Non Normal Data Managing - Clements Method to get Process Characteristics

[Mark_Navigator]

Hi all,

I read about the simple Clements method to get process characteristics of non normal data referred to Pearson curves model.
The Teta standard values table allows to choose the appropriate Upper teta & lower teta values with a predetermined skewness and kurtosis scale, but if these last curve characteristics have values between 2 of the scale, which teta values have to be choosen? Is there a method to determine them? And if the dimension is unilateral with a boundary limit, for example the 0, have the Lp sense to be calculated? How is possible to calculate the Natural tolerance?

 

[Stijloor]

Hi all,

I read about the simple Clements method to get process characteristics of non normal data referred to Pearson curves model.
The Teta standard values table allows to choose the appropriate Upper teta & lower teta values with a predetermined skewness and kurtosis scale, but if these last curve characteristics have values between 2 of the scale, which teta values have to be chosen? Is there a method to determine them? And if the dimension is unilateral with a boundary limit, for example the 0, have the Lp sense to be calculated? How is possible to calculate the Natural tolerance?

Any statistics experts who can help?

Thank you!

Stijloor.

 

[Steve Prevette]

I can't find on the internet any references to "teta" values (except for this thread itself). There is a reasonable Wikipedia writeup on Pearson out there.

Since this is in the SPC section, I do want to state that SPC methods do not depend upon the distribution of the data (second time I've posted that today).

 

[bobdoering]

Since this is in the SPC section, I do want to state that SPC methods do not depend upon the distribution of the data (second time I've posted that today).

As long as the process produces random variation - the fundamental assumption of the underlying statistics for traditional SPC. And it is the process output - not the process sampling - that needs to be random. Otherwise, you are confounding the analysis with the variation caused by the randomization process. In fact, it may mask the true variation, causing terrible mistakes in decision making. Non-random data may require a non-traditional SPC treatment.

 

[Bev D]

I've seen articles on the Clements method. But while they are theoretically 'interesting' they have little actual value for real world SPC.

again Mark - can I ask what you are trying to do? I suspect that you probably have a relatively simple situation that others (who publish articles for tenure and not for the advancement of manufacturing) have made entirely too complicated. Most industrial processes are relatively straightforward.

I would suggest that we concentrate on what you are actually trying to accomplish.

 

[Mark_Navigator]

Simply, in our company we use Minitab as official software to make statistical analysis. Then, having normal distribution everything is ok, because with STD.DEV. value that the program give, we're able to calculate the natural tolerance of the process, but if the process fit with a non normal distribution model, the program gives only Cp and Cpk values, so, I need a way to calculate natural tolerance of the process too........

 

[Barbara B]

Greek letters could be used as placeholder in every way an author likes them to put, so there are only very few greek letters which have a common meaning (like mu and sigma). If you're interested in the meaning of your theta, you have to give the reference for the article or book where you found it.

There is an article about the Clements-method written by John Clement himself, published in Quality Progress in september 1989. The title is "Process Capability Calculations for Non-Normal Distributions". The archive for past issues of QP go only back until 1995, but maybe you could find a university nearby which has older issues as hardcopies.

But the theta you mentioned is not included in this article. (Skewness and curtosis are used, but with different notations than theta.)

Theta isn't mentioned in the standard werk for distributions also, there are betas and kappas in the section about Pearson curves (Johnson, Norman; Kotz, Samuel; Balakrishnan, N. [1994]: Continuous Univariate Distributions: Volume 1. John Wiley & Sons, 2nd edition, ISBN 978-0471584957, p.15ff.)

Besides I agree with Bev: The Clements method is a nice method if you want to do research in a difficult mathematical area, but not applicable for normal process data.

Regards,

Barbara

 

[Barbara B]

Simply, in our company we use Minitab as official software to make statistical analysis. Then, having normal distribution everything is ok, because with STD.DEV. value that the program give, we're able to calculate the natural tolerance of the process, but if the process fit with a non normal distribution model, the program gives only Cp and Cpk values, so, I need a way to calculate natural tolerance of the process too........

It's a common problem that process outcomes are not normally distributed. Process data without any systematic influence (e. g. due to material, process parameters, operators, measurement instability) will randomly vary among the mean value. In the real world most processes underly systematic influences and therefore it is "normal" that the process data do not follow a normal distribution.

To get reliable estimations about the natural tolerances or rather limits of the process spread (usually 99-99.73%) you have to check if the process data is at least stable. A simple method to conduct a stability analysis is to test if the sample means (rational samples like data per hour/day/week or samples made by hand with ~5 obs in each sample) are normally distributed. The Central Limit Theorem states that for every stable distribution the means of samples are normally distributed. You should have 30 sample means minimum for this analysis.

If your process is stable but not normally distributed, you could conduct a tolerance analysis (e. g. in Minitab R16 in stat > quality tools > tolerance intervals) and use the nonparametric values as tolerance limits.

Mostly you will see that the process isn't stable due to systematic influences. Therefore you have to build a process model to describe the outcome appropriately. This can be done out of process data with informations about the influencing variables (historical data analysis, methods: Regression/ANOVA/GLM) or with DOE-methods (require new tests with a special DoE-plan). In both cases a good model will not necessarily have normally distributed outcomes, but the residuals of the model should be random with constant variation both in the modeled space of the outcome and in observation order and therefore follow a normal distribution (Gauss-Markov Assumptions).

To get limits for the process spread you have to take into account in which way influencing variables like material, batch, temperature, etc. appear in a specific situation. Without stability you cannot calculate absolute values for the limit of the process spread, but you can give reliable limits with consideration of the influencing variables.

Regards,

Barbara

 

[Barbara B]

If your process is stable but not normally distributed, you could conduct a tolerance analysis (e. g. in Minitab R16 in stat > quality tools > tolerance intervals) and use the nonparametric values as tolerance limits.

Without a software providing these calculations it is much harder to get the tolerance limits (see attachments). They are calculated based on the distribution of the ranked values of the data.

Barbara