Non-Normal Data - Measurement for "straightness" with a 0.001" max tolerance

S

Shantin10

#1
Hi All, I could use some help with "non-normal" data. The measurement is for "straightness" with a 0.001" max tolerance. Some of the data =0. Using Box-Cox power transformation does not help. The measurement system is capable. The largest value measured is 0.0005", with the smallest being 0. Any thoughts?
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
Re: Non-normal data

why are you worried about Non-Normal data? are you doing a measurement system analysis or a capability analysis?

it is most helpful if you can post your data...
 

bobdoering

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#3
Re: Non-normal data

Probably should be using a beta, weibull or lognormal transformation for a unilateral physically limited tolerance. But, the raw data would help figure best fit. Remember, gage error and measurement error might mask the true distribution, if they are statistically significant.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#5
are these values from sequential parts? are they in time sequence or are they randomly selected from a lot?

How many change points are included? (by change points I mean different setups of the equipment, raw material lots, operators, etc.)
what is your specification?

Are you trying to calculate a Cpk value? if so why? is it a Customer requirement or do you want to understand the defect rate /yield of the process?




The data is 'chunky', meaning that there are only a few values that actually occur - this will overinflate your standard deviation and make any Cpk calculation useless. not to mention the non-normality of the data. If you can answer the above questions we can give you a useful approach to understanding your capability. *I* never transform data...there are many useful ways to deal effectively with non-normal data and transforming data tends to enable you to miss the really important things about it...
 
S

Shantin10

#6
Great questions! The values are random, but from an entire population. The parts are cut in a fixture that can hold up to 40 parts; there were 8 runs, seven full fixtures and one partial. The parts were measured after the process was complete. The customer is looking for Cpk. Thanks for your help!
 

bobdoering

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#7
The customer is looking for Cpk. Thanks for your help!
If your customer is automotive, they should not be looking for Cpk. They should be reading the AIAG PPAP book:

Section 2.2.11.5 Processes with One-Sided Specifications or Non-Normal Distributions

NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center).
When this is not true, using this analysis may result in unreliable information
.

Therefore, it does not apply to straightness.

If they are not automotive, they are lost in the Cpk bramble.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
Bob has a very good point if you are automotive. you have a perfect platform fro discussing with your customer what they really need. In this case I would show them the frequency distribution of your data plotted against the spec limit. period.

On the other hand if you aren't in automotive then a discussion with your customer is still appropriate. I have attached an analysis using both continuous data and categorical data.

the continuous data uses a formula for a generic truncated distribution and it fits well enough for the purpose. although again the chunky data overinflates the standard deviation and results in a Ppk that is probably smaller than reality.

the categorical data takes into account that you had several set ups and you randomly sampled from the lot. it is a more conservative estimate and yields an even smaller Ppk.

If you look a the histogram you are well within specification...

some advice for the future: in capability studies its always better to plot your data in time sequence noting the lots, operators etc on the x axis. also put your specification on the plot. THIS is how one can assess stability and capability simultaneously. (it is known as a multi-vari chart, or in its simplest case a run chart)...
 

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