How do you put confidence bounds around bimodal data?

debun

Starting to get Involved
#1
Summary
I am receiving product from a supplier that falls outside of our tolerance spec. The inspection shows a real bimodal distribution and from the sample I would like to put a 95% confidence bounds around it. The data is not normal, what method should I use to create confidence bounds?

Boring details yet important.
The feature they are struggling with is a drilled hole. The tolerance is 10.1-10.35mm (for those that like inches over 0.012”) They are drilling between 10.1-11.1 WTF right? There challenge is the material is very abrasive and drills to not last long so are replaced often. The span on part is large and I suspect chattering so in these areas the holes are lager hence the bimodal distribution. When the drill bit is replaced you get a repeat of this pattern and it never becomes normal.
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#2
are you looking for:
  • confidence intervals around the mean?
  • 'confidence intervals' around the individual values?
  • confidence intervals around the defect rate?
 

debun

Starting to get Involved
#4
I am looking for confidence around the mean, so that I can see the range of values we would expect.

In response to mdurivage this is a bimodal, not binomial distribution. I have two distinct peaks in the data.
 
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bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#5
Can you post some sample data to look at?

Has anyone pondered doing a two step drill/ream or hone? You may be able to get better control than just drilling. Drilling is not precision machining, and its capability is very limited - even with easy to drill materials.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#6
just for clarity: your statement can be interpreted as wanting confidence intervals for spread or range of the individual values around the mean. Is this what you want? (I hate to ask again, sorry) If this is what you want there is no straight forward way to calculate these intervals. There are few ways that will be useful for you, but as Bob requested it is best if you post your data so we can look at what may be the best answer for you.

If you are looking for confidence intervals of the mean (the amount of 'accuracy' or precision of the estiamte of the mean) then the distribution of the individuals doesn't have to be Normal. The confidence intervals are not based on any assumption of Normality in the distribution of the individual values.
 

debun

Starting to get Involved
#7
Please see the attached data. Each part has 18 holes, each row is a part. Some parts don't have all 18 holes measured. Holes were measured by pin gauges. Below is a histogram of the data where you can see the bimodal distribution. This bimodal distribution even exists in the individual parts. If it were normally distributed you could use a student t an put a confidence interval around the data, but this data is not normal. I was thinking you could treat this as two separate distributions and use the tails to get the full range, but what would happen if there was an intersection of the data and not 2 distinct groups.
 

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Dave Mac

#8
If I understand you correctly the small holes are in area "A" of the part, and the large holes are in area "B" of the part (area B is where there is a long standout on the tool, thereby causing chatter, so the hole is getting enlarged)

If this is the case (or something similar) - i.e. you have a rock-solid system to split between the small and the large holes, then you could consider this as 2 normal distributions, and do the standard analysis for each distribution. - If you do not have solid reasoning to split the data ie the data is too muddy - you cannot do this.

It might be interesting to take the part drawing and mark up each individual hole on the drawing with it's mean size/min size & max size and send this back to your supplier so he can review his m/cing process.

Also the Confidence Interval on the mean will tell you with 95% confidence that the mean lies between 2 values. I'm not sure that this is what you are looking for.
If you are looking for the range of values that you would expect to see from the process this is something different, I think it is called a tolerance interval -
Link here to a calculator here (You'll have to remove the spaces from the link) - http: // statpages.org / tolintvl. html - Note: I cannot vouch for this calculator.
Cheers
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#9
If I understand you correctly the small holes are in area "A" of the part, and the large holes are in area "B" of the part (area B is where there is a long standout on the tool, thereby causing chatter, so the hole is getting enlarged)

If this is the case (or something similar) - i.e. you have a rock-solid system to split between the small and the large holes, then you could consider this as 2 normal distributions, and do the standard analysis for each distribution.
I would agree - and if so, I would treat them as two separate issues, and look to control each individually.

As an evaluation of the probability of what you would see as an overall effect, you could do this analysis:
I was thinking you could treat this as two separate distributions and use the tails to get the full range.
But, by blending the issues, it would not provide an answer on how to better control the issue - just a gross view of the impact.
 

Steve Prevette

Deming Disciple
Staff member
Super Moderator
#10
Options at this point:

Can you split apart the bimodal into the two underlying distributions? Even modeling by estimating two normal distributions, and a random split between the two (maybe 50-50, maybe not).

There is alway "non-parametric" analysis, up to and including the Tchebychev inequality.
 
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