Control Chart (Short-Run Z-MR)

Z-MR — Standardised I-MR for Short Runs

In workshops or tooling environments many different parts are produced in small batches. A classic I-MR chart needs 20–25 points per part — short runs cannot meet that. The Z-MR chart works around this by standardising each value within its part; all parts then live on one single chart.

Standardisation: For each part j compute mean x̄_j and σ̂_j (from MR̄_j/d₂). Each value is transformed to z_ij = (x_ij − x̄_j) / σ̂_j. Under stable conditions z is ~N(0,1).

Control limits: On the z chart: CL = 0, UCL = +3, LCL = −3 (3σ convention). On the MR chart: CL = MR̄_z, UCL = D₄·MR̄_z, LCL = 0.

Pros: one chart for many parts, continuous monitoring across job changes. Cons: lose the direct meaning of the original unit on the chart (interpretation is in σ units).

Pitfalls

Too few points per part: With n=1 or n=2 per part σ̂_j becomes unreliable. Rule of thumb: at least 5 points per part before standardisation is meaningful. Parts with too few points are handled as z=0 and surfaced via a warning.

Worksheet order: The chart plots in worksheet order. The group column must match the actual production order; otherwise within-part trends are invisible.

Heterogeneous σ: If spread differs strongly between parts, a 1σ shift on part A can look the same as a 0.3σ shift on part B. The chart normalises this, but diagnosis needs the per-part σ̂ table.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Available in the following cycles

• DMAIC: Control
• DMADV: Verify
• 8D: D6 — Implementation