EWMA Control Chart
Exponentially Weighted Moving Average (EWMA) Control Chart · Also known as: exponentially weighted moving average chart, EWMA control chart, geometric moving average chart, EWMA kontrol kartı
The exponentially weighted moving average (EWMA) control chart, introduced by S. W. Roberts in 1959, monitors a process using a weighted average that gives the most recent observation the greatest weight while letting older observations fade geometrically. Like CUSUM, this memory makes it highly effective at detecting small, sustained shifts in the process mean, with a single smoothing parameter λ controlling how much past information the chart retains.
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When to use it
Use an EWMA chart, like CUSUM, when the goal is fast detection of small, persistent shifts in the process mean and the data are individual measurements or subgroup means. It is a natural choice when you also want a smoothed estimate of the current process level (the EWMA itself doubles as a one-step forecast), and it is robust to mild non-normality. Choose λ to match the shift size of interest — smaller λ for smaller shifts — and L jointly to hit the target average run length. It assumes a known target and standard deviation and approximately independent data; like other memory charts it reacts more slowly to very large abrupt shifts, so it is frequently paired with a Shewhart chart that handles those.
Strengths & limitations
- Highly sensitive to small, sustained shifts in the mean, comparable to CUSUM.
- A single, interpretable parameter λ tunes the memory and sensitivity.
- The smoothed statistic doubles as an estimate/forecast of the current process level.
- Robust to mild departures from normality.
- Slower than Shewhart charts at detecting very large, abrupt shifts.
- Requires choosing λ (and L), with results depending on that choice.
- Needs a reliable in-control target and standard deviation.
- Autocorrelation in the data distorts the limits and run-length behaviour.
Frequently asked
What does the smoothing parameter λ control?
λ sets how much weight the current observation receives versus the accumulated history. Small λ (e.g., 0.05–0.25) gives long memory and high sensitivity to small shifts; λ close to 1 weights recent data heavily and makes the EWMA behave like a Shewhart chart. It is chosen jointly with the limit width L to achieve a target average run length.
How does EWMA compare to CUSUM?
Both are memory-based charts with similar ability to detect small sustained shifts. EWMA is often considered easier to design and interpret and degrades gracefully across a range of shift sizes, while CUSUM can be marginally more efficient for a specific shift it is tuned to. In practice the choice is largely one of preference and convention.
Why are EWMA limits sometimes curved at the start?
The EWMA's variance starts small and grows to a steady-state value as more observations accumulate. Using the exact time-varying variance produces control limits that widen over the first several points, improving sensitivity early on before settling to the constant steady-state limits.
Sources
- Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1(3), 239–250. DOI: 10.1080/00401706.1959.10489860 ↗
- Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6th ed.). John Wiley & Sons. ISBN: 978-0-470-16992-6
How to cite this page
ScholarGate. (2026, June 2). Exponentially Weighted Moving Average (EWMA) Control Chart. ScholarGate. https://scholargate.app/en/statistics/ewma-chart
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Attributes Control ChartStatistics↔ compare
- CUSUM ChartStatistics↔ compare
- Shewhart Control ChartStatistics↔ compare