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??

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. :mg:

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??

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).

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.

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.

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

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

ok, that thread was helpful.

Basically, SPC plays no role in our finished process. We ship and approve intermediate product based on whether the test (one per batch) meets specifications. Therefore we have a system that promotes operator tampering. (see recent conversations about the funnel experiment). We do not reject/alter finshed/intermediates based on control limits.
Therefore If I understand the terminology-- we have lots of special cause variation and our process ISN'T in satical control.

Since the process data lacks rational subgroups and statistical control, we must use Pp and Ppk as the thread states, correct??

You must do your best, with limited time and parts, to eliminate special causes and stabilize the process (obviously you cannot know the long term stability of the process). Then, yes, you would calculate using Pp / Ppk.

ok, that thread was helpful.

Basically, SPC plays no role in our finished process. We ship and approve intermediate product based on whether the test (one per batch) meets specifications. Therefore we have a system that promotes operator tampering. (see recent conversations about the funnel experiment). We do not reject/alter finshed/intermediates based on control limits.
Therefore If I understand the terminology-- we have lots of special cause variation and our process ISN'T in satical control.

Since the process data lacks rational subgroups and statistical control, we must use Pp and Ppk as the thread states, correct??

If I were you I would step back and re-consider the whole situation. Process capability is an indication of whether your process is capable of meeting the specifications. If you have special cause variation and your process is not in statistical control then you should not even bother to calculate the process capability since it is not meaningful. (See Grant & Leavenworth, Chapter 5).

I am also confused by your statement that "SPC plays no role in our finished product" but on the intermediate product which you "ship and approve". Is an intermediate product one that you ship from one department or plant to another and then they make it into a finished product? No matter what the answer is, SPC can be used to monitor finished product final testing, intermediate final testing or even the process controls such as temperature, pressure, reflux ratios etc. while you are making the product. Actually, there would be more value in learning what process variables have the most effect on your intermediate or final product and control chart those variables with the intent that you would find problems early and correct them before you get out of control or out of spec on your final product tests.

Also, control charts are used to determine if your process has changed and is not related to specification or product rejection. As a matter of fact, G&L Chap 9 caution practitioners about the confusion that can be caused when mixing control limits and specification limits in a discussion of control chart theory. It is possible to have a process that is not in control and still make product that passes final testing. Depending on how out of control the process is, I would not recommend that you wait too long to bring it back in control or you may find yourself with an entire batch that needs to be re-run or even worse, disposed of.

Rational subgroups is related to sampling methodology and must be done correctly if you want a meaningful control chart. G&L Chap 9 has information on this topic also.

Don't be shy about asking questions. In spite of what you may have read or taught in a class, control chart theory is not that easy and takes time to learn. If you are wondering about my references to Grant & Leavenworth, my book is liberally marked with post it notes on this subject and plenty of written notes in the margins. I was a "real" control chart user and a "real" engineer at one time and you have brought back some memories that are deeply buried but still there. When people talk about putting out fires at work, I always note that I may be the only one that actually did put out real fires. :lol:

Bill Pflanz

Hi Oliphant, the second tread of Rob Nix states my point of view (may be not all), to me the only way to manage is to measure, without all the theorical background each capability indicator is usefull if you compare it with it self, but there are more robust indicators than others and conditions such that one indicator SHOULD NOT BE CALCULATED (ie. Cpk in one spec condition). For the Cp againt pp indicators: I like Cp indicators because I try to see my process not how does it behabe, the control limits are calculated with the same estimate than Cp, I tink this is a good point.

To answer your questions:

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??)

Any calculation is an estimate, even if you measure the same item several times you can obtain different values (operator or instrument variation).

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

Autocorrelation is the relationship of one value with the previous ones, it affects primary the IX-MR charts, because, if subgroup increases the autocorrelation usually gets lower, you can say the same with the time (if the lag between samples increases the autocorrelation gets lower and usually is a solution for the most of the people, but why you have an sensor taking measures every hour if no cost is involved to take them more frequently?).

Donald Wheeler in "Advanced Topics in Statistical Process Control" show the calculations, you may look at the net for magazines and found presentations about autocorrelation since 1996.

There are other ways:

* Like using non parametrics to calculate the index, I love nonparametrics (median and interquartile or percentile calculation of variation). I know that is not common, but remember the objective of Capability of Performance Index: "To evaluate your process and know if it goes better or worse". The use of standard deviation is just to obtain the size of the natural variation of your process, so if you don't trust any estimate of standard deviation, use the estimate using non parametrics, it's stronger for outliers and non gausian behabiur.

* There are some practitioners that don't like them because the over simplification of the evaluation, the used box plots (I tink its a good idea, I allways use both to compare between periods of time).

We aren't in statistical control in these steps in our process and we never will be.

What is in control for you?, Shewhart wrote something like "A phenomenon will be said to be controlled when, through the use of past experience, we can predict,
at least within limits, how the phenomenon will vary in the future."

http://www.spcpress.com/ink_pdfs/Wh%20Modest%20Proposal.pdf

The "in control" Rules don't apply for all cases, you may need to see if each rule apply to you.

:eek:

:agree1: Great thread Darius, I particularly enjoy Dr Wheeler's breakdown of three viewpoints of SPC.

One viewpoint is particularly common here, is the idea that SPC is a complicated way to make sure that the product is within spec. To them, SPC seems a complex route to a simple objective so it is 'quality by inspection'

For my validation friend, his assigned task is to conduct a study that "establishes documented evidence which provides a high degree of assurance that a specific process will consistently produce a product meeting its pre-determined specificaions and quality attributes." He was directed to use statistical tools and historical data to prove this.

Naturally, he finds the capability indexes as an appealing measurement. What he does not appreciate is that the data is rife with special cause variation.

By now many of you have told me I need to clean up my processes (get them under statistical control) before the indexes have much relevance. I agree. But its' not my project, this is a BB running this project and he really doesn't seem to understand my objection to his analysis. He betrayed his knowledge when I point out on one of his control charts of a test that was above the upper control limit. He replied back to me that it wasn't a problem because the Cp/Cpk were above 1.0.

Darius challenges me to know explain what I mean when I say the information is not statically controlled. Control charts are not run on products as they are produced. On occasion however, customers ask for charts and we produce charts for material that has already shipped. There are runs, there are (alot) of skewed distributions,they are out of control points on many of these charts. Management is not concerned with these results; only if they are out of specification.

I see no recognition (at all) of SPC as a tool for process improvement. Six sigma is the only recognized tool for process improvement and more often not if it changes process target it will place the target even closer to a spec, by the calculation of some raw material reduction,etc.

I really appreciate the information- I am learning a lot.

Check for the attachement r001.pdf in

http://elsmar.com/Forums/showthread.php?t=6572

There is no size fit all in rules (as most of the programs or documents pretend to be).

There are runs, there are (alot) of skewed distributions,they are out of control points on many of these charts.

The runs is a common condition on batch processing (specialy with autocorrelation), so it doen't apply (if it's the case), don't use it.

There are a lot of process variables that don0t follow a gausian distribution and it doesn't imply "not in control".

And if is out of limits, it may be (specially with high autocorrelation) that the control limits doesn't represent the process.
:bonk:

He betrayed his knowledge when I point out on one of his control charts of a test that was above the upper control limit. He replied back to me that it wasn't a problem because the Cp/Cpk were above 1.0.

Even when you have a 2 or more in a Cpk, there is no guarantee that all points will be inside of the control limits (a teacher here said to me ones that you can have 2 points from each 100 without the variable being out of control), it really doesn't has to do with the Cpk being above 1.0, the indicator (Cp, or Pp or what else) depend on the sample size, if you obtain by calculus a Cpk of 2 you may have a 1 or less in your process (they are just estimates). IMHO a more realistic value could be "Wich is your indicator "at least" value?, but not many present that value (if looks better show it that way).

Darius / William;

thanks for hanging with me- I'm still thinking hard about all this stuff. There is clearly stuff in regards to IMR that just isn't yet understood.

First the the topic of autocoorelation: I did a little more digging:
"Autocorrelation Function
The first of these correlation functions we will discuss is the autocorrelation, where each of the random variables we will deal with come from the same random process.
Definition 1: Autocorrelation
the expected value of the product of a random variable or signal realization with a time-shifted version of itself
With a simple calculation and analysis of the autocorrelation function, we can discover a few important characteristics about our random process. These include:
How quickly our random signal or processes changes with respect to the time function
Whether our process has a periodic component and what the expected frequency might be "

I really don't think MY process has much autocoorelation. we are talking about compounding a whole tank, taking one single measurement- completely draining that tank (or draining 99-99.75% of it) then compounding it again. there is little relationship from one batch to the other. Still it's complex and not a cut and dried issue:

if a tank of soup (which I don't make -just for an example) is
made of 60% BATCH 200 of beef broth.
30% BATCH 210 of carrots
10% BATCH 220 of onions

and next batch we use
60% BATCH 300 of beef broth
30% BATCH 310 of carrots
10% BATCH 222 of onions...

would these two results show autocorrelation? I'm not sure.

Darius, I really find your logic here hard to understand (no offense)- if we're not even charting our process, and points are outside the control line, the distributions is severely skewed and all kinds of point rules are being broken-- Surely we don't have our process under statistical control.

for the last point, If a point outside the control line sounds like a bigger deal then a high capability index, then We agree. I completely agree that you can have outlier tests and unexplained special cause variation and have a high Cp/Cpk.

Jay

My last try :frust:
I really don't think MY process has much autocoorelation.
Autocorrelation happends primary when you take several meassures of the same batch with a small time lag (It's not you case, I agree but you didn't tell before that only one meassure was taken from each batch). I just said that point outside of control limits could happen because the variation estimate was wrong because of that.

if we're not even charting our process, and points are outside the control line, the distributions is severely skewed and all kinds of point rules are being broken-- Surely we don't have our process under statistical control.
If you don't chart it; DOESN'T HAS TO DO ANYTHING WITH CONTROL. As I told you before, the distribution has a lot to do with control limits and rules, if you readed the article r001.pdf in the tread I told you about, even Wheeler said that not allways all rules apply. Don Wheeler showed that even for "non normal" (non gaussian) distributions control limits worked, but the rules depend on the probabilities calculated for such distribution.

and at last remember Shewhart definition of control:
"A phenomenon will be said to be controled when, through the use of past experience, we can predict, at least within limits, how the phenomenon will vary in the future."

and Deming (1986): “no process, except in artificial demonstrations by use of random numbers, is steady and unwavering”

I did some simulations using all GE rules and Excel "random generator", rules hapen ones and ones again.

Auswiedersehen meine lieber freunde, Ich kan hier nicht mehr machen.

ok. no more hitting ones head against a wall.

We do have the process under 'control'. that is after any number of adjustments with spices in our 'soup', we can get that tank in spec. If we didn't have the process under control my GMP customers would be Hot in a hurry. :mad: The distribution are not usually visibly gaussian, and they are not measured in process.

Normally, I am told having a process under statistical control means you have common cause variation that leads to a stable (and many times guassian) distribution. It is not just one point rule that gives me fits, at times and places we break all of them. so Wheeler's caution against using all the point rules really doesn't fit. If I use any of them occasionally I break it, and in that instance I most likely 'special cause' variation.

I imagine that charting important properties and understanding distibution BEFORE operator adjustments have been made is an important step in SPC. But I have NOT implemented SPC. I don't have approval to implement SPC. And I lack proof of any kind that it will save $$$ to implement SPC on our 'BATCH' compounding steps. But if I could--charting the results, understanding the distribution and eliminating outliers would be a first step, right???

Just out of friendly curiousity, Darius. what does the german mean?? I'm not frustrating you, Am I?

I will also be a good CQE and study out what books and references mean, but sometimes what is written about SQC at other industries doesn't seem to apply. Nevertheless I think several how give me hope that SPC by G&L, is an espacially relevant book for me.

Jay

J,

The German was nothing bad...Darius was just asking other Cove members to help explain the point in a different way because he wasn't having much luck.

Chemical processing is a entirely different ballgame than the one I'm use to using SPC for, so I suggest that you look at Chapter 9 of "Statistical Quality Control". Having said that, here are my thoughts on what Darius was explaining.

Your sample size is 1 and your assuming it is from the entire population. This paints you into a corner because you aren't allowing the measurement to be comparred to anything else. That means there is no value in charting or using any SPC rules.

Darius' point, I think, was that you should be comparing it to the other batches. This increases your population size and degrees of freedom. Again, chemicals are not my industry, but it seems like this would be a good way to reliably use SPC tools without any additional measurements. This only works if you are using the same recipe for every batch.

The other way around this entire discussion is to increase your number of samples within a single batch. Probably not an option because of time, money, wasted product, etc.

Hopefully this helps.

Swanee

Chemical processing is a entirely different ballgame than the one I'm use to using SPC for, so I suggest that you look at Chapter 9 of "Statistical Quality Control". Having said that, here are my thoughts on what Darius was explaining.

Your sample size is 1 and your assuming it is from the entire population. This paints you into a corner because you aren't allowing the measurement to be comparred to anything else. That means there is no value in charting or using any SPC rules.

Darius' point, I think, was that you should be comparing it to the other batches. This increases your population size and degrees of freedom. Again, chemicals are not my industry, but it seems like this would be a good way to reliably use SPC tools without any additional measurements. This only works if you are using the same recipe for every batch.

The other way around this entire discussion is to increase your number of samples within a single batch. Probably not an option because of time, money, wasted product, etc.

Since I have done control charting in the chemical industry, my experience tells me it definitely has value. The moving average control chart solves the problem of the sampling issue. The same SPC rules for out of control apply for this chart.

Using the same recipe for every batch is equivalent to making the same product on a machine. If you change the recipe then you change the product and plotting the data on a single control chart would be mixing data from multiple products. Increasing the number of samples within a single batch will only demonstrate variability in testing.

Control charting final product batches is okay but there is more value in control charting key parameters further back in the process. Batch to batch variation (assuming the same product is being made) is determined by the process. As Jay is finding out, tampering with process controls during intermediate processes can increase variation in the final product. Testing time can be a problem because you continue to make lots of product while waiting for the test results. The control chart, if probably used, can signal a change in the process and allow correction earlier.

Through emails with Jay, I have encouraged him to focus less on the product specifications and more on process control. Plant managers get in big trouble, very quickly if they make off-spec product since there can be expensive re-work costs or, even worse, high costs for waste disposal of chemicals. The control charts are used to improve the efficiency of the process not make on-spec product. Continual tampering will increase the variation until the process gets more and more out of control (off into the Milky Way per Deming) until you will get off-spec.

Bill Pflanz

regarding the initial Ppk vs Cpk question:

Mean = SumXi / N
SD(short term) = MR-bar/1.128 (from IX-MR moving range chart)
SD(long term) = (Xi – X)^2 / N-1
Cp = (USL – LSL) / 6 * SDst
Cpk = min [(X – LSL) / 3 * SDst] , [(USL – X) / 3 * SDst]
Pp = (USL – LSL) / 6 * SDlt
Ppk = min [(X – LSL) / 3 * SDlt] , [(USL – X) / 3 * SDlt]

No?

Within the training I've had the Cp(k) is referred to the "process potential" (what might the capability be if all special causes could be removed...i.e. "potential") while the Pp(k) is referred to as "process performance" (what is the actual process capability you're experiencing today..i.e. "performance out the door"). Cp gives one view, based on one distribution/data-set. Pp gives another view, based on another distribution/dataset. Both are useful, they're just different views.

KMAAA,

If you're curious, check out some previous related discussions in the following threads:

http://69.93.111.34/Forums/showthread.php?t=6444

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

Rob,

Thanks for the links...good lord what a sticky wicket. The definitions(equations) I use come from our enterprise-wide software (InfinityQS) & previous to that the statisticians that wrote the software at Lyle-Kearsley. LKS has a fairly extensive customer list in the Fortune 500 & 100 so I'm guessing their "version" of Cp(k) & Pp(k) must to reasonable to quite a few folks.

I've heard the (quality) stats in general suffers from a lack of standardization..I'm guessing this is an example of that need?

Bill,

Thank you. I was hoping someone from the chemical industry would elaborate on my try at an explaination. Always fun to learn something new!

I agree that SPC is useful, it just seemed like Jay was limiting the scope of the chart to a point that it wasn't providing any usefull data.