Cp Cpk Formulas versus Pp Ppk Formulas
Formulas for Cp Cpk and Pp Ppk are Similar
Cp, Cpk Formula & Calculations
(Cpk > 1.33 is desirable)
Cp and Cpk use Sigma Estimator.
Pp, Ppk Formula & Calculations
(Ppk > 1.33 is desirable)
Pp, Ppk use standard deviation.
One-Sided or Unilateral Specification Limits
Use CpU (USL) or CpL (LSL) for Cpk.
Thinking About Trying to Do This Yourself? Don't. Here's Why:
Time: You will probably spend hours trying to figure it out. Why not download a free trial of the QI Macros and start doing it correctly immediately?
Multiple Complicated Formulas to Choose From: You can try to calculate Cp, Cpk and Pp Ppk manually, but you'll probably make mistakes and aggravate customers. And you will find your homegrown template hard to maintain.
- 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. Then they question our results!
- For example, they use standard deviation instead of sigma estimator for Cp and Cpk. Or they get the constant wrong based on their sample size. Or they don't understand there are several methods of calculating sigma estimator.
If you're providing these results to your customers shouldn't you use a tool that's proven and affordable?
Sigma Estimator - There are Three Different Ways to Estimate Standard Deviation
n represents the subgroup size in these Sigma Estimator formulas
Pooled Standard Deviation
Use when n > 2
Average of the Subgroup Standard Deviations
Use when n > 4
c4 is a constant based on subgroup size
sbar = Σ(σi)/n
Average of the Subgroup Ranges
Use when n = 1 to 4
d2 is a constant based on subgroup size
Rbar = Average(Ri) (Average of the Ranges in samples)
Sigma Estimator Calculation Used in QI Macros
QI Macros versions dated after May 2015 use these defaults:
- Pooled Standard Deviation when n > 2 and
- Rbar/d2 when n = 1.
Users can change the sigma estimator calculation after they have run a histogram by changing the estimator fields on the far right of the histogram data sheet.
In addition between changing from Pooled Standard deviation to Sbar or Rbar, users can also choose Between/Within Deviation. This option was added to QI Macros in December 2015.
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.