Process Capability for parameters with non-normal distribution.

Bev D

Heretical Statistician
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Super Moderator
#11
I have attached two approaches - assuming the data is homogeneous.
The data isn't homogenous...most statistical calculations are based on the assumption/requirement of homogeneity. This is why we must ALWAYS plot our data in time series FIRST before any calculations.
 
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bobdoering

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#12
The data isn't homogenous...most statistical calculations are based on the assumption/requirement of homogeneity. This is why we must ALWAYS plot our data in time series FIRST before any calculations.
It could very well be that over time this process has natural shifts - perhaps even cyclical with environmental changes. However, capability is a high level overview concept with an extremely low sampling compared to the life of the process. In this case it would indicate that so little of the tolerance is used by whatever variety of variances (from that process' total variance equation) that further process changes may have no economic value. That is, it is an appropriate process with acceptable variation.

Because total variance is the sum of all of many variances in a process, each of which can be at a different level at any time, most process output is not truly homogeneous. You have a very unique process to get all of your variations to be statistically insignificant - except one - to bear true homogeneity over time. But, agreed, plotting is surely important to understanding the types and degrees of effect of the variances in the process.
 

Miner

Forum Moderator
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#13
...now, given the background, and based on your comment, is it reasonable to assess the (nearest) distribution based on visual/techno_functional assessment and evaluate the cpk/ppk ?
You COULD calculate a rough estimate of your capability. However, the problem with doing this, is that the process, being unstable, is also UNPREDICTABLE. This means that your estimate is only valid for the batches in the study, and may not be valid for the future batches.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#14
if you are not required to calculate Cpk/Ppk by your Customer my recommendation is to NOT do it. While it can give a high level estimate of process performance it's not precise nor is it actionable. It is not a requirement of an "SPC program". it was a misguided bolt-on in the eighties by people who were enamored of providing a "bright line" of acceptable performance: Managers who wanted a simple 'goal line' to tell them if they were 'good enough'. I have attached a paper I've written (still in progress) concerning the Perils of Process Capability Indices. It is attached. If you really want a precise, actionable quantification of your process capability, calculate and plot the actual defect rate. I know it's "old-fashioned" but that's what you are really interested in. No need to go around the proverbial barn to get to the outhouse...

Please note that even if you are bent on calculating the index, the FIRST step is an MSA. Then you plot your data in time series (read about multi-vari charts*) and look at stability. (read about rational subgrouping and the effects of non-homogeneity on statistical analysis**.) Only after these steps will you be able to understand process capability. Remember that your goal is to understand, improve and control your processes - not to calculate a Cpk index.

* multi-vari articles
If you are an ASQ member these are free:

Robert D Zaciewski and Lou Nemeth, “The Multi-Vari Chart: An Underutilized Quality Tool”, Quality Progress, October 1995, pp. 81-83

Snee, Ronald, D., “My Process is Too Variable – Now What?”, Quality Progress, December 2001

If you are an ASQ member these are available at the knowledge center fro $5, $10 if you are not. well worth the cost:

Leonard A. Seder, “Diagnosis With Diagrams – Part I”, Industrial Quality Control, January 1950, pp. 11-19

Leonard A. Seder, “Diagnosis With Diagrams – Part II”, Industrial Quality Control, March 1950, pp. 7-11

** These are available for free at Quality Digest

Wheeler, Donald, “What is a Rational Subgroup?”, Quality Digest, October, 1997 http://www.qualitydigest.com/oct97/html/spctool.html

Wheeler, Donald, “Rational Subgrouping”, Quality Digest, June 2015 http://www.qualitydigest.com/inside/quality-insidercolumn/060115-rational-subgrouping.html

Wheeler, Donald, “Probability Models do not Generate Your Data”, Quality Digest, March, 2009 http://www.qualitydigest.com/magazi...bability-models-don-t-generate-your-data.html

Wheeler, Donald, “Why We Keep Having Hundred Year Floods”, Quality Digest, June 2013, http://www.qualitydigest.com/inside/quality-insider-column/why-we-keep-having-100-year-floods.html

Wheeler, Donald, “The Secret Foundation of Statistical Analysis”, Quality Digest, December 2015 Source http://www.qualitydigest.com/inside...-secret-foundation-statistical-inference.html

Wheeler, Donald, “Statistics 101 and Data Analysis”, Quality Digest, March 2016 http://www.qualitydigest.com/inside...statistics-101-and-data-analysis-example.html
 

Attachments

#16
How would you like your attachment, "The Perils of Process Capability Indices" cited? I would like to add it as a reference in an article I have been working on.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#17
Simply state the title, my name and that it was posted here and the date. A link to the post is most helpful.
 
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