Q
AshToolbox Quality Lean Six Sigma Suite
Foundational Category: Statistical Process Control (SPC) • ~6 min read

Individuals and Moving Range (I-MR) Chart

Establish control limits for low-volume production, destructive tests, and batch chemical processes.

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Q:

When should an Individual and Moving Range (I-MR) chart be used?

Use an I-MR chart (also called an X-MR chart) when data is collected as single observations rather than subgroups, such as batch chemical assays, destructive testing, or automated 100% inspection where subgrouping is impossible or artificial.

Mean (X̄)10.3133Center Line
Average MR (MR̄)0.1793Moving Range CL
Est. Sigma (σ̂)0.1589MR̄ / 1.128
Process StabilityIn ControlNelson Rules
Individuals (X) Limits:LCL = 9.8366 | UCL = 10.7901
Moving Range (MR) Limits:LCL = 0 | UCL = 0.5857
Individuals (I) ChartCL: 10.313
UCL: 10.790CL: 10.313LCL: 9.837

Individual Measurements & Moving Range Architecture

The I-MR chart pairs an Individual measurements chart with a Moving Range (MR) chart between successive points. The within-sample dispersion is estimated using d₂(2) ≈ 1.12838.

Formulas

Moving Range: MRᵢ = |Xᵢ - Xᵢ₋₁|
Average Moving Range: MR̄ = Σ MRᵢ / (N - 1)
Sigma Estimate: σ̂ = MR̄ / d₂(2) = MR̄ / 1.1284
Individuals Limits: UCL = X̄ + 2.660 × MR̄,   LCL = X̄ - 2.660 × MR̄
Moving Range Limits: UCL_MR = 3.267 × MR̄,   LCL_MR = 0
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