six-point example, and choose their parameters with false alarms in mind.
Sensor drift is a slow, systematic change in a reading while the true input stays constant. It shows up through redundant sensor comparison, checks against a known state, physical balances and long-term baseline trends. Drift must be separated from real process change, or the conclusion will be wrong.
Drift is a systematic change in a sensor's reading over time, while the input stays the same. It differs from noise because its direction is consistent and its rate is slow. A single reading rarely reveals it, since the effect can sit inside normal process variation. For that reason, drift is usually found by comparing against a reference, or by looking at a trend over a long time window.
Drift is a property of the sensor. Process drift means the process itself has changed. The two can appear on the same chart, yet their causes and the actions they need are different. Common causes of sensor drift include calibration shift, fouling, mechanical wear and temperature-dependent behaviour.
Suppose two temperature sensors sit on the same pipe (hypothetical). At the start, the difference between them is 0 °C. Assume sensor A drifts by 0.2 °C per month relative to sensor B. After six months the difference is 6 × 0.2 = 1.2 °C. If a tolerance band of 0.5 °C is chosen, the difference exceeds it in the third month, when 3 × 0.2 = 0.6 °C. The difference alone does not say which sensor moved, so a third reference or a check at a known temperature is needed. To catch a small, sustained drift earlier, methods such as EWMA or CUSUM can signal sooner than a single threshold crossing.
The most important mistake is treating drift as process change, or the reverse. If the process really changed, correcting the sensor hides that change. The second mistake is retraining an ML model on drifting data: the model learns the new level as normal, so the anomaly never appears. The third is relying on statistics without a reference check. A single sensor can show a slow drift as normal when judged against its own past. Redundant sensors can also drift together if a common cause, such as a shared heat source, affects both.
A calibration error usually appears at one moment, as an offset found during a comparison with a reference. Drift builds up between calibrations and shows as a trend in the as-found values. Using both kinds of information together shows when the deviation probably started and how fast it grew.
Partly. A multivariate model can flag a sensor when its relation to other variables breaks. Yet a slow drift is often learned as normal variation. Do not treat a model output as proof on its own; combine it with reference checks and physical balances.
Example numbers are hypothetical, not measured field results.