7.1 Statistical Process Control (SPC): Cp & Cpk

SPC is the difference between inspecting quality in (reactive) and building quality in (proactive). Inspection tells you that you just made a bad part; SPC tells you that you are about to make a bad part. It is the practice of listening to the "heartbeat" of the machine. If you ignore the statistical trends, you are driving blind, waiting for the crash (scrap) to tell you to stop.

Cp vs. Cpk: The Physics of Capability

We use two metrics to determine if a process can meet the customer's requirements. Do not mix them up.

Cp (Process Potential): The Width

• Definition: Can the car fit in the garage if we drive perfectly? It compares the width of the tolerance (Spec Limits) to the natural variation of the process (6σ).
• The Logic:
  • If Cp < 1.0 → Then the car is wider than the garage door. No amount of operator skill will fix this. Action: Invest in better tooling or loosen the tolerance.
  • If Cp ≥ 1.33 → Then the process is potentially capable.

Cpk (Process Capability): The Centering

• Definition: Is the car actually parked in the center of the garage? It accounts for the shift of the mean.
• The Logic:
  • If Cpk < 1.0 → Then parts of the distribution are hitting the wall (out of spec). You are producing scrap.
  • If Cpk = Cp → Then the process is perfectly centered.

Pro-Tip: A high Cp and a low Cpk means your machine is precise (tight grouping) but inaccurate (aimed at the wrong target). This is the easiest problem to fix: just adjust the offset.

Control Limits vs. Specification Limits

This is the most common error on the shop floor. Operators often think the Control Limit is the "Fail" line. It is not.

• Specification Limits (USL/LSL): Defined by the Customer/Print. These are the "Cliffs." If you cross them, the part is dead.
• Control Limits (UCL/LCL): Defined by the Process Data (typically ±3σ from the mean). These are the "Guardrails."

The Rule of Law:

• If a point exceeds the Control Limit (UCL/LCL) → Then the process has changed. Stop and investigate. The part is likely still good (if inside USL/LSL), but the process is out of control.
• If you adjust the machine because a part is "close" to the Spec Limit but still inside the Control Limit → Then you are introducing "Tampering" (over-correction), which actually increases variation.

Reaction Rules (The "Nelson" Logic)

When do you stop the line? Do not rely on "gut feeling." Use defined statistical triggers.

Stop & Fix If:

1. The Outlier: One point falls outside the Control Limits (±3σ).
2. The Trend: Seven consecutive points are moving in the same direction (Up or Down). Tool wear is occurring.
3. The Shift: Seven consecutive points are on the same side of the Mean. The process center has shifted.

Final Checklist