QM Bench

SPC simulator: watch a control chart react live

A machined diameter is produced and measured in subgroups of 5. Change the setting, add a disturbance and see how the X̄-R chart, the Nelson rules and Cpk respond. Then play the game: a hidden special cause starts at a random moment. Can you name it?

Cpk (last 30)
–
Ppk (last 30)
–
Mean
10.000
Subgroups
0
Phase 1: collecting 20 subgroups to calculate control limits…
X̄ chart (subgroup means)
R chart (subgroup ranges)
Histogram of the last 30 subgroups against the specification
LSLUSL
Event log

No interventions yet.

What to try

  1. Let it run. Points move up and down but stay inside the limits: this is common-cause variation. Adjusting the machine now only makes it worse (try the Deming funnel).
  2. Tool wear. Watch for six points in a row rising (rule 3) before anything leaves the limits. SPC warns you before you make scrap.
  3. New material batch. The mean jumps. Nine points on one side of the centre line (rule 2) is often the first signal.
  4. Untrained operator or loose gauge. The R chart reacts first. Note how Cpk drops even when the parts themselves did not change (gauge case): that is why a Gage R&R comes before capability.
  5. Corrective action. Bring the process back to standard and watch the chart return to control.

Key ideas for your assignment

  • Control limits come from the process (±3σ of the subgroup means); specification limits come from the customer. They are different things.
  • “In control” means predictable, not necessarily good. A stable process can still be off target or too wide for the tolerance (low Cpk).
  • Cpk uses the within-subgroup variation (R̄/d₂); Ppk uses the total variation. When special causes are present, Ppk falls below Cpk.

Try it with your own data in the process capability calculator, or test yourself in the SPC quiz.