Why "In-Tolerance" Parts Are Still Ruining Your Assembly Line

You receive a shipment of plastic components from your molder. The Quality Assurance (QA) report states that 100% of the sampled parts are within your ±0.15 mm tolerance. But when the parts hit the assembly floor, the snap-fits feel inconsistent, and operators are scrapping 10% of the units.

Why is the assembly line failing if the parts passed inspection? Because you are relying on Quality Control (sorting) instead of Process Capability (C_pk).

If a supplier relies on sorting, they are just measuring parts and throwing away the bad ones. But QA sampling isn't perfect. If the underlying manufacturing process is out of control, defective parts will inevitably slip through. To guarantee assembly success, you must measure the health of the entire production process using the Six Sigma C_pk index.

The Process Capability Index (C_pk) measures how close a process is running to its specification limits, relative to the natural variability of the process.

The Equation:

C_pk = min( (USL - μ) / (3 · σ), (μ - LSL) / (3 · σ) )

Where:

• USL = Upper Specification Limit
• LSL = Lower Specification Limit
• μ = The actual Mean (average) of the manufactured parts
• σ = The Standard Deviation of the process

💡 The Example

You have a critical snap-fit width designed at 10.00 mm ± 0.15 mm.
(USL = 10.15 mm, LSL = 9.85 mm).

The molder runs the press. They sample the parts and find the process has a Mean (μ) of 10.10 mm, with a Standard Deviation (σ) of 0.04 mm. Because 10.10 mm is technically less than your 10.15 mm limit, QA approves the batch.

Let’s run the true C_pk math:

• Upper half:
  (10.15 - 10.10) / (3 · 0.04) = 0.05 / 0.12 = 0.41

• Lower half:
  (10.10 - 9.85) / (3 · 0.04) = 0.25 / 0.12 = 2.08

Your C_pk is the smaller of the two numbers: 0.41.

The Result: The absolute minimum acceptable C_pk in standard manufacturing is 1.33 (which equates to a theoretical 99.99% yield). A C_pk of 0.41 is a statistical disaster.

It means your process average (10.10 mm) is shifted dangerously close to the upper limit (10.15 mm). Because the natural variation of the machine (±3σ) extends 0.12 mm in both directions, the tail end of your production bell curve is physically bleeding past the upper specification limit. Statistically, roughly 10.5% of the total production run is out of spec—the QA inspector just happened to miss them when pulling their tiny sample size.

🛠️ The Solution

Stop asking suppliers for "First Article Inspection" reports and start demanding C_pk data on critical dimensions. If C_pk < 1.33, you must intervene using one of three levers:

1. Center the Mean (μ): The process is shifted. Have the molder adjust the pack pressure, holding time, or cooling rate to drive the average dimension back down to the nominal 10.00 mm.
2. Reduce Variation (σ): If the mean is centered but C_pk is still low, the bell curve is too fat. This is a machine or tooling problem. You must fix the worn check-ring on the injection barrel, stabilize the chiller temperature, or fix unbalanced gate sizing to reduce cycle-to-cycle variation.
3. Widen the Spec (USL/LSL): If the supplier's process is fully optimized and σ simply cannot be reduced, your engineering tolerances are mathematically too strict for the chosen manufacturing method. You must redesign the assembly to accept a wider tolerance bandwidth.

Great engineering guarantees the process, not just the part.