Process Capability Analysis Binomial or Normal using Minitab 15

bobdoering

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#41
In addition ,your ultrasonic flaw detection process could contain a huge MEASUREMENT UNCERTAINTY FACTOR and GRR VARIATION.
That was one of the concerns I was getting at - and when the distribution of the measurement error masks the distribution of the process variable being measured - all bets are off.

That is one of the issues with Minitab. It does not comprehend, it just calculates.
 
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Jim Wynne

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#42
That was one of the concerns I was getting at - and when the distribution of the measurement error masks the distribution of the process variable being measured - all bets are off.

That is one of the issues with Minitab. It does not comprehend, it just calculates.
I would change that last bit to "That is one of the issues with many Minitab users. They don't comprehend; they just let Minitab calculate."
 

tahirawan11

Involved In Discussions
#43
One of the things we have not discussed is the variation from the measurement process. Have you performed a gage R&R to see how much of the variation - or even the fliers - come from the measurement itself? Both the measurement and the process are very "organic", so it would be good to sort out each one's participation.

A key to any statistical evaluation is total variation. Your data represents all variation - not just the variation of the process. It is always a good reminder to consider that when we look at data.

:topic: Your process reminds me of the old days when I molded carbon fiber/polyimide composite aircraft engine bearings and components. Ah, those were the days.... Do you look at cracking (in addition to porosity) as a participant in the voids, too?



Yes Bob, A Gage R&R has been performed and the measurement error is around 10% and we know that we dont have the perfect meaurement system but this is the best we can get now as improving the measurement system is a costly option. and i guess sometimes we have to bend statistical rules as management is more interested in the bottom results and not if the data coming from the process can be modeled by a distribution.

:topic: Well its good to know that you are familiar with the process and how organic the process is. Our part is a carbon fibre/epoxy composite section of a wind turbine blade which has to sustain loads for upto 20 years continously, unlike aircraft wings which are under loading condition only during flight. we do not look at 'cracking' in addition to porosity but focus on porosity, inclusions and delaminations.
 
B

brahmaiah

#44
What is wrong with using the capability analysis for a nonnormal distribution that is available in Minitab? It also has capability for binomial and Poisson.
Could you please tell us more about how to apply minitab for non-normal distribution.Please attach examples .
V.J.Brahmaiah
 
E

equesnel

#45
Agreed. I suggested a transformation of the data, since it was non-normal and uni-lateral, but was told by one individual I was too "Wild" in my suggestion. Minitab 15 has a Poisson's capability & Binomial analysis, which might solve all this without having to transform the data.

The Binomial and Poisson's plots will show you which distribution the data fits, as it should follow a straight line.

Check out this link:

http://www.minitab.com/uploadedfiles/Shared_Resources/Documents/Tutorials/method-chooser_capability_analysis.pdf

I hope this helps!!
 
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bobdoering

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#47
Here are some slides I developed to explain non-normal data capability analysis. Hope it sheds some light on Minitab's analysis.
Very nice! I wouild add the point from a previous slide to your conclusion slide:

An alternative approach to transforming the data is to find a different distribution that fits the data well and use it.

One of my favorite approaches for the uniform distribution, of course.
 
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E

equesnel

#48
Agreed..I suggested that the information be transformed as well, since it is non-normal and unilateral in nature.
 

Bev D

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#49
I did the attached analysis some time ago and thought that I had posted it.

I did this in Excel, but Minitab could do it if you know which buttons to push. Some easier in Minitab some easier to accomplish in Excel. (my org uses JMP not Minitab...)

basically I started with a simple line chart of the %voids against the 15% USL and just looked at the data. without knowing what the change was I can make only general conclusions. It appears that the failure rate and the amount of voiding are better; certainly there are really high values and there are more units with no reported voids than before.

Since the failure rate is Binomial but the before data clearly doesn't follow a roughly Normal distribution (long tail on the high side, bounded on the low side with censored data below 6%) and it isn't not large enough after the change to utilize the Normal approximation for the Binomial, I utilized EXACT BINOMIAL confidence intervals to see if the difference was statistically significant. It isn't. the confidence intervals overlap. This may simply be due to the relatively small sample size particularly for the after data. In this case the trend chart - or an SPC chart is a better indication than confidence intervals or other hypothesis tests as the failure rates aren't 'estimates' based on random sampling. Time will tell if the difference is sustainable.

I also calculated the Ppk value and sigma value (without the 1.5 sigma shift which I fell is silly and cheating) they are included in the analysis.

If we look only at the %voiding as a measure of improvement rather than the failure rate, our statistical analysis is more complicated but does provide more compelling evidence that there is a statistically significant difference. Since the %voiding has no modeled distribution, so I used the Chi Square test and looked at using a truncated distribution…

I also added control chart that is based on the number of blades with no reported voids in between blades with reported voids. (Charting for events – you plot the activity rather than the failure events…higher is better) I have found this chart to be extremely useful for rare events…
 

Attachments

B

brahmaiah

#50
I did the attached analysis some time ago and thought that I had posted it.

I did this in Excel, but Minitab could do it if you know which buttons to push. Some easier in Minitab some easier to accomplish in Excel. (my org uses JMP not Minitab...)

basically I started with a simple line chart of the %voids against the 15% USL and just looked at the data. without knowing what the change was I can make only general conclusions. It appears that the failure rate and the amount of voiding are better; certainly there are really high values and there are more units with no reported voids than before.

Since the failure rate is Binomial but the before data clearly doesn't follow a roughly Normal distribution (long tail on the high side, bounded on the low side with censored data below 6%) and it isn't not large enough after the change to utilize the Normal approximation for the Binomial, I utilized EXACT BINOMIAL confidence intervals to see if the difference was statistically significant. It isn't. the confidence intervals overlap. This may simply be due to the relatively small sample size particularly for the after data. In this case the trend chart - or an SPC chart is a better indication than confidence intervals or other hypothesis tests as the failure rates aren't 'estimates' based on random sampling. Time will tell if the difference is sustainable.

I also calculated the Ppk value and sigma value (without the 1.5 sigma shift which I fell is silly and cheating) they are included in the analysis.

If we look only at the %voiding as a measure of improvement rather than the failure rate, our statistical analysis is more complicated but does provide more compelling evidence that there is a statistically significant difference. Since the %voiding has no modeled distribution, so I used the Chi Square test and looked at using a truncated distribution…

I also added control chart that is based on the number of blades with no reported voids in between blades with reported voids. (Charting for events – you plot the activity rather than the failure events…higher is better) I have found this chart to be extremely useful for rare events…
Thank you for you attachments.
Your void trend chart indicates by and large your process is under control.A few cases of out of contol observations could easily be due to some assignable causes.It also indicates that a correction to process has taken place after which the results are under control.Applying advanced statistical methods to a shop floor operation will be of less use as it becomes only post martem analysis.SPC serves its purpose only when immediat correction to process parameters is effected during production when assignable causes occur.
V.J.Brahmaiah
 
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