Cp/Cpk Formula (Standard Quality Management Definition)
Cp (Process Capability Index) measures process spread relative to the spec width: Cp = (USL β LSL) Γ· (6 Γ Standard Deviation), showing theoretical capability assuming the process is centered on the spec midpoint. Cpk also accounts for how far the process is off-center: Cpk = min[(USL β Mean) Γ· (3 Γ Std. Dev), (Mean β LSL) Γ· (3 Γ Std. Dev)]. For example, with USL=10.5, LSL=9.5, mean=10.1, std. dev=0.15: Cp = 1 Γ· 0.9 β 1.11, but since the mean sits above the midpoint (10.0), Cpk = min(0.89, 1.33) = 0.89 β lower than Cp. This means the process has theoretical headroom but is actually skewed toward the upper spec limit, creating defect risk.
02
DPMO and Sigma Level
DPMO (Defects Per Million Opportunities) is a standardized defect-rate metric. Six Sigma methodology converts DPMO to a sigma level using the standard 1.5-sigma-shift convention, which accounts for the mean drift observed in long-term process performance. Under this convention, a DPMO of 3.4 is, by definition, exactly the "Six Sigma" benchmark β the lower the DPMO, the higher the sigma level. The standard Six Sigma reference table below is widely used in quality management practice.
DPMO
Sigma Level
691,462
1Ο
308,538
2Ο
66,807
3Ο
6,210
4Ο
233
5Ο
3.4
6Ο
Frequently asked questions
Which matters more, Cp or Cpk?
Cpk matters more in practice. Cp assumes the process is perfectly centered on the spec midpoint, while Cpk accounts for actual off-center drift. A large gap between Cp and Cpk signals that re-centering the process should be the priority improvement.
Why is DPMO 3.4 the benchmark for "Six Sigma"?
In a purely short-term process, the probability of falling outside six standard deviations is minuscule, but real long-term operation tends to drift by about 1.5 sigma over time. Accounting for that drift, the conventionally defined long-term defect rate at six sigma works out to DPMO 3.4.
Is a Cpk of 1.33 good enough?
A Cpk of 1.33 or higher is generally considered capable, but safety-critical industries like automotive and aerospace often require a higher bar (1.67+). Check the specific standard for your industry.