EWMA Chart

The EWMA (exponentially weighted moving average) chart is a SPC Chart PRO chart type for catching small, sustained shifts in a process far sooner than a Shewhart chart can.

Like the CUSUM chart, EWMA is a time-weighted chart: instead of judging each point on its own, it blends every point with the smoothed history before it. A small, steady bias that no single point would flag builds up in the moving average until it crosses a control limit. EWMA and CUSUM detect the same kinds of shifts — EWMA presents the result as a single smoothed line, which many people find easier to read.

Select EWMA chart (time-weighted) in the Chart Type dropdown.

How It Works

Each plotted point is a weighted average of the current observation and all previous ones, with the weight decaying exponentially into the past: zᵢ = λ·x̄ᵢ + (1 − λ)·zᵢ₋₁.

The weight λ (between 0 and 1) sets how much the newest point counts. A small λ leans on history and smooths heavily — best for detecting small shifts — while a λ near 1 approaches a plain Shewhart chart. The moving average starts at the process mean and is compared against control limits a distance L sigma from the center line.

A distinctive feature: the control limits start narrow and widen over the first several points before settling at a steady width. Early on the moving average has little history, so its variability is smaller and the limits are tighter; as history accumulates they open to their steady-state width. This is the flared look at the left of the chart.

The weight and the limit width are usually chosen together from an ARL (average run length) table; the defaults, λ = 0.2 and L = 3, are a common general-purpose choice.

Panel Options

EWMA options appear in the SPC section when the EWMA chart type is selected.

Option	Description	Default
Weight (λ)	How much the current point counts in the average, between 0 and 1. Smaller values smooth more and detect smaller shifts.	0.2
Limit width (L)	The distance from the center line to the control limits, in sigma units.	3
Historical mean	The center line the average is measured against. When empty, the mean of the data is used.	Mean of data
Historical σ	The process standard deviation. When empty, it is estimated from within-subgroup variation.	Estimated

Individuals or Subgroups

EWMA works on individual measurements or on subgroups. Set the Subgroup size in the SPC section: a size of 1 treats each row as one point, while a larger size smooths the subgroup means and tightens the limits by √n.

Reading the Chart

Follow the smoothed line, not the raw points. While the process is on target the line drifts gently around the center; a real shift bends it steadily toward a limit until it crosses and the point is ringed. Because the line lags the raw data, a crossing confirms a shift that began a few points earlier — the trade-off for the chart's sensitivity to small shifts.

Methods and Formulas

For each point i, with subgroup mean x̄ᵢ, process mean μ, and the standard error of the mean σ_x̄ = σ ⁄ √n:

• Statistic: zᵢ = λ·x̄ᵢ + (1 − λ)·zᵢ₋₁, starting from z₀ = μ
• Center line: μ
• Control limits at point i: μ ± L·σ_x̄·√( (λ ⁄ (2 − λ))·(1 − (1 − λ)²ⁱ) )

The term under the root grows from a small value toward λ ⁄ (2 − λ) as i increases, which is why the limits widen and then level off. The within-subgroup sigma is estimated the same way as for the matching Shewhart chart — the average moving range for individuals, the pooled subgroup deviation for subgroups — unless a Historical σ is supplied.

Run Rules on EWMA

Because each EWMA point already carries the history of every point before it, the pattern-based Nelson rules — runs, trends, and zone tests — do not apply; they would fire on the smoothing itself. For an EWMA chart the panel therefore shows only Rule 1, which flags any point beyond a control limit. The remaining rules are hidden automatically.

Point Exclusion on an EWMA Chart

Point exclusion works the same way on EWMA as on the CUSUM chart: an excluded point is dropped from the mean and sigma estimates, so the whole chart re-baselines to the estimate without it, but the point stays plotted and remains in the moving average. Excluding a point removes its influence on the center line and limits, not from the running average.

EWMA vs CUSUM

EWMA and CUSUM target the same problem — small, sustained shifts — and perform similarly. Choose by preference and context:

	EWMA	CUSUM
Plotted	One smoothed line	Two cumulative sums (upper and lower)
Reading	Follow the trend of the line	Watch either sum cross its boundary
Tuning	Weight λ and limit width L	Reference value k and decision interval h

For large, sudden shifts a Shewhart chart (XmR, Xbar-R, Xbar-S) still reacts faster; EWMA and CUSUM are the tools for the small, slow ones.

info

The weight, limit width, historical parameters, and subgroup size are saved with the dashboard. Like every chart type, EWMA works with both a time and a numeric X-axis.

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EWMA is part of SPC Chart PRO. For requirements, licensing, and support, see the SPC Chart PRO documentation.