# Spec. Limits and Gage RR

Six Sigma – iSixSigma Forums Old Forums General Spec. Limits and Gage RR

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• #38050

Tim Wright
Member

One of my customers insists on reducing the specification limits for a given feature when the corresponding gage R&R results (% tolerance) exceed 10%.  For example a specification for a pilot diameter is 54.8910 +/- 0.0125 mm and the gage R&R (%tolerance) is 19.6%.  How should the specification limits be adjusted?
1) Shrink the tolerance on both sides (adjust upper and lower specification limits) by 19.6%.
2) Shrink the toleance on both sides (adjust upper and lower specification limits) by (19.6%/2) = 9.8%.
3) Shrink the tolerance on both sides (adjust upper and lower specification limits) by (19.6% – 10%) = 9.6%.
4) Shrink the tolerance on both sides (adjust upper and lower specification limits) by [1/2 x (19.6% – 10%)] = 4.8%.
Likewise, how would a unilateral specification such as “indicator runout not to exceed 0.150 mm” be handled?

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#113346

Solo
Member

Tim,
It has been my unpleasurable experience that if you phrase a question and then give 1) 2) 3) 4) options as to the answer of that question, no one will reply, because “We don’t answer peoples homework questions on this forum!” (To quote Dr. Darth ;-)
If, however, you provide more detailed information as to the business process and Six Sigma application in question, thereby introducing the credibility that you are in fact NOT asking the question for a homework assignment, people may be more willing to help…
Respectfully,
-Solo

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#113605

Tim Wright
Member

Thank you for the advice.  While I wish the question that I posted was purely academic it comes from a real situation in which I’m involved.  I presented the options because this is what had been discussed with my customer.  We produce 480,000 parts per year and presently have a PPM rate of 17,347 based upon use of the entire blueprint specification (LSL = 54.8785 mm, USL = 54.9035 mm).  Please note that the total tolerance is 0.025 mm which is approximately 0.001 inch (a fairly “tight” tolerance).  At a cost of \$4.62 per piece my present cost due to non-conformance is about \$38,000/year (480,000 x 1.73% x \$4.62).  As mentioned previously the gage R&R is 19.6% of tolerance.  Depending upon which “revised” specification limits are chosen our cost will change accordingly.
Option 1:  Shrink each side by 19.6%.  This predicts 66,600 PPM rate which would account for an annual cost of about \$148,000 (increase = \$110,000).
Option 2 & 3: Shrink each side by 9.8%/9.6%.  These predict about 34,400 PPM which would account for an annual cost of about \$76,000 (increase = \$38,000).
Options 4: Shrink each side by 4.8%.  This predicts 24,700 PPM which would account for an annual cost of about \$54,000 (cost increase = \$17,000).
My question remains; should the specification limits be adjusted based upon the gage R&R results?  If so how should the specification limits be adjusted (option 1, 2 & 3, 4 or something else)?

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#113616

Kraft
Participant

Tim,
I guess I missed something in your explanation. But, it seems to me that if your process is using all of the print tolerence then your process is clearly not capable. You should be asking for Tolerence Relief from your Customer or asking your management for a better process to produce pilot diameters.
The rule of thumb I’ve always used states, if the SD of the measurment system is more than 1/4 the SD of the manufacturing process the measurment system has inadequate resolution.
Perhpas I’ve missed the point completely, but after reading your posts these two observations were the most obvious and disturbing to me.

Bob K

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#113629

Tim
Member

Bob,
Our PPM is 17,347 (1.73% out-of-spec).  The Cp for the process is 1.05.  The process standard deviation is 0.004 mm.  There is an opportunity to bring the mean closer to the nominal diameter of 54.9035 mm but this will not address the issue in question.  There is no room for negotiation with the customer regarding the blueprint specification limits.  That is a matter defined by our contract.  We are using state-of-the-art CNC turning machines and state-of-the-art cutting tools.  A capital investment in more advanced equipment (CNC grinding machines) is simply not feasible.  The standard deviation for the gage is 0.0008 mm.  According to your rule of thumb the standard deviation of the measurement system is less than 1/4 of the tolerance so the measurement system should have sufficient resolution.  In fact the number of distinct categories reported for the gage R&R is 27.  I would be concerned if it were below 5 or 6 but it isn’t.  I hope that this clarifies the situation.
I would like to be able to use the allowable tolerance but the customer is squeezing us.  I think that I can make an argument for reducing the upper and lower specification limits by only 4.8% but I’m just not sure.  I thought that others on this forum might have had similar experiences that would shed light on my predicament.  That’s why I posed the question here.
Tim

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#113633

Kraft
Participant

Tim,
I would like to help you .if I can. But with all due respect, you’ve misquoted me. I said, “if the SD of the measurement system is more than 1/4 the SD of the manufacturing process the measurements system has inadequate resolution. You, in turn have supplied these two values in your reply and they equate to 5. Good but not great. Perhaps its time to become concerned.
Youve also stated your process has a 1.05 Cp and that you have concluded there is an opportunity to move the mean closer to nominal. Without a Cpk value Im not sure how your came to this conclusion. Again, Id like to help you .but Im confused.
Bottom line, state of the art equipment should produce a Cp much better than 1.05 on feature that has a +/- .0125 mm tolerance. We do it everyday across multiple machine centers that arent state of the art.
Send me some data, R&R data and process data; Ill sort it out and give you a conclusion you can take to your customer. If they want to squeeze tell em the price of poker just went up.
Bob K

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#113652

Tim
Member

Bob,
Rather than risking another misinterpretion of your “rule of thumb” lets consider the number of distinct categories found during the gage R&R instead.  That number is 27.  I believe that this is a measure of resolution.  It’s arguable that it should be better but in my experience a “shop hardened” gage with this type of performance for a dimension having a tolerance of 0.025 mm is acceptable.
Cp = 1.05, CpK = 0.73 (CpL = 0.73, CpU = 1.38).  The histogram of the data set showed me that the mean value wasn’t centered and hence there was an opportunity for improvement.  However for this situation even a perfectly centered process will generate scrap.
Whether or not state-of-the-art equipment can achieve a given process capability depends upon a number of factors.  I agree that you may be able to generate better process capability for this particular tolerance on a less-than-state-of-the-art machining center.  However it depends upon the process.  We routinely reach CpK values in the neighborhood of 2 or better with some machining processes.  The process in question is a single point turning operation.  Because tool wear is appreciable the machine operator must monitor the bore size and adjust the machine accordingly.  Although the machine itself can accurately and repeatably put the tool within 0.002  mm of it’s intended position the process (tool wear) and the operator (tool adjustment) add additional variability.  Thus the process standard deviation is 0.004 mm.  That is the cold, cruel reality.
Given that the process is “not capable” all parts are measured and scrapped when they exceed the upper and lower specification limits defined by the blueprint.  The customer wants my measuring system to have a gage R&R less than 10%.  It doesn’t.  I want a process with a CpK greater than 2.  I don’t have it.  It will take time to improve the measuring system and the process.  The customer wants me to start using “adjusted” specification limits and wants action now.  Which option can I credibly argue; 1, 2, 3, 4 or something else and why?  And by the way renegotiating the selling price is not an option.
Tim

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#113653

Kraft
Participant

Tim,
1.) Throw your Gauge R&R data out the window, just from the data youve provided its unmistakably clear your measurement system simply cannot distinguish 27 distinct categories. It’s impossible!!!
2.) And, if  these Cp and Cpk values reflect a process where and operator is constantly making changes, we call that chasing your tail by-the-way, you really don’t have any idea what your process capability really is anyway.
Bob K

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#113655

Thaly
Member

I understand you are doing a 100% inspection.
One way to improve your gage R&R is by looking at the control limits of the R&R experiment and attack the points out of control due to operator error. (Reproducibility). see if you could get all the points within the control limits. This brings down the operator error part of your R&R. If you can’t simply discard those values and recalculate the Range.
If you dont want to do the above, here’s something you might like to do.
%R&R of 19.6 means that your gaging system contributes to 19.6% of the sigma(total variation) and NOT your tolerance limits.
So you might be better off shrinking your tolerance limits by 19.6% of the SIGMA and not that of the tolerance limit itself.
Hope this helps.

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#113659

beverly daniels
Participant

not sure how you are calculating ndc.  Using the intraclass correlation coefficient I get a discrimination ratio of 7, or you can divide your process (actual) variation into 7 distinct categories.  I typically guardband by moving the spec limits in by 1/2 of the width of a distinct category…(assuming a roughly symmetrical and Normal distribution your process width is 6*.004 = .024.  1 category width is then = .024/7 = .0034 and half of that is .0034/2 = .0017.  (the extremely conservative approach is to use one category width but that tend to reject far more good parts tahn bad parts).  So you would guardband the limits by +/- .0017.
Then you shoudl immediately start work on improving the process capability to avoid this issue.

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#113661

Tim
Member

Beverly,
The NDC that I reported came directly from the Minitab gage R&R output (using the ANOVA method).  I definitely need to discover where I made my mistake.  Your value of +/-.0017 mm works out to 6.8% of the tolerance (0.025 mm) and presents a fifth option with an explanation that I think will satisfy my customer.  Your answer was precisely what I was looking for and yes, I need to improve the process.  Thank you very much for your help.
Tim

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#113678

beverly daniels
Participant

going back to the intial post, Tim does state that the 19.6% number refers to the percent of the TOLERANCE that the measurement error consumes (typically, although not always, calculated as a straigh tratio of six times – or on old approaches 5.15 times – the measurement error standard deviation divided by the tolerance range.  Technically this is mathematically incorrect as standard deviations don’t add.  And in this case 19.6% is probably way overstated…although without the raw data is really tough to tell so I’m just making inferences from the data provided…
Again using the IntraClass Correlation Coefficient approach, the measurement error calcualtes to be only 4% of the total observed variation…not too bad.  However, with the process capability at a little more than 1 and the fact that he states that he’s got defects, guardbanding as first step is a good approach if the characteristic is critical (as defined by the customer’s supplier quality group, not necessarily the product itself, of course)
My recommended guardband limits are in an earlier post.  In my experience this approach tends to provide a good balance:  excellent protection for th ecustomer without undue hardship for the manufacturer…we must remember that measurement error goes both ways symmetrically

An alternate approach for those characteristics that aren’t susceptable to stackup with other characteristics is to take units that fall into the guardbanded region and measure them multiple times and use either the average or median to accept or reject the unit.  (WITH Customer approval of course).  This is a reasonable approach with expensive parts or constrained parts to ensure an acceptable supply flow without compromising quality…

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#113680

Mikel
Member

You can always tell someone who has been trained by Wheeler – dogma on top of dogma.
P/T is not matematically incorrect. It represents the amount of the tolerance the measurement error consumes. The +/-3 sigma spread is quite conservative by not incorrect.
IntraClass correlation coefficicient and distinct categories are baiscally the same (there is a -1 missing from the distinct categories) and are just a different spin of P/TV (%Study for you Minitab users).
I do agree about the guardband, but stop spreading that Wheeler nonsense about a “better” or “correct” method.

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#113688

Tim
Member

Stan,
Unfortunately I wasn’t able to decipher your response.
I don’t know:
1) Who Wheeler is.
2) The dogma to which you refer.
3) Anything about the IntraClass correlation coefficient.
4) Why the number of distinct categories output by Minitab don’t correlate with the value that Beverly found for #3 (above).
5) Where the terms “better” or “correct” appeared in Beverly’s explanation.
However I would like to know more.
I do know:
1) Beverly’s response was the only reply that truly addressed my question.
2) Her explanation appeared clear and logical.
3) While her method may not be mathematically perfect it certainly did provide a practical approach for solving my dilema.
I would be happy to provide anyone who is interested with the data for the gage R&R study and capability study that were used in my analysis.  I would certainly like to learn other ways to solve this problem.
Tim

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#113693

beverly daniels
Participant

Tim – in response to your post:
“Wheeler” is Dr. Donald Wheeler, one of many statisticians that publish their work.  His primary area of interest is Control charts (He refers to them as beahvior charts).
To somewhat answer your question about “dogma”:  Some people seem to have a penchant for “deifying” or elevating to guru status certain of the more public or well known figures in the Quality/Statistical professions.  Others have a penchant for “demonizing” or belittling teh work of others who are in the public arena.  Wheeler is apparently one of thos epeople.  But so are many others who are more famous and make more money than either you or I.  Personally I don’t get it.  I study as much as I can given my work load, try it out, and use what works for me in my situations.  I do offer up options based on my experiences – whether it worked or didn’t.  I actually learned about the intraclass correlation coefficient and other approaches to Gage R&R independently of Wheeler and only really heard about his affinity for the technique after I started using it (because it worked for me).
If you are interested in the Intraclass correlation coefficient a simple web search will give you a few articles to begin with.  There are many approaches to gage R&R and only your experience will help you choose what works for your situation.  Or as another public statistician once said:  All models are wrong, some are useful.
Good luck!  I hope you are able to come to a reasonable accomodation for your customer and your company.  You certainly have several viable options to work with…

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#113696

Mikel
Member

Beverly,
I am responding to your statement of P/T (or %Tolerance for you Minitab users) being mathematically incorrect. If you have been taught this, you need to question your teaching.
To Tim, get Wheeler’s book Measurement System Evaluation (SPC Press, Knoxville, Tn.). It is good. Just skip the part about his meathod being right and everyone elses being wrong. If I know Wheeler’s number, I can get everyone elses and vice versa. If your distinct categories from Minitab is different than Beverly’s, I would suspect Beverly’s number is wrong. The formulas are exactly the same except there is a -1 in the denominator under a square root. On rare occasions, the Wheeler number is one higher, but it is because both number always round down, so if Minitab gets 3.99 they will report 3, if Wheelers number is 4.01, they will report 4. No real difference.

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#188496

Sinnicks
Participant

No one answered the question, how do you computer GR&R% for a unilateral tolerance, such as surface flatness:
Upper tolerance=.020mm
Lower tolerance=0.0
The nominal or target is 0.  It simply cannot be correct to compute %GR&R=.20/6*standard deviation!

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#188498

Ken Feldman
Participant

Glad you were patient and waited 5 years to reply. Here is an excerpt from a Minitab dialog box. No problem with a one sided spec.Process tolerance: Enter either the known tolerance range (upper spec – lower spec), the lower specification limit, or the upper specification limit. A %Tolerance column will be displayed in the bottom table of the Session window output and in the components of variation graph. This column shows the percentage of the process tolerance taken up by each variance component. Enter at least one specification limitLower spec: Choose if you only have a lower specification limit. Enter the value of the lower specification limit. Upper spec: Choose if you only have an upper specification limit. Enter the value of the upper specification limit.Upper spec – Lower spec: Choose if you have both an upper and a lower specification limit and are not interested in calculating the probabilities of misclassifying product by either calling it good when it is bad, or calling it bad when it is good. Enter the difference between the specification limits. This is also known as the tolerance range.

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