# Measurement system question

Six Sigma – iSixSigma Forums Old Forums General Measurement system question

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• #31732

Ben R
Participant

I have a supplier who provides a product that is 80 to 150 inches in length. He measures this product with a tape measure that has been verified.
He records the measurements he takes in 1/16th of an inch.
My company requires Cpk studies on critical characteristics. The supplier took the appropriate number of measurments, then converted the 1/16ths into the decimal equivalent. From there he calculated averages, standards deviations, etc.
I am very uncomfortable with the process of converting fractions to decimal equivalents, then manipulating the results as if they were continuous data.
Are there other options?
Thnaks.

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#83956

howe
Participant

Ben,
I agree that you should be cautious about the practice in general, but I do not believe it is warranted in this case.  For all practical purposes there would appear to be way more than enough resolution with the method he is using.  i.e. the range in question is 150 – 80 = 70 inches.  The number of measurement intervals is 70 x 16 = 1120.  Generally 10 intervals is the minimum you would need for a useful gauge (when comparing to tolerance).  When comparing to process it depends on the total spread.  i.e. – the final analysis depends on exactly what his distribution is relative to the specs, and without that info it is hard to make a judgement.  I could give you a very specific answer with that info.  A really good reference on this topic is Concepts in R&R Studies by Barrentine.  Its a relatively inexpensive paperback.

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#83970

Gabriel
Participant

The data is ALLWAYS discrete, because no instrument as an infinitely small resolution.
If you measure with a digital caliper in mm, you get values in steps of 0.01. If this resolution fits several times (like 10) in what you are measuring then assuming it is continous is a good approximation.
Now if you are measuring let’s say a specification 10 +0.01, then it works more like a go/nogo gage (the only Ok results are 10 and 10.01, any other result is a reject. In such a case, taking the reading as continous would lead to missleading results.
In this case you are asking for Cpk, so the “parameter” to compare is the process varaition, not the specification.
If the process spread is from 80 to 150 in, even rounding the readings to the closest inch would be Ok to calculate Cpk. Now, if that’s the specification but the process spread goes, let’s say, from 110 to 112, then a one inch resolution is clearly not enough and a 1/16 may be Ok if the measurement variation is very small (i.e. if every time a measurement is done in the same part you get about the same 1/16th value) but may be not ok if you have a measurement variation of several 1/16th’s.
Of course, if the spec is 80 to 150 and the process is about 110 to 112, you don’t care about a precise value of Cpk. It is just a lot more than good enough.

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#83972

Jamie
Participant

I agree with what Gabriel has said here (i need to find a post of yours I dissagree with, that would be more fun). To restate all measurements with be discrete because of the finiteness of the system, this does not make the variable you are measuring discrete. You are still measuring a continuous variable.
But, let me question this…. does the product truly vary from 80 to 150 in length? or do you really receive different products that vary from 80 to 150 where for a particular length you have a tolerance that is much smaller. For example, do you get products that are 80, 90, 100…150 units in length and you are trying to determine the capability of these and the specification of each product is +-0.01 unit. If so then apply Gabriel information with respect to tolerance to help undestand whether the gage resolution is acceptable. I hope I didn’t digress, I’m not positive of your original question.
Jamie

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#83973

B Royal
Participant

Gentlemen,
Thank you for the information. I fear I did not adequately describe the dimensions we require. Some examples:
79 1/4″ +/- 5/16″
146 1/16″ +/- 5/16″
The tape measure my supplier uses has a resolution of 1/16″. Ten 1/16″ will fit within the tolerance. So that gives us the rule-of-thumb10:1 resolution.
He did conduct the usual Gage R&R – three operators, 10 parts, three measuements per part. After converting the resutls from fractions to decimal equivalent , he ran the numbers per AIAG and got gage capablities of 17.17% and 16.59%.

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#83974

Ravi Khare
Participant

I would agree with Jamie’s observation. An 80 to 150 inches tolerance on the same product appears too gross to need a fine measurement system. If this is indeed the case, a 1/16″ least count would be excellent.
However if we are referring to different products in the range of 80 to 150, we will have to look at the tolerance of each of the products.
Ravi

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#83977

Carl H
Participant

Ben,
I agree that the 1/16 inch divisions can be treated as continuous.
I wonder about the Gage R&R results.  Did they pick parts over the entire 80-150 inch length range in their study?  If so, the % study varaition may be artifically low.  If the % P/T is OK (<30%) then you shold be OK.

Carl

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#83979

Jamie
Participant

Ben, One of our business units produces lumber so I’m use to seeing lengths which is why it jumped out that you were probably dealing with seperate products. One question I have is (to be certain as to what we are looking at) the %’s you provide are they P/T, % contribution or % study. Also consider how capable the supplier is. For example if he were close to six sigma (I’m guessing he is not) then you only need a measurment system that picks up gross changes since you are so far from the specification limit (again I’m guessing this is not your case). From the numbers I see, I’d say its marginal. You now have other things to consider. I’d ask for the actual gage study. Its very easy to do a gage study that makes the gage look very good when indeed it is not. For example what is the range of parts that were measured. If the gage study was done on a wide range then the percent variation would go down (this is not true for P/T, the range is identified by the tolerance which is fixed). Also a course measurement system can make a gage look artificially good. For example ask operator/inspectors to measure to the nearest 1/4″. You can see they they could probably all do this very well. I’d say all operators could repeat this measure and reproduce each other. For any part if they measure it exactly the same then your % would be 0. But this doesn’t mean the gage is good. Again measuring to the nearest 1/16″ appears marginal to me. Also if he reports % contribution, but you think you are looking at percent study then you might draw then wrong conclusion. Just some things to consider.
Jamie

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#83987

Gabriel
Participant

It’s true. The actual length is continous. The mesured length is discrete. But the data is allways made of the measurement results and not of the actual values. That’s why I said that the data is allways discrete. If we have sevral distinct points in the range, we use the data as if it was continous. If you check a diameter with a go/nogo plug gage, the diameter is continous, the measurement is discrete, and you can not treat it as if it was continous because you have only three distinct “points” (results): small, Ok, big.

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#84071

Leung
Participant

Jamie,
When you say “P/T” you mean part variation/Total variation?
And to all, thanks for the dialogue. Since I started reading this web site I have become a much more efective BB, facilitator, and teacher.
Ben

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#84096

Jamie
Participant

Ben, Sorry to not be more clear. What I meant by P/T is the precision to tolerance ratio. For your example I believe your products should be +-5/16 of an inch. If this is true then the tolerance is 10/16″… this is the range of the spec limits. The precision is generally 5.15*S(gage). The 5.15 corresponds to the number of standard deviations that cover 99% of the variation of the gage (not sure I said that exactly correct, but thats close)… this is the same as +-2.575 std devs. So to get P/T just take 5.15*S(gage)/(tolerance). If you have a gage with S(gage) = 1/16″ then P/T would be ((1/16)*5.15)/(10/16). This would mean your precision to tolerance is 51.5% (not too good). Now be carefull here too because the standarard of 5.15 can be changed to whatever you want to use. So P/T tells you how good the gage is for the range of the spec limits.
Hope this helps, Jamie

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#84110

Leung
Participant

Jamie, Thanks so much. I pulled the precision from Minitab (they label it 5.15 *SD) and divided that by the tolerance.
I got a P/T ratio of of 26.2%.
That doesn’t make my heart jump, but it provides me and my supplier with a better understanding.
Again, thanks.

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#84111

Jamie
Participant

Ben, Glad I could help, sounds like you have what you need. One last passing comment… minitab can calculate P/T for you. Under options there is a place to put in the process tolerance. If you do that it will include P/T in the analytical output.
Best of luck, Jamie

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