Machined shafts travel under a measuring head. Each subgroup contains independent diameter readings from a seeded normal process. Plot the subgroup means against fixed three-sigma control limits and distinguish a process signal from an individual specification failure.
• A 3D laboratory scene with: Lathe spindle and cutting tool; Diameter measuring head; Subgroup sample tray; Live X-bar control chart; Individual specification comparison. • Controls: Subgroup size (2-10); Known baseline standard deviation (0.02-0.1 mm); Mean shift after subgroup 10 (0-0.3 mm); Post-change spread multiplier (1-3); Random sequence seed (1-20). • Live readouts: Latest subgroup mean; Upper control limit; Lower control limit; Latest subgroup range; Mean-chart signals; Sampled parts beyond specification. • Guided experiments: Stable baseline; Mean shift; Spread increase without mean shift.
• Samples Xi ~ Normal(μ,σprocess²), baseline μ0=10 mm • Subgroups 1–10: μ=10, σprocess=σ; afterward μ=10+shift and σprocess=σ×spread • X̄=(ΣXi)/n; UCL/LCL=10±3σ/√n, fixed baseline • Signal only if X̄ lies outside these limits; R=max(Xi)−min(Xi) • Individual specification interval: 9.8–10.2 mm.
Known-baseline Shewhart mean chart with independent Gaussian samples and a reproducible seed. A subgroup is acquired every two model seconds. Only the single-point beyond-three-sigma rule is implemented. The displayed range is diagnostic and has no R-chart limits. No capability certification, measurement error or baseline estimation.
No. Control limits describe process statistics; specifications define acceptable individual products.
No. It is evidence to investigate, not a diagnosis by itself.
Most subgroup means remain inside limits; random false signals remain possible.
Known-baseline Shewhart mean chart with independent Gaussian samples and a reproducible seed. A subgroup is acquired every two model seconds. Only the single-point beyond-three-sigma rule is implemented. The displayed range is diagnostic and has no R-chart limits. No capability certification, measurement error or baseline estimation.