# Non Normal Data Managing - Clements Method to get Process Characteristics

M

#### 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

Super Moderator
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

##### Deming Disciple
Super Moderator
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

Trusted Information Resource
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

##### Heretical Statistician
Super Moderator
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.

M

#### 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........

B

#### 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

B

#### 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

B

#### 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

#### Attachments

• two sided tolerance interval for non-normal distributions.jpg
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• one sided tolerance interval for non-normal distributions.jpg
16.3 KB · Views: 237
Need to calculate tolerance Intervals with a set of non-normal data and 3-Parameter Weibull distribution Using Minitab Software 0
Ppk results shown as asterisk after the transformation of Non-normal data Using Minitab Software 4
L How to evaluate the process capability of a data set that is non-normal (cannot be transformed and does not fit any known distribution)? Capability, Accuracy and Stability - Processes, Machines, etc. 14
R Non Normal Data in a historically normal process Capability, Accuracy and Stability - Processes, Machines, etc. 6
Y Process Capability for Non-Normal Data - Philosophical Questions Capability, Accuracy and Stability - Processes, Machines, etc. 6
P Non-normal Data Cpk Statistical Analysis Tools, Techniques and SPC 5
S Non-Normal Data - Measurement for "straightness" with a 0.001" max tolerance Capability, Accuracy and Stability - Processes, Machines, etc. 10
D Calculating Cpk on Non-Normal Data Distribution Capability, Accuracy and Stability - Processes, Machines, etc. 10
J Non-Normal Distribution Data - Tolerance Intervals and Minitab Using Minitab Software 7
M t-test with Non Normal Data Statistical Analysis Tools, Techniques and SPC 16
K Non-Normal Data Analysis Literature, Websites, Books for Learning Quality Tools, Improvement and Analysis 2
R Transforming or not Transforming - Dealing with Non-Normal Data Statistical Analysis Tools, Techniques and SPC 10
Non-Normal Data F test and T test Capability, Accuracy and Stability - Processes, Machines, etc. 19
M Non-Normal Data & Minitab Statistical Analysis Tools, Techniques and SPC 17
M How to Do Ppk on Non-Normal Data Capability, Accuracy and Stability - Processes, Machines, etc. 10
T Non-normal data for Cp Cpk indices Statistical Analysis Tools, Techniques and SPC 1
U Calculate Z-Score for Non-Normal Data - I have two set of data Statistical Analysis Tools, Techniques and SPC 9
S Capability Analysis of Non-Normal Data Statistical Analysis Tools, Techniques and SPC 23
T Cp and Cpk calculation for Non-normal data? Statistical Analysis Tools, Techniques and SPC 11
T Capability with Non-Normal Data - Component Strength Statistical Analysis Tools, Techniques and SPC 11
Y Perform 2 ways ANOVA in minitab with non normal data involved Using Minitab Software 5
B How to identify whether my data is non-normal? Statistical Analysis Tools, Techniques and SPC 26
Quality control with non-normal, censored and truncated data examples needed Statistical Analysis Tools, Techniques and SPC 0
Use of Non-Parametric Statistics and Non-Normal Data Statistical Analysis Tools, Techniques and SPC 33
N Analysis of non-normal stratified data for cpk/ppk? Rupture test Capability, Accuracy and Stability - Processes, Machines, etc. 6
R P-value is 0.05 - Normal or non-normal data? Capability, Accuracy and Stability - Processes, Machines, etc. 31
L How to calculate tolerance intervals for non-normal data? Reliability Analysis - Predictions, Testing and Standards 13
J Is a t-test used in non-normal data analysis? Six Sigma 7
C Analyzing Data with a Non-Normal distribution Statistical Analysis Tools, Techniques and SPC 41
A Capability Analysis - Dealing with non-normal data in Minitab Using Minitab Software 8
V MINITAB and non-normal unilateral tolerance data - Cannot confirm Ppk values Using Minitab Software 15
J Non-Normal Data - Transforming the Data to Normal Statistical Analysis Tools, Techniques and SPC 12
R Bootstraping and Resampling Statistics - Capability for non-normal variable data Inspection, Prints (Drawings), Testing, Sampling and Related Topics 6
A Non-normal Distributions in SPC - How do I Normalize Data? Statistical Analysis Tools, Techniques and SPC 55
Comparing process parameters on non-normal batches Capability, Accuracy and Stability - Processes, Machines, etc. 11
Apply control limits to a non-normal distribution Statistical Analysis Tools, Techniques and SPC 13
Non-normal Distribution Selection where the system is constantly being corrected Capability, Accuracy and Stability - Processes, Machines, etc. 11
Process Capability for parameters with non-normal distribution. Capability, Accuracy and Stability - Processes, Machines, etc. 16
M Is it possible to get Natural Tolerance (Tn) with Non Normal Distribution? Statistical Analysis Tools, Techniques and SPC 9
Test of Means or Medians for Non Normal Populations? Using Minitab Software 6
S Which Normality Test more acceptable to FDA; Also, Non-Normal Threshold? Qualification and Validation (including 21 CFR Part 11) 5
S How you define 'Normal & Abnormal' Conditions and 'Routine & Non-routine' Activities ISO 14001:2015 Specific Discussions 8
A Finding Control Limits for a Non-Normal Distribution Statistical Analysis Tools, Techniques and SPC 3
R Torque Confidence Testing (Non-normal Distribution) Statistical Analysis Tools, Techniques and SPC 5
F Non-Normal Distribution vs. Gamma Distribution Statistical Analysis Tools, Techniques and SPC 18
F Process Capability for Non-Normal Process Statistical Analysis Tools, Techniques and SPC 5
C Designing control chart for non-normal variables Statistical Analysis Tools, Techniques and SPC 3
M Cp, Cpk, Dpm, or other? Diameter of a Hole - Non-Normal Distribution Capability, Accuracy and Stability - Processes, Machines, etc. 20
A ANSI Z1.4 or Z1.9 for non-normal distributions? Inspection, Prints (Drawings), Testing, Sampling and Related Topics 5
D Ppk of non-normal bounded proccess, one sided specification Capability, Accuracy and Stability - Processes, Machines, etc. 3