Cp, Cpk Formulas - Pp Ppk Formulas

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.

Use Cp Cpk  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

Pp and Ppk
Process Performance Metrics

  • Pp measures how well the data fits within the spec limits (USL, LSL)
  • Ppk measures how centered the data is between the spec limits.

Use Pp Ppk when you have the total population and are testing the performance of a system to meet customer needs.

Pp, Ppk use standard deviation.

Cp, Cpk Formula

Cp, Cpk formulas

(Cpk > 1.33 is desirable)

Pp, Ppk Formula

Pp, Ppk formulas

(Ppk > 1.33 is desirable)

Sigma Estimator Formula

sigma estimator formulas
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

One-Sided or Unilateral Specification Limits

Use CpU (USL) or CpL (LSL) for Cpk.

Capability Ratio - Cr Formula

The Capability Ratio 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 Formula

Cpm = (USL-LSL)/(6√(sigma2+(Xbar-Target)2)

Cpm can be used when you have a target value.

Mistakes to Avoid When Using Cp Cpk and Pp Ppk Formulas

You can calculate Cp, Cpk and Pp Ppk manually or you can use the QI Macros for Excel. Based on calls to our tech support line, most people who try to perform manual calculations or build their own Excel formulas end up with incorrect results.

For example, they use stdev instead of sigma estimator for Cp and Cpk. Or they get the constant wrong based on their sample size. If you're providing these results to your customers shouldn't you use a tool that's proven and affordable?

QI Macros Tools that Calculate Cp, Cpk and Pp, Ppk

  • Histogram - calculates Cp, Cpk, Pp, Ppk and 20 other metrics using your data and spec limits.
  • Capability Suite - creates six charts including histogram, control charts, probability plot, values plot and capability plot. Also calculates Cp, Cpk and Pp, Ppk.
  • Cp Cpk Template - calculates Cp, Cpk and Pp, Ppk on multiple sets of data.

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