cpk

Cpk (Process Capability Index) quantifies how well a process output stays within specification limits relative to its natural variation, measuring both centering and spread. **Definition**: Cpk = min[(USL - mean) / (3*sigma), (mean - LSL) / (3*sigma)]. Takes the worse of upper and lower capability. **Interpretation**: Cpk = 1.0: Process spread equals spec width, 0.27% out-of-spec (2700 ppm). Cpk = 1.33: Standard minimum for production processes (~63 ppm). Cpk = 1.67: High-capability process (~0.6 ppm). Cpk = 2.0: Six-sigma capable process (~0.002 ppm). **Cp vs Cpk**: Cp measures spread only (ignores centering). Cpk accounts for process mean offset from specification center. Cpk <= Cp always. **Cpk < 1.0**: Process is not capable - significant fraction of output falls outside specifications. Immediate improvement required. **Requirements**: Semiconductor fabs typically require Cpk >= 1.33 for established processes, >= 1.67 for critical parameters. **Calculation requirements**: Need sufficient data (typically 25+ subgroups). Process must be in statistical control (stable). Normal distribution assumed. **SPC relationship**: Cpk calculated from SPC data. Ongoing monitoring ensures process remains capable. **Improvement**: Increase Cpk by reducing variation (sigma) or centering process on target. **Short-term vs long-term**: Cpk from short sample may overstate capability. Ppk uses long-term data and is often more realistic. **Reporting**: Cpk reported for key process parameters in qualification reports, process reviews, and customer quality reports.