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 would fit within the spec limits (USL, LSL)
  • Cpk measures how centered the data is between the spec limits.

Use the Cp Cpk formula 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 would fit 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

Pooled Standard Deviation is the default estimator for Cp and Cpk since May 2015.
Cp and Cpk Pooled Standard Deviation Formulas - QI Macros

Between/Within Deviation is an option added to the histogram macro and template in December, 2015.

Between/Within formulas for Cp/Cpk in QI Macros

Sbar/c4 and Rbar/d2 can still be used by changing the estimator field on the histogram data sheet.
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.

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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