Moving Average (MA) chart

The Moving Average (MA) chart is a time-weighted control chart that smooths process data by plotting the average of the most recent observations within a fixed window. It is more sensitive to small shifts than a standard Shewhart chart while remaining easy to interpret.

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)

Moving Average

For each point i, the moving average is computed over a window of size w (span):

window start  = max(0, i - span + 1)
window size w = i - window start + 1     (ramps up until span is reached)
MA[i]         = (y[window start] + … + y[i]) / w

Control Limits

Control limits narrow as the window fills up, then stabilize once i ≥ span − 1:

Upper Control Limit (UCL):

UCL[i] = Target + (L × σ / √w)

Lower Control Limit (LCL):

LCL[i] = Target - (L × σ / √w)

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 (typically 3 for 99.7% confidence)
A larger span provides more smoothing but slower detection of shifts; a smaller span reacts faster
The default span is 5 (or n if n < 5)
Control limits are variable during the initial ramp-up period (i < span) and become constant once the window is full

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