Detect small, sustained process shifts faster than a Shewhart chart. Paste your time-ordered data, set a target, choose EWMA or CUSUM, and see the chart, control limits, and signal points — all client-side.
Paste your time-ordered data, set a target, choose EWMA or CUSUM, and press Calculate to plot the chart and flag any signals.
Watch: CUSUM and EWMA Charts for Detecting Small Shifts
A process drifts by a small amount and an ordinary control chart misses it for weeks. Enter the lab to see how EWMA and CUSUM catch slow, sustained shifts much sooner.
Paste your measurements in time order, set your process target (the normal, in-control level), and enter the process standard deviation — or leave it blank to let the calculator estimate it.
EWMA creates a running average that weights recent readings more heavily than old ones, so it notices drifts quickly. The control limits gradually widen to a steady band as you add more data.
CUSUM keeps a running tally of how far each reading is from your target. Because it adds up small drifts over time, it can catch slow changes much earlier than standard charts — a signal goes off when the tally passes a threshold.
EWMA and CUSUM charts are time-weighted control charts built to catch the small, sustained shifts that a standard Shewhart chart misses. By accumulating information across consecutive points, they signal a drift of half a standard deviation or so long before any single point breaches the 3-sigma limits.
EWMA (Exponentially Weighted Moving Average) and CUSUM (Cumulative Sum) are time-weighted control charts. Rather than judging each point in isolation like a Shewhart chart, they pool information from past observations — EWMA through a weighted moving average, CUSUM through a running sum of deviations from target. This memory makes them especially good at detecting small, sustained shifts in the process mean.
Both charts are built to catch small, slow shifts that an ordinary chart would miss. EWMA keeps a running weighted average where the newest reading counts most and older ones fade, so a gentle drift gradually bends the line until it crosses a limit. CUSUM instead keeps a running total of how far each reading sits from target; while the process is on target that total stays near zero, but a sustained shift makes it steadily build up until it passes a decision threshold. Either way, the point where the line breaks its limit is roughly where the shift began.
A fill-weight process is set to 500g. The standard control chart looks fine for weeks — no alarm points. But a CUSUM chart of the same data reveals a consistent downward drift starting around day 18.
Standard charts detect big sudden shifts. CUSUM catches small, steady drifts — the kind that quietly erode quality for weeks before anyone notices.
What to do with this: Investigate day 18. Was a pump recalibrated? Did a supplier batch change? Catching this early saved potentially thousands of underweight units.
Many real process problems are slow drifts — tool wear, gradual contamination, creeping temperature — not dramatic spikes. A Shewhart chart can take 40+ samples to notice a 1σ shift, by which point a lot of off-target product has been made. EWMA and CUSUM cut that detection time dramatically, so you intervene before scrap and rework pile up.
Reach for EWMA or CUSUM in the Control phase of DMAIC when you are monitoring an established process for small, sustained shifts, especially with individual measurements rather than subgroups. They complement — not replace — Shewhart charts: many teams run an I-MR chart for large shifts alongside an EWMA or CUSUM for small ones.
Time-weighted charts are a core part of the advanced SPC toolkit taught at Black Belt level. They give the Control phase a sensitive early-warning system, helping teams sustain hard-won improvements and react to creeping degradation long before capability indices slip.
When the chart signals, trace back to where the statistic first started drifting and look for what changed around then — materials, settings, people, environment. Remove the special cause, then confirm the fix by continuing the chart and watching the statistic return toward target. If no shift is real (a false alarm), review your σ and target estimates and your λ / k / h settings. Pair the chart with a run chart or I-MR chart for a complete monitoring picture.
Combine EWMA and CUSUM charts with run charts, control limits, and a DMAIC project structure for sensitive, sustained process monitoring.
A Shewhart chart (such as an I-MR or X-bar chart) reacts mainly to a single point falling outside the 3-sigma limits, so it catches large, sudden shifts well but is slow to detect small ones. EWMA and CUSUM charts both accumulate information from past observations, which makes them far more sensitive to small, sustained shifts of around 0.5 to 1.5 standard deviations. EWMA uses an exponentially weighted moving average of the data; CUSUM accumulates the running sum of deviations from the target.
For an EWMA chart, lambda (λ) controls how much weight is given to the most recent point — a smaller λ of 0.05 to 0.2 is more sensitive to small shifts, while a larger λ of 0.3 to 0.4 reacts faster to larger shifts; λ=0.2 with control-limit width L=3 is a common default. For a CUSUM chart, k is the slack or reference value, usually set to half the shift you want to detect (k=0.5σ for a 1σ shift), and h is the decision interval, typically 4 or 5 sigma. Larger k and h reduce false alarms but slow detection.
A standard Shewhart chart treats each point in isolation, so a shift smaller than about 1.5 standard deviations rarely pushes a single point past the control limits. EWMA and CUSUM both pool evidence across many consecutive points: EWMA smooths the data with a weighted average, and CUSUM adds up the small deviations from target until they cross a decision limit. Because a small sustained shift produces many points that are slightly off-target in the same direction, this accumulated evidence crosses the limit long before any single point would on a Shewhart chart.
On an EWMA chart, a signal occurs when the EWMA statistic z crosses above the upper control limit or below the lower control limit; the crossing point marks roughly when the shift began. On a CUSUM chart, the upper sum SH and lower sum SL stay near zero while the process is on target but climb steadily once a shift occurs — a signal is raised when either sum exceeds the decision interval h. In both cases, investigate the special cause around the point where the statistic first started drifting, not just where it crossed the limit.
An EWMA or CUSUM signal is an early warning that your process has drifted. Structured training shows you how to investigate, correct, and sustain control.
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Want to detect small process shifts inside a full DMAIC project? The Black Belt covers EWMA and CUSUM charts, advanced SPC, and the complete Control phase toolkit.
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