Statistical Methods
Choose the memory of an exponentially weighted monitor
Choose the memory before seeing the alert
An exponentially weighted moving average (EWMA) updates a running value by adding a fraction of the difference between the new observation and the previous running value. A small weight retains a long history. A large weight follows recent observations more closely. The observation interval matters because five updates can mean five hours or five months.
Demonstrate the response with a step
Initialize the series at a historical target. Apply one or more hypothetical shifts of practical concern and tabulate the response at each update. Decide whether the resulting delay is acceptable. Keep the baseline and the timing rule with the monitoring specification.
Hypothetical calculation
Beginning at 100 units, take observations of 108 and 108 with weight 0.25. The first update is 102 and the second is 103.5. The original target still carries weight 0.75², or 56.25%, after two updates. With weight 1 the series immediately equals each observation. These different paths should be visible in a design check before operational use.
For independent observations with constant dispersion, steady-state EWMA variance scales by the weight divided by two minus the weight. Early values initialized at a fixed target have a different variance. Distinguish startup from steady-state behavior when setting limits. A smoother alone supplies neither a signal threshold nor evidence that a change is real.
Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 6.3.2.4. EWMA Control Charts.