Data Analysis - Johnson Transformation/Weibull Distribution/Capability Analysis

P

packrat

#1
I have a set of seal strength data (30 bags, 4 seals per bag as a subgroup for each bag) within a specification range of 0.5 to 2.5 and actual values of 1.3 to 1.7. The probability plot shows the data are not normally distributed. The Johnson transformation in Minitab transforms the data to acheive a p-value greater than 0.05 which is acceptable to me. When I perform a Six-Pack analysis of the data, I get a capability histogram (LSL: -3.61, USL:2.83) with normal probability plot (AD:0.487, P:0.208). I am concerned about the negative numbers on the capability histogram after applying the Johnson Transformation. Should I be concerned? I am wondering whether the best approach is to find a non-normal distribution that best fits the data. When I consider Weibull and Largest Extreme Value Distributions, neither is able to meet the 0.05 significance without removing the extreme outliers in the data set. I am not certain how to best approach analyses of these data and I am looking for help.
 
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Miner

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#4
A "bump" means that someone posted to the thread to bring it back to the top of the list in the hope that someone will see it an respond.

Can you post your data? It is much easier to help with hard data rather than working from theory.

Technically, there should be nothing wrong with your approach. Without seeing the data and your analysis, I cannot comment on the specific details of how you implemented that approach. For example, if you truly have extreme outliers, the Johnson transformation may still be incorrect. I cannot tell without seeing the data and analysis.

I, personally, do not like using the Johnson (or Box-Cox) transformation for capability studies (or SPC). There are a lot of drawbacks to it, such as not being able to explain the resulting histogram and transformed specifications to non-statisticians. I prefer fitting the actual non-normal distribution to the data.
 
P

packrat

#5
:) Thank you for the bump! Really appreciate the help. Data are attached. SS_T (seal strength top seal) and pouch width (W) seem to be giving me the most trouble. Yes, I am having a problem explaining these results in a report.
 

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Miner

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#6
I reviewed your data. SS_T does appear to have 2 probable outliers. Can you identify anything unusual that would explain these? If these were removed, the resulting distribution passes the normality test. I do question the number of results that are exactly 1.40. It does not fail the statistical test, but appears unusual. If these results were more dispersed, the other two points may not appear as outliers.

W appears to fit a Largest Extreme Value distribution fairly well.

A general comment: When performing a capability study, you really need more samples, ideally about 100 since you are estimating both the average and the standard deviation. For non-normal distributions, this is even more important because, in many cases, you are estimating 3 parameters instead of 2.
 

bobdoering

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#7
The other thing to look at is the total variance equation. Rather than looking at the output data as "the process", what variances does the data actually represent? A major error in evaluating data from a process is assuming the data directly represent the process. That is very, very rare. I would expect normal distributions from the type of process you describe, so beyond the process itself there may be other variances affecting the distribution. One may be measurement error. Tensile testing - especially of polymers - is fraught with error.
 
P

packrat

#8
:yes: I asked for a Gage R&R on the measurement system and was concerned when I received the report. It appears to me that the measurement system is unacceptable but everyone involved seems to have a different perspective. I guess since there was no concensus on how to interpret the results of the Gage R&R study, we are stuggling on which perspective to go with. Can you take a look at the attached Gage R&R reports. The report at the top of the page was sent first. I rejected its results and the second report (at bottom of page) was then sent and I was told that the measurement system is acceptable at 19%. Would you agree with this interpretation?
 

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bobdoering

Stop X-bar/R Madness!!
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#9
Would you agree with this interpretation?
Do you have the raw data? Since this is destructive - how was the Gage R&R performed? Did anyone watch to see if there was any material slip in the jaw, etc. that could account for error? It can happen.
 
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Bev D

Heretical Statistician
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Super Moderator
#10
How about an alternative to all that statistical math?
I plotted the data. First in a basic histogram vs. the spec limits. for the data you gave us, the process is EXTREMELY CAPABLE. Just look at the chart. Then a time series in a multi-vari chart. That showed a significant within bag difference. The data within a bag is NOT random. This throws off your standard deviation calculations and results in a slightly non normal distribution.

Why are you trying to calculate a Cpk value? Is your customer requiring it?
Cpk values are far less informative or actionable than a simple plot of the data.

Transformations hide what is really going on with your process - the value is in the charts of the raw data. You are having trouble explaining the transformed data because it has no informative value - besides the fact that it makes no sense. Show your organization the charts - not only will they get it instantly, they will know what they should or shouldn't do about it.

you can do a similar analysis of the width data. It has a small within bag difference.
 

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