8.11 Statistical Process Control (SPC): Cp & Cpk
Manufacturing processes naturally vary. The engineering question is not "did this part pass?" but "is the process capable of consistently producing passing parts?"
8.11.1 Cp (Process Potential)
- Definition: Relates the width of the specification limits (Tolerance) to the width of the process variation ($6 \sigma$). It answers: "Could we fit inside the limits if we were perfectly centered?"
- Formula:
$Cp = (USL - LSL) /6 \sigma$6sigma
8.11.2 Cpk (Process Reality)
- Definition: Measures the actual capability by accounting for how centered the process is relative to the limits. It considers the "worst case" tail of the distribution.
- Formula: Cpk = min
- The 1.33 Standard: A Cpk of 1.33 (4 Sigma) is the minimum industry standard for a "stable" process. A Cpk of 1.67 (5 Sigma) is required for safety-critical automotive/medical features.
- Cpk < 1.0: The process is incapable. Defects are statistically guaranteed. Inspection must be 100%.
8.11.3 Western Electric Rules (Stop Triggers)
Operators must stop the process if any of the following statistical anomalies occur on a Control Chart:
- One point beyond the 3 sigma Control Limit.
- Two out of three consecutive points beyond the 2 sigma zone (Warning).
- Seven consecutive points on one side of the centerline (Process Shift).