Cp, Cpk Formulas - Pp Ppk Formulas

See How Easily You Can Analyze Process Capability

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 & Calculations

Cp, Cpk formulas

(Cpk > 1.33 is desirable)

Pp, Ppk Formula & Calculations

Pp, Ppk formulas

(Ppk > 1.33 is desirable)

Sigma Estimator Formula & Calculations

QI Macros 2015.05 began to use Pooled Standard Deviation to calculate Sigma Estimator.

Cp Cpk formulas using Pooled Standard Deviation

d - degrees of freedom
ni - samples per subgroup
- number of subgroups

Prior versions use Rbar or Sbar.

sigma estimator formulas
d2 is a constant based on subgroup size
c4 is a constant based on subgroup size (Sbar) or degrees of freedom (d for sp)

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.

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?

Pp and Ppk Calculations in Weibull Histogram

Unlike the Pp and Ppk calculations which rely on a Normal distribution, the Weibull histogram uses the WEIBULL (or WEIBULL.DIST) function to calculate the Z-scores for the USL/LSL and from these it cacluates Pp and Ppk. There is no Cp or Cpk calculation possible in the Weibull Histogram.

If there is only a USL or LSL, the Weibull histogram Ppk is either PpU or PpL.

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.
  • Weibull Histogram - calculates Pp, Ppk and 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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