EWMA chart

The EWMA (Exponentially Weighted Moving Average) chart is a time-weighted control chart that assigns exponentially decreasing weights to older observations. It is highly effective at detecting small to moderate sustained shifts in the process mean.

Map the data fields

• Subgroup/Lot: The sequence, time, or batch identifier for each observation.
• Process value: The measured values to be monitored.
• UCL: Optional field for a custom upper control limit (overrides the calculated UCL).
• LCL: Optional field for a custom lower control limit (overrides the calculated LCL).
• Central line: Optional field for a custom center line (overrides the calculated target).

Calculation Methodology

Sigma Estimation

When no standard deviation is provided, sigma is estimated from the average moving range:

MR[i]   = |y[i] - y[i-1]|  for i = 1 … n
MR̄      = mean of all MR[i]
σ       = MR̄ / 1.128       (d₂ constant for subgroup size n = 2)

Target

Target = user-specified target  OR  ȳ (mean of all observations)

EWMA Statistic

The EWMA is initialised at the target and updated at each observation:

EWMA[0] = λ × y[0] + (1 - λ) × Target
EWMA[i] = λ × y[i] + (1 - λ) × EWMA[i-1]

Where λ (lambda) is the smoothing factor (0 < λ ≤ 1).

Control Limits

The steady-state (asymptotic) control limits are used:

Limit factor:

Limit factor = L × σ × √(λ / (2 - λ))

Upper Control Limit (UCL):

UCL = Target + Limit factor

Lower Control Limit (LCL):

LCL = Target - Limit factor

Center Line (CL):

CL = Target

Notes:

• If custom limits are provided, they override the calculated values
• L is the sigma multiplier for the control limits; L = 3 is typical for 99.7% confidence
• λ = 1 reduces the EWMA to a standard Shewhart Individuals chart
• Smaller λ (e.g. 0.1–0.2) gives heavier weighting to historical data and is better for detecting small shifts; larger λ reacts faster to large shifts
• The default λ is 0.2 if not specified or out of range