# Interpretation with regards to Ppk > Cpk

#### Arnefer1206

##### Registered
Good Day!

New member here

I am currently searching for interpretation with regards to Ppk > Cpk, and seems I found already with this forum, however it is way back 2007

Merely, I encountered this condition and here is my data. Could anyone assist me for the interpretation of the result

USL = 25
LSL = -25

6.70
7.27
-0.64
6.23
-5.76
10.65
6.00
5.51
-0.60
3.30
2.07
-5.46
1.06
-4.69
-0.70
-4.42
11.73
-1.07
3.24
0.34
-4.56
-5.74
6.87
2.02
-7.69
2.70
-1.94
6.14
2.04
2.94

Cp = 1.47 / CpU = 1.39 / CpL = 1.56 / Cpk = 1.39
Pp = 1.64 / PpU = 1.54 / PpL = 1.73 / Ppk = 1.39

#### Bill Levinson

##### Industrial Statistician and Trainer
I get what you get but Ppk, which includes long and short term variation, cannot exceed Cpk, which includes only short term variation. I could however envision the estimate of Cpk exceeding the Ppk because the short term variation estimate must come from a moving range and, noting especially -4.42 next to 11.73, the order of the measurements can result in different Cpks and possibly generate one less than Ppk which depends on the standard deviation of all the data regardless of their order.

There is by the way no obvious reason to suspect the process is not in a state of statistical control nor is there evidence of non-normality. (Charts are by Minitab.)

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#### Bill Levinson

##### Industrial Statistician and Trainer
I wanted to randomize the order of your data to see whether I would get a different Cpk, and StatGraphics did this for me.
2.07
10.65
-0.64
2.04
11.73
6.87
-7.69
6.23
6.00
7.27
3.24
2.02
5.51
0.34
-5.46
-4.56
2.94
6.14
-0.70
-4.69
-4.42
-0.60
3.30
2.70
-1.94
-5.74
-1.07
-5.76
1.06
6.70

and now Cpk > Ppk but not by all that much. My belief is that, the first time around, we simply got lucky (or unlucky) and the order of the data was such that some of the moving ranges were large enough to make the short term variation estimate exceed the long term variation estimate.

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#### Welshwizard

##### Involved In Discussions
Hi Arnefer 1206,

If the data is gathered rationally and in time series order it appears reasonably homogenous and therefore we can say predictable.

I agree with Cpk,Cp and Pp but have a small discrepancy for Ppk.

Ppk = 2DNS/6s = 47/30.51 = 1.54 not the 1.39 shown.

If we make the assumption that the process is predictable and centred then all these indexes describe the same thing. The differences you see are due to the differences in the computation of the global standard deviation vs the within subgroup estimate of this, for example the within subgroup estimate of Sigma X is 5.673 whilst the global estimate of standard deviation is 5.086.

Of course, if Ppk is more than Cpk then it just means that the divisor for the Ppk is less than that for Cpk which in this case it is.

So, the differences are marginal here, it appears that the process is quite healthy.

Hope this helps.

#### Bev D

##### Heretical Statistician
Super Moderator
Why would an answer from 2007 not be sufficient? Math and physics haven’t changed in the last 12 years...

#### toniriazor

##### Involved In Discussions
There is always a confusion about Ppk and Cpk.
In some places I read Cpk is given to be a long-term indicator if the process is in statistical control. Then some weeks later I read Ppk is the long-term indicator about process in statistical control. Really this is so confusing for beginners.
Any good read explaining once and forever these two with clear examples ?

thank you.

#### Bill Levinson

##### Industrial Statistician and Trainer
Ppk is the long term indicator because it includes both short and long term variation sources, while Cpk accounts only for short term (within sample, or between successive individuals) variation.

#### John Predmore

Trusted Information Resource
On one level, the formula is the same, you have to understand where the estimate for standard deviation came from. Ppk uses the standard deviation of a sample compared to the tolerance range. Cpk uses the standard deviation calculated from SPC, such as R-bar divided by d2. The way SPC works is to separate short-term variation (within groups) from long-term (between groups), but it is not the calculation which does the magic, it is the fact the data are organized chronologically and there are "logical subgroups". If you took data from a year's production in random order and plotted an X-bar/R chart, your estimate of R-bar/d2 would include long-term variation. Ppk includes long-term variation only if the sample includes parts made over a long period of time. I have seen suppliers take a sample from a single batch and calculate "Ppk", but that calculation does not include batch-to-batch variation over time even though the calculation is the same.

#### Bev D

##### Heretical Statistician
Super Moderator
What John said!

While there is a lot of confusion around these indices it mostly just boils down to what formula is used for the variation and the sampling scheme.
Using within subgroup variation to estimate the SD or using a small run (no lot to lot or setup to set up or operator to operator variation is short term capability. Using the total sample standard deviation across all components of variation is long term capability. The use of the letter Cpk or Ppk are not reliable or consistent indicators of short or long term.

Of course the bottom line is that the whole Ppk/Cpk thing is an abomination and should be eliminated from the quality profession...

#### bobdoering

Trusted Information Resource
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