In Control AND Capable: The Number That Passes a Failing Process

Here is a process-capability report on 200 real measurements: Ppk = 1.36. By the universal rule of thumb — anything above 1.33 is capable — that is a pass. Sign it off, ship the process.

It's a lie. Not an arithmetic error — every digit is correct — but a lie all the same, because that one number is describing a process that was drifting out of control while it made those parts, and a single capability index physically cannot see it. This is the story of how a control chart catches exactly what the capability number hides, why quality engineers insist on control before capability, and how to run the whole loop — no code — in about four minutes.

The spec is 74.00 mm ± 0.05 (lower limit 73.95, upper 74.05). The data is 40 batches of 5 rings = 200 measurements off a forging line.

Step 1 — Look before you compute

A quick Summary: mean 74.001 mm, standard deviation ≈ 0.011. Dead-centered on target, and tight relative to a ±0.05 tolerance. It looks excellent. But a histogram pools every measurement into one pile and discards the order they were made in — so it can describe the shape and stay completely silent on whether the process was stable. Capability indices are predictions of a future defect rate; a process without a stable behavior has no future rate to predict. So before any index, we test for stability.

Step 2 — Prove control (X-bar & R)

Take the 25 baseline batches and run an X-bar & R chart — Value = Diameter, Subgroup = Sample. The control limits are computed from the process's own batch-to-batch variation, not from the spec:

• X-bar center 74.001, limits 73.988 – 74.014
• R-chart center 0.0228, upper limit 0.0481

All 25 batch means fall inside the limits; the range chart is calm; no Nelson-rule violations. The process is in statistical control. Now — and only now — does "capable" mean anything.

Step 3 — Judge capability (Cp / Cpk)

Analyze ▸ Process Capability, Measurement = Diameter, spec LSL 73.95 / Target 74.00 / USL 74.05. The capability histogram drops the two spec limits on as vertical lines with a fitted normal curve — and the whole distribution sits in the middle third of the tolerance.

Cpk 1.66 against a "capable ≥ 1.33" bar is genuinely excellent. σ within-batch is 0.0098; overall 0.0101. This is the report you'd frame.

Step 4 — The drift the chart caught

The process didn't stop at batch 25 — it ran 15 more. Put all 40 batches on the X-bar chart. The first ~34 hug the center line. Then it climbs, and batches 37, 38, 39 punch through the upper control limit (batch 39's mean 74.023 vs the limit 74.014) — flagged in red. A tool wearing, a temperature creeping, a new material lot; whatever it was, the chart caught it the instant the process left its own statistical envelope — a red dot, not a gut feeling.

Step 5 — The lie of the combined number

Now the trap. Skip the control chart, grab all 40 batches, run one capability study — drift included:

Ppk 1.36 is still above 1.33 — still "passing." And it's meaningless: it averages a good process together with a drifting one, smearing 15 batches marching toward the edge into a single reassuring digit. The control chart three inches away is lit up red. That's the whole lesson: capability without control isn't a smaller number — it's an untrustworthy one. Establish control first. Then the index is a real prediction.

What we actually did

Two questions — in control? then capable? — in that order, in one window, on real data. That's why Stratum ships SPC control charts and Process Capability as a pair.