Detect a sustained shift with a one-sided CUSUM

Translate the shift into measurement units

A one-sided cumulative sum can reveal a sequence of moderately elevated values. Choose the direction before examining the monitoring data. Use a stable reference mean and dispersion, and decide what shift would justify investigating the measurement process. For an upward chart, subtract the reference mean and a positive allowance from each new observation, add the previous cumulative sum, then reset negative totals to zero.

Keep a decision trace

Start at zero unless the protocol specifies a head start. Record each cumulative sum and the first occasion that meets the prespecified decision rule. The allowance determines which increments accumulate. The decision interval affects false signals and detection delay. Calibrate both to the intended process before interpreting an alarm rate.

Hypothetical sequence

For a reference mean of 10 minutes, allowance 0.5 minute and decision interval 3 minutes, observations 11, 11, 12 and 12 produce cumulative sums of 0.5, 1, 2.5 and 4. Under a rule that signals at or above 3, occasion four triggers review. One further observation of 9 would reduce the unreset sum to 2.5. Decide in advance whether monitoring stops or restarts at an alarm.

Check for a changed measurement instrument, staffing pattern or sampling rule. A crossing locates an occasion for investigation. It cannot identify the cause of the shift.

Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 6.3.2.3. Cusum Control Charts.

Upper CUSUM signal trace · Download the monitoring alarm investigation record