Cp, Cpk and Process Capability Analysis
Capability analysis determines if a process will deliver a product that meets the customers specifications (USL/LSL) and how well it is centered between the specification limits.
Not Capable to Centered & Capable
Cp < 1, Cpk <1
Cp >= 1, Cpk >= 1
Cp and Cpk Process Capability Metrics
- Cp measures how well the data fits within the spec limits (USL, LSL)
- Cpk measures how centered the data is between the spec limits.
A Cpk of 1.33 is considered to be at 4-Sigma.
Use Cp when you have a sample, not the population, and are testing the potential capability of a process to meet customer needs. Cp and Cpk use Sigma estimator.
Sigma estimator Formula
d2 is a constant based on subgroup size
c4 is a constant based on subgroup size
Rbar = Average(Ri) (Average of the Ranges in samples)
sbar = Σ(σi)/n
Cp, Cpk Formula
(Cpk > 1.33 is desirable)
The Capability Ratio (Cr) indicates what proportion of tolerance is occupied by the data.
Cr = 1/Cp Cp = 1.33 ~ Cr = 0.75 (data fits 75% of tolerance)
Cpm = (USL-LSL)/(6√(sigma2+(Xbar-Target)2))
(Cpm can be used when you have a target value.)
One-Sided Specifications or Unilateral Spec Limits
Use CpU (USL) or CpL (LSL) for Cpk.
Pp, Ppk Process Performance Metrics
Use Pp when you have the total population and are testing the performance of a system to meet customer needs. Pp, Ppk use standard deviation.
Pp, Ppk formulas
(Ppk > 1.33 is desirable)
σ = stdev(Xi)
Cp, Cpk vs Pp, Ppk
Use Cp, Cpk when you have a sample and are testing the potential capability of a process to meet customer needs.
Use Pp, Ppk when you have the total population and are testing the performance of a process to meet customer needs.
For example, if you test a sample of 10 widgets from a batch of 100 widgets:
- Use Cp, Cpk to evaluate short-term process capability.
- Use Pp, Ppk to evaluate long-term process capability.
The histogram with Cp Cpk and other metrics is just one of the tools included in the QI Macros for Excel SPC Software for Excel.
To analyze Process Capability in Excel, purchase QI Macros SPC Software for Excel through our secure shopping cart or try a free, QI Macros 30-day trial!