XmR chart

XmR chart (Individuals and Moving Range chart) is a type of control chart used in statistical process control to monitor individual measurements and the variation between consecutive values in a process over time.

Map the data fields

• Subgroup/Lot: This field represents the different observations or time points being measured.
• Process Value: This field contains the individual measurement value for each observation.
• UCL (SPC Variable): Optional field for custom upper control limits for the SPC Variable (X) series.
• LCL (SPC Variable): Optional field for custom lower control limits for the SPC Variable (X) series.
• Central line (SPC Variable): Optional field for custom center line values for the SPC Variable (X) series.
• UCL (SPC Range): Optional field for custom upper control limits for the SPC Range (MR) series.
• LCL (SPC Range): Optional field for custom lower control limits for the SPC Range (MR) series.
• Central line (SPC Range): Optional field for custom center line values for the SPC Range (MR) series.

Calculation Methodology

The XmR chart consists of two charts: the Individuals (X) chart and the Moving Range (MR) chart. Calculations are performed as follows:

Process Mean (X̄)

X̄ = Sum of all individual values / Total number of observations

Moving Range (MR)

MR_i = |X_i - X_(i-1)|  for i ≥ 2

Average Moving Range (MR̄)

MR̄ = Sum of all Moving Ranges / (Total observations - 1)

Control Limits — Individuals (X) Chart

Upper Control Limit (UCL):

UCL = X̄ + 3 × (MR̄ / d2)

Lower Control Limit (LCL):

LCL = X̄ - 3 × (MR̄ / d2)

Center Line (CL):

CL = X̄

Control Limits — Moving Range (MR) Chart

Upper Control Limit (UCL):

UCL = D4 × MR̄

Lower Control Limit (LCL):

LCL = D3 × MR̄

Center Line (CL):

CL = MR̄

Notes:

• If custom limits are provided, they override the calculated values
• Constants d2 = 1.128, D4 = 3.267, and D3 = 0 are used for a moving range of span 2 (consecutive pairs)
• The first data point has no moving range value and is excluded from MR calculations