When to use Ppk/Pp and Cpk/Cp - Difference between population and sample

[J Oliphant]

I am going to bring back an old topic discussed here around 99. When to use Ppk/Pp and Cpk/Cp. someone then wrote

"Speaking strictly as someone trained (somewhat) in statistics, I have never, before the QS thing, thought that Ppk was required, nor necessary (never heard of it, actually). Ppk is something for those who do not understand the difference between population and sample. The unbiased estimate of sigma should be more than enough."

Well in my industry-I believe I am an exception, and let me explain why. We are a chemical process industry that sends large batch runs into tanks. These tanks are kept homogenous by stirring and then sampled.

Therefore, the sample's standard deviation is the sigma of the population.

I allege that we must use Ppk/Pp because we don't need to estimate population standard deviation -- We already have it. It is sigma of the individuals and so we should use Ppk/Pp. my only complaint with this is that most software packages use the degree of freedom correction for standard deviation, when none is warrented.

why is this relevant? Another analyst has been doing a GMP validation study and making these sweeping conclusions based upon Cpk/Cp. what do the guru's of the cove say??

[Darius]

I am not a guru my self but this may help you.

Donald Wheeler in his book "Advanced topics in Statistical Process Control", SPC press 1995 (pag. 56-60) show that there is no guarantee in the use of any estimator (biased or unbiased), and that the prejudice or favor for any of then is just theorical, not practical. Just stick to the estimator you use.

I don'nt see why you say:

I allege that we must use Ppk/Pp because we don't need to estimate population standard deviation -- We already have it. It is sigma of the individuals and so we should use Ppk/Pp.

The use of any indicator Ppk/pp,Cpk/Cp,Cpmk/Cpm,Ppmk/ppm, or whatever else is independent on the type of the estimator (not the same as the dispersion statistic that it's what really apply).

You say that

We are a chemical process industry that sends large batch runs into tanks. These tanks are kept homogenous by stirring and then sampled.

Beware on autocorrelation, IMHO this affects more to your indicators than the type of estimate.

[J Oliphant]

Originally Posted by Darius

The use of any indicator Ppk/pp,Cpk/Cp,Cpmk/Cpm,Ppmk/ppm, or whatever else is independent on the type of the estimator (not the same as the dispersion statistic that it's what really apply).

However the method of dispersion IS The only difference between Cp and Pk (and also Cpk and PpK): [quoted from Gorden Constable, PHD of Qualityadvisor.com]
" The technical difference is that the 6 sigma used for the Cp calculation (or the 3 sigma used for the Cpk calculation) comes from the estimate of sigma based on the average range, and the 6 sigma used for Pp calculation (or 3 sigma used for the Ppk calculation) comes from the estimate of sigma based on using all the data and the classical formula for the standard deviation. The formulas for Cp and Cpk are here; formulas for Pp and Ppk are here. "

He then goes on to outline that estimated sigma uses the average/d2 and individuals sigma calculates the standard deviation of the actual results.

My big point is that since we assume that we sample All product the value of D2 (which is used to estimate sigma) is Wrong. commonly it is set to a n value of 2 (moving range charts), which implies a very few samples taken of the whole population. In fact we sample All of the population.

I admit that the assumption that we test the WHOLE population is a little shaky. but it is unchallenged in our industry- and it would saves a lot of $$$ from the reduced testing.

Is my logic flawed??

[Darius]

Thats what I wrote

The use of any indicator Ppk/pp,Cpk/Cp,Cpmk/Cpm,Ppmk/ppm, or whatever else is independent on the type of the estimator (not the same as the dispersion statistic that it's what really apply).

Wich means the same thing that Gorden Constable, the diference is the dispersion static, NOT IF BIASED OR UNBIASED ESTIMATE IS USED.

we assume that we sample All product the value of D2 (which is used to estimate sigma) is Wrong. commonly it is set to a n value of 2 (moving range charts), which implies a very few samples taken of the whole population. In fact we sample All of the population.

It looks confusing, if the sample size is 1 (for individual and moving range) does'nt imply that a few samples are taken (we use it for automated sampling in batches every few minutes and work ok), the n for the formula take 2 because the moving range is calculated between two points.

How does your control limits look like (to narrow??, the problem of autocorrelation is too common with IX-MR charts and it also affects the indicators).

[Bev D]

The traditional statistical formula of Cp & Cpk is based on multiple subgropus and estimating the standard deviation from the within subgroup variation (std dev or Range). The 'problem' with this can be that Cp/Cpk only represents the variation within subgroups and doesn't take into account the variation between subgroups. IF the subgrouping scheme is not rational then this difference can be very significant and you will seriously underestimate the actual dispersion of your process.

The standard deviation for Ppk is a simple standard deviation of ALL values from samples taken over time. the subgroup size for these samples is mathematically unused. Ppk includes teh between subgroup variation...if the samples are taken over a sufficient period of time to allow all variables to vary naturally given your physical process controls.

IF your subgroups are statistically rational, then the within subroup varitation will be very clsoe to the total variation. The best way to determin this is to plot your data and look at it. You can use a control chart, but I prefer a multi-vari format as it is only one chart and I don't have to translate the range onto the average...its' easier for this middle aged mind to grasp.

[J Oliphant]

Originally Posted by Darius

Thats what I wrote



Wich means the same thing that Gorden Constable, the diference is the dispersion static, NOT IF BIASED OR UNBIASED ESTIMATE IS USED.
....

How does your control limits look like (to narrow??, the problem of autocorrelation is too common with IX-MR charts and it also affects the indicators).

ok. I'm sorry Darius, I'm just simply not understanding your statement above. yes the dispersion static is different. "NOt if biased or unbiased estimate is used"?? Ppk/Pp doesn't use an estimate (does it). Isn't it precisely the standard deviation of all the points (particularly, if you remove the n-1 degrees of freedom??)

I also do not understand the concept of autocoorelation. Can you steer me to more information on this concept??

BEV, I find this point to support my line of thought (and actually a part of the conversation we had)... because we Have NO rational subgroups. Since we take one single measurement on a tank, then completely recompound the tank- there is no relationship (at all) between consecutive measurements (n=2) or groupings of 3,4,5,whatever. Since there is NO rational subgroups How can you estimate a statistical standard deviation from it? But you should be able to get a very accurate standard deviation from performing the 'Actual standard deviation' of the whole population.


As for questions about my control charts. We aren't in statistical control in these steps in our process and we never will be. We generate control charts after the fact (and they actually control nothing). so perhaps they should be called 'run charts with meaningless control limits'.

It simply would cost $$$ (Increased testing/decreased flexibility) and actually hurt our reputation with our customers to use control charts. It is standard practice (I think) in our industry. Does any one know any different? I am in the Oil/petroleum industry (just happen to be making a FDA grade product).

Perhaps this last fact means that ALL capability analysis is invalid. All the more reason that a FDA-mandated cGMP validation using Cp/Cpk capability analysis irks me.

I am still curious if others agree with me. Darius, you still do not-perhaps you can give me just a little more information why. Also if you can send me to some pertinent resource(s), I will look them up.

Thankx for the comments.

[Bill Pflanz]

J,

If you do not have a copy of Statistical Quality Control by Grant & Leavenworth than I would highly recommend that you purchase it. The book has many references to the use of statistical control in the chemical industry. I believe Eugene Grant came from chemical. I was fortunate to take a class from Dr. Leavenworth and was able to ask specific questions about its applications for chemical processes.

Chapter 9 on special process control procedures specifically discusses how to do control charts for chemical processes. I always used moving average control charts as recommended by Grant & Leavenworth. You did not provide enough information to provide more detail but I will tell you that I always used CpK and I had a statistician who was available for guidance. It has been some time since I did that work so I need to review my files (not an easy effort) to get some more information. I will private message you so that we can share email addresses.

Bill Pflanz

[Rob Nix]

Good points Bill! I used Grant & Leavenworth's text for years when I first started out in this business.

Marc has a good definition within this site:

http://elsmar.com/APQP/sld220.htm

Another thread also discussed the Cpk vs. Ppk issue:

http://69.93.111.34/Forums/showthread.php?t=7065