Process Capability Index (Cpk) Calculator
Calculate the Process Capability Index (Cpk) to determine how well your process performs relative to specification limits. A Cpk ≥ 1.33 is generally considered capable.
Fill in the fields above and click Calculate.
Formulas
CPU (Upper Capability Index):
CPU = (USL − μ) / (3σ)
CPL (Lower Capability Index):
CPL = (μ − LSL) / (3σ)
Cpk (Process Capability Index):
Cpk = min(CPU, CPL)
Cp (Process Capability Ratio — assumes centered process):
Cp = (USL − LSL) / (6σ)
Where: μ = process mean, σ = process standard deviation, USL = Upper Specification Limit, LSL = Lower Specification Limit.
Assumptions & References
- The process output is assumed to follow a normal (Gaussian) distribution.
- The process is assumed to be in statistical control (stable over time).
- Standard deviation (σ) entered should be the long-term process standard deviation. For short-term capability, use the within-subgroup standard deviation.
- A Cpk ≥ 1.33 (4σ) is the widely accepted minimum for a capable process in most industries.
- A Cpk ≥ 1.67 (5σ) is required in many automotive and aerospace applications.
- When Cpk = Cp, the process is perfectly centered between USL and LSL.
- Cpk can be negative if the process mean lies outside the specification limits.
- References: Montgomery, D.C. (2019). Introduction to Statistical Quality Control, 8th ed. Wiley; AIAG (2010). Statistical Process Control (SPC) Reference Manual, 2nd ed.