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Interpretation with regards to Ppk > Cpk

#11
Process Capability (Cp, Cpk) and Process Performance (Pp, Ppk) - What is the Difference? - iSixSigma agrees with you: "“Cpk tells you what the process is CAPABLE of doing in future, assuming it remains in a state of statistical control. Ppk tells you how the process has performed in the past. You cannot use it predict the future, like with Cpk, because the process is not in a state of control. The values for Cpk and Ppk will converge to almost the same value when the process is in statistical control. "

The process capability is how the process would perform if no long-term variation sources were present, and the sample range or standard deviation reflected all the variation sources present. The process performance index reflects long-term variation sources as well.

I can see, however, where the perception that special causes affect Ppk comes from. Here is a batch process I simulated for an SPC presentation. The control limits are based on the sample ranges and they reflect the short-term (within batch) variation. They do not reflect the long-term variation because there is also between-batch variation. The between-batch variation is however not a special or assignable cause, it is common cause variation that exists because of differences between setups and so on. It is true that the means of the batches are different, so the process mean changes from batch to batch, but this is an expected part of the job so we cannot call it a special or assignable cause. It is however why single-unit flow is preferable to batch processes.

Another example would be an autoregressive process that involves, for example, successive fluid elements in a pipe. The moving range will reflect the variation between fluid elements, which we expect however to be very similar to one another. It will not reflect long-term variation that is inherent to the process so Cpk >> Ppk in this case. I suppose the long-term variation would indicate a lack of ability to control the process to such an extent that the mean remains absolutely constant (typical automatic process control systems do not even pretend to be able to do this) but this does not mean a special or assignable cause is present that requires intervention.
 

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Bev D

Heretical Statistician
Staff member
Super Moderator
#12
Cpk (calculated using the within subgroup variation) and Ppk (calculated with the total variation) will converge IF and only if the process is homogeneous. While rational subgrouping will verify that a non-homogeneous process is in statistical control/stable, it CANNOT overcome the non-homogeneity when it comes to process performance. (It was designed explicitly to deal with non-homogeneous processes) So many processes are not homogeneous.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#13
I posted this on a different website a couple of years ago to explain some of this:

On Cpk, Ppk and long & short term capability. A mathematical conundrum.

Besides the fact that Cpk and Ppk are worse than useless and an abomination on the face of the earth (IMHO), the original definitions (and the ones most reputable statistical software use) are this:

Cpk = the ratio of the process spread to the tolerance using the within subgroup standard deviation. This assumes a homogenous process where the between subgroup variation is nothing more than sampling error. It is also referred to as the 'capability' index or short term capability because there is no subgroup to subgroup variation in the index.

Ppk = the ratio of the process spread to the tolerance using the total standard deviation; within subgroup and between subgroup. This is essential when we have a non-homogenous process where the between subgroup variation is more than sampling error. It is also referred to as the 'performance' index or long term capability because there is subgroup to subgroup variation.

IF the process is homogenous then Ppk and Cpk will yield very similar numbers...

Non-homogenous processes can be stable and predictable and capable. The appropriate control chart would require a rational subgroup schema different than the traditionally taught subgrouping based on sequential parts. In these cases, yes Ppk can be predictive if the other assumptions are met. (random representative sampling, Normal distribution, yada yada.)

There is a corruption of these original definitions perpetuated by some automotive and aerospace companies where the Ppk formula is used for short term studies in development phases where 30-60 sequential parts are made under the same conditions (same equipment, material, operators, etc.). (This is a valid method for short term capability)

Adding to the confusion, some companies will specify the calculation of "Cpk" but provide the formula for Ppk. This goes back to the original index which used the total standard deviation and was called Cpk.

So the ‘names’ Cpk and Ppk do not correlate to the phrases “short term” and “long term”. Nor do the formulas, as the Ppk formula using the total standard deviation is good for both short term and long term studies, depending on the study design.


Posted February 19, 2016 on www.qualityforumonline.com
 

John Predmore

Quite Involved in Discussions
#15
What Bev D said in her tag line:

"The manipulation of mathematical formulas is no substitute for thinking. "

It does not matter what you call the terms, it does not matter which source you reference, confusion will persist as long as many people interchange similar terms without understanding, in contradictory ways. The difference occurs not in the calculation, not from what they are called, but how in the samples are collected and how the data are organized. The safest advice is to label your charts and tables to indicate where and how your estimate of process sigma was generated.
 
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