What are the units of percent? It is my understanding that there are no units. That being the case, why does everyone dismiss % Contribution and jump to % Study Variation and % Tolerance. It is stated that coverting to standard deviation puts it in the same units of your measurement - however - you lose the proportionality and the columns do NOT add up to 100%. Shouldn't that concern people?
it concerns many people (although not AIAG apparently). See the works of Donald Wheeler for example. there are also many posts here discussing this concern.
It doesn't concern people who just want to 'check the box'. that includes suppliers and customers...
% contribution and % study variation are actually the same thing when the study is properly conducted - the math is a little different but the correct math is an estimate anyway so the difference has no practical impact. As you say, to have a real percent you must have the same units in the numerator and denominator. AIAG violates this law of mathematics in it's %tolerance. And it all started in a paper published in the early sixties by Robert Traver titled "The Rubber ruler"...
This is like any other 'time-honored' practice - since we've always done it that way we can continue doing it that way. Is that wrong? yes. is it laziness? yes. is it in direct conflict with the alleged intent of quality improvement, continual improvement and advances in science in engineering? yep.
If you had part variation in your study that matched exactly your tolerance spread, then the Variance of Part-toPart Variation would equate to the tolerance. If you then divided the Variance of Total Gage R&R by the Variance of Part-to-Part Variation, you would then have a PROPORTIONAL value that would represent a true % Tolerance. Find a Gage R&R where your part variation equaled or almost equaled the tolerance spread. Divide the Variances of Total Gage R&R by the Part-to-Part Variation and compare that to the caluated % Tolerance using Standard Deviations. Do they even come close?
yes this is a viable approach. what about acceptance criteria? is the percent 10%, 20% 30% (these are just rules of thumb, randomly selected by some unknown group of people. they were never derived. they have no basis in science or statistics. they have no more informative or scientific value than a p-value of less than .05.
we must also acknowledge that the overall standard deviation is highly effected by the selection bias of the parts that span the tolerance range. If these parts do not have the same distribution as the underlying process then the SD will either be overestimated or underestimated...
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