Control-chart laboratory

Learning objectives

• Build I-MR and p charts in a free spreadsheet.
• Separate common-cause from special-cause variation.
• Apply a reaction plan without tampering with common cause.

Core idea

Control charts plot data in time order with a centre line and statistically derived limits (typically ±3σ); signals identify special causes to investigate, not specifications to widen.

Spreadsheet lab

• I-MR: MR_i = ABS(x_i − x_{i-1}); σ̂ = AVERAGE(MR)/1.128; UCL_I = X̄ + 3σ̂; LCL_I = X̄ − 3σ̂.
• p chart: p̄ = Σd / Σn; σ_i = SQRT(p̄(1−p̄)/n_i); UCL_i = p̄ + 3σ_i; LCL_i = MAX(0, p̄ − 3σ_i).
• Flag: any point beyond limits; 8 in a row on one side of centre; trend of 6 consecutive.

Garment-factory example

Daily shrinkage on a knit style shows X̄ = 3.1%, MR̄ = 0.22 → UCL_I ≈ 3.68%, LCL_I ≈ 2.52%. Day 14 hits 3.9% after a boiler change: investigate before adjusting the setter.

Method

1. Confirm gauge and rational subgroup.
2. Establish a clean baseline before setting limits.
3. Investigate signals; recompute limits only when stable and different.

Common mistakes

• Confusing specification limits with control limits.
• Adjusting the process for common-cause noise ('tampering').
• Mixing unlike styles or lines on the same chart.