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capability studies on positional tolerances (rfs)
capability studies on positional tolerances
position with rfs (regardless of feature size) can be used but why not maximum material condition (mmc)?
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if one has a positional tolerance at mmc, it reflects a virtual condition boundary and not the centers per asme y14.5m-94.
what would affect the virtual condtion boundary? certainly the size of the feature and its location (position) from true position but also the shape of the feature. we could play with stats on the centres but we could not include shape.
one could have a calculated tolerance (actual to virtual) and have a centre of a round hole (as an example) just inside the calculated tolerance. we still may not get a checking pin in this hole once we set the part in a checking fixture. why? the shape of the hole may not be round.
if the secondary and tertiary datums were also at mmc, you are in a real mess now.
use checking fixtures for positional tolerances at mmc. call them "major functional characteristics" and keep away from faking the stats if you can.
dave d.
capability predictions can be done for both position tolerances with constant value specification limits (rfs) and position specifications with variable specification limits (mmc / lmc).
the problem with doing these predictions with variable specification limits is that the basic formulas for cpk-ppk are designed only for constant value limits. that problem can be fixed by changing the equation to include the variable portion of tolerance and its inherent variation. the variable portion of tolerance is a distribution itself. it is actually the distribution for size and if that distribution is considered properly in relation to the distribution for the position deviation then the interference of the two distributions represents the “probability of a defect�for a variable limit tolerance.
if you were to make a histogram for a position deviation distribution you would likely see a skewed distribution with greater frequencies of smaller deviations crowding the lower boundary (zero position) and fewer frequencies larger deviations approaching or even exceeding the usl. to make that histogram reflective of a variable tolerance you would need to show the distribution for size on the same graph. to do that you must recognize that the (zero position) boundary corresponds to the “virtual condition size� the usl corresponds to the size limit that represents the minimum variable tolerance, and the position tolerance extends to the value for size that represents the maximum variable tolerance or the “resultant condition�
when you align the legend values for size and position next to each other you will see that the values ascend and descend correspondingly for holes with tolerances specified at mmc and shafts at lmc. consequently the values ascend and descend in opposite directions for holes at lmc and shafts at mmc.
if you have done the histogram properly you will see two distributions side by side, one for position (typically skewed) and one for size (typically normal). the area of the intersection of those two distributions reflects the probability of a defect for a “variable limit�tolerance and if both distributions were “normal�it could be accurately estimated by using the classic reliability formula for strength vs. stress.
i posted a presentation that i gave at a conference last year to another forum. it is toward the end of the 2nd page of comments,
paul:
loved your presentation method that you sent me. it is kind of neat but i still do not agree with you but i have worked in the quality field forever, so you know where i am coming from.
you are correct that 5.3.2.1 reflects positional at mmc using a centre line but the note at the bottom indicates where shape may not be perfect (extreme form deviation) then "the surface interpretation shall take precedence". are the holes perfectly round. if not, then the surace condition supercedes centres. are they confirmed prior to the study?
sure we can calculate the actual diametrical tolerance zone at mmc. it is simply the difference between the actual diamter and the virtual condition diameter.
+ 3 and -3 are they the same???  if the true position is 0, then each reading is 3  digits away but are they the same - no. in statistics we look for repetition (estimate of the standard deviation) and then aim of the process.
referencing datum holes at mcc as in most cases are changed to rfs so that we can measure the position of each feature. i don't think that is correct either. we lose tolerances.
how do we reflect the position of the holes relative to primary datum a. do we check each hole at the bottom or top and report the worst case situation? no we don't. we are only interested in the x and y axis only.
if the holes were slots, how would the centres confirm the orientation? they don't.
i love stats and used in the correct situation, they really do help but on positional at mmc, it's more show than go. you got to have a ppk of at least 1.67 or greater so everyone does.
dave d.
so brandy7 now you have insight into why we can’t predict capability with variable tolerances! it’s complicated.
the problem that you proposed still lingers without common resolve. those that understand dimensioning and tolerancing see finite limits and can articulate their boundaries with all due respect. they know that if you just relied upon “functional gauging�your problems would be solved. those that understand uncertainty see variation as infinite and can prove that if you employ their equations with all due caution you can predict conformance and. they know that if you just analyze the data according to their equations your problems will be solved.
the problem that i see is that few statisticians and software developers understand dimensioning and tolerancing well enough to realize that the limits can themselves be variable and few quality practitioners realize that a sometimes significant portion of tolerance is being ignored when they compute capability. without popular recognition that there is a problem there is no need for a cure. if you study and employ the resources that i suggested you will still find yourself in a predicament because you, as a producer, will find yourself attempting to convince your customer that his analysis of the data is flawed. good luck!
i developed a method to include “datum shift�in the statistical analysis by considering each features�residual or remaining tolerance in a simultaneous requirement pattern and then iterating shifts and rotations of the drf respective of the actual datum feature size limits to maximize the smallest residual but as you can see it is even more complicated. if we can’t convince statisticians and software developers that measurements can have “variable tolerance limits�and we can’t convince gd&t people that “attribute gauging,�is highly inefficient way to control the quality of a production process then why pursue more complicated stuff.
there is another dilemma that you should be aware ofâ€?it is that variable tolerance modifiers are often applied to features that they shouldn’t be.  you can test whether an application of a variable tolerance modifier is functional by answering a simple question. does the function worsen as this feature is permitted to deviate from its ideal location or orientation? if the answer is yes then the modifier should be rfs and if no then mmc or lmc may be appropriate. from assembly to gauging to clearance stack calculations many will claim when and where mmc or lmc should be used but i have found that often the modifiers are selected more out of habit to support “attribute gaugingâ€?than from a critical analysis of function. “Functional gaugesâ€?are just “attribute gaugesâ€?when the tolerance modifiers don’t reflect the functional liabilities of variation. so when “bonusâ€?tolerance is ignored in a capability analysis for a feature that shouldn’t functionally have a variable tolerance that is a good thing. consequently when it is applied in the capability analysis for a feature that shouldn’t functionally have a variable tolerance that is a bad thing.
paul
thank you all for the explanations and comments.  as design checker i try not to use mmc as much as possible-but the suppliers are always trying to get every bit of bonus or extra shift tol.-i give it to them on clearence holes,etc.  i will in addition to your test question ("does the function worsen as this feature is permitted to deviate from its ideal location or orientation?")use rfs on all cpk-ppk or criticals. i will keep adding to the this list as we go along.  shift i usually do not use  because it really is not "design intent"-but suppliers are alway after that little extra tol. any comments or additions to the list would be appricated.
thanks brandy
brandy:
there is a reason why the suppliers are asking for mmc on positional tolerances and also on the datums if the datums are holes.
they want to develop a checking fixture which simulates the assembled state in the worst possible case. years ago, we used to try out nonconforming products on the assembly line and if they worked, the hold tag was taken off and the parts were shipped. unfortunately, we didn't know how the mating parts were made.
now, the checking fixture is the mating part made as the worst possible state.
if you have holes as datums, what goes in those holes? if it is a tapered pin locating on the datum holes, then go rfs. i don't think so though. i think that there are bolts or shafts that go in the holes and they are cylindrical in shape.

if that is the case, then the datum holes should be referenced at mmc to simulate the assembly. if we make the datum holes larger, there would be accrued tolerances just like on the assembly line.
there is no "hocus - pocus" here. the gauge now is made to simulate assembly. once a gauge is made, then the feature would be checked on the shop floor hourly by the operator.
dave d.
brandy and dave,
i am not saying that it is inappropriate to use variable tolerance modifiers i am just saying that their use should reflect the functional liabilities to variation. let me give you a couple of examples to illustrate my point.
one of the first persons to inquire about variable tolerance capability was a black-belt was trying to solve a piston leakage problem on a transmission clutch cylinder assembly. the outer cylinder surface is part of roll formed (grobed) sheet metal shell. it is welded to an inner turned hub. when assembled there is a inner od cylinder surface on the hub and an outer id cylinder surface on the shell that will function with a flat aluminum piston that has both inner and outer seals. typically the specification has one of the cylinder surfaces serving as the datum feature for the position of the other. both cylinders have size tolerances and unfortunately they historically have mmc modifiers for both the datum feature and the measured feature. the gauge that they had to verify conformance was sized to the maximum inner cylinder diameter and the virtual condition of the outer cylinder diameter.
the black-belt called me and asked how to predict conformance of the tolerances with continuous data. i told him that if this was simply a static fit problem with no functional consequences then he could use the formulas and predict conformance just like the attribute gage that they had. but…I told him that the seals react differently to the problem. if the i.d. size on the outer cylinder was big and the o.d. size on the inner diameter was small allowing maximum variable tolerances then the seals could experience vast differences in static pinch from one side to the other. i told him that the use of mmc modifiers with these positional tolerances was inconsistent with the function of the assembly.
to further exacerbate the issue he cited on of my earlier papers where my equations that claimed that when there is a one-to-one relationship between the datum feature and the referenced feature, both with variable tolerance modifiers and no other simultaneous requirements, then the datum shift can be included in the equation with its mean bonus and squared stdev (variance). it’s true but it is too susceptible to misuse if the conditions are not proper.  
the callout with its variable tolerances insured assembly of the piston without stacked physical interference but it totally discounted function. they were running that stupid “functional gauge�as a containment measure until the print got fixed by removing the variable tolerance modifiers. then they finally focused on the problem.
one more example to illustrate lmc…which many designers feel is un-gauge-able and therefore shouldn’t exist.
in a transmission valve body there is a separator plate with precision orifices/holes that serve as a connection between the labyrinths of the upper and lower bodies (the hydraulic equivalent to thru circuit connections of a double sided electronic circuit board). some of the holes permit clamping bolts to pass thru and the others permit pressurized oil to pass thru. the ones that permit the fasteners to pass thru are variable tolerance problems that match mmc conditions. if the hole is bigger and more off location it will still permit the fastener to pass thru without interference. the others (the oil connection orifices) are sized to allow maximum or regulated flow without encroaching on the boundaries of the labyrinth. one problem is position at mmc while the other is position at lmc.
the supplier has a precision punch die that installs all holes and orifices simultaneously. if all of the holes are toleranced with mmc modifiers (which they commonly are) then the “functional gauge�will look exactly like the die that produces the holes (at their virtual conditions) and if he runs his punch sizes big they will be less likely to break, more likely to fit the “functional gage�and “life is good.�
function however is compromised when “bigger-is-better�orifices are permitted additional location tolerance because they are “bigger�they are more likely to interfere with the labryinth walls and gasket boundaries! the designers have to predict the interference in their stacks which reduces the possible size of the orifices just because they are toleranced with mmc modifiers that permit “functional gauging.�nbsp; what a crock!
i counseled them to use the appropriate functional modifiers and they said that it couldn’t be gauged. i told them that the attribute gauge would look exactly like the gasket with its orifice boundaries at their virtual condition (an overlay if you will). why must we use an overlay attribute gauge? because we cannot predict capability of variable tolerances with continuous data!  let’s fix this problem by predicting conformance of variable tolerances with continuous data.
one more (i’m on a roll) a boring tool and subsequent reamer fashion a coaxial series of cylinders (lands) in that same valve body. the position tolerance for every land is 0.01mm @  mmc, the datum for the measurement is the axis of all of the coaxial lands at mmc. the size tolerance for each of the stepped lands is 0.02mm. these specifications are typical of automotive valve bores. 30 microns total tolerance from the virtual condition to the resultant condition. this is a classic variable tolerance problem. most of the oem suppliers use a plug gauge (resembling the bore tolerances at their virtual conditions). but there is bore distortion from fastener clamp loads and bending from surface warpage. the question is??? what size should the reamers be set to…to insure uninhibited free movement of the valves with bore distortion while limiting leakage for calibration stability? you will find that optimization calculation in the spreadsheets and presentation materials that i referenced earlier.
paul
btw, i am retired but looking for work if you need assistance write me. mailto:
capability studies on positional tolerances (rfs)
               to the next level
the same question as above except on the next drawing level-sub-assembly drawing.  i have a detailed part-leg-to attatch to base part(welded).  i will use a ref. hole dia.(9) that i will attach gd&t position callout of 0.5-but i can not make it mmc because ref.(9)does not have tol. specipied at this dwg.- thus no bonus tol.  because it is detailed on lower level dwg. do i have to live with rfs or can i legelly add tol. to the ref. dia. (9+-0.02)? it is now ref. dim. with a tol. and also fully dim. on detail with tol.  can you give this same hole a mmc bonus twice-once on detail and once on sub-assy?  hope you can follow what i'm getting at. thanks
bonus tolerance?? that does not exist in the asme y14.5m-94 standard.
what goes in the 9 mm diameter hole? is it a tooling hole or does it have a function? if something cylindrical goes in this hole at assembly, then i would suggest mmc on the datum. if it  is a tooling hole, then rfs would be sufficient.
if i were looking at this drawing and it had a positional tolerance at mmc referencing a 9 mm dia. hole on another part at mmc, i would make a checking fixture simulating assembly. one would have to go to the detail drawing of the mating part to find the tolerance of the 9 mm diameter hole but that is ok. there is nothing wrong with that.
note: i have seen design people arguing with mfg. engineering or quality who want mmc on the drawing. sometimes the design person would say something like "i will put mmc on the drawing but the dia. tolerance of 0.4 is now 0.3". that is just plain wrong.
dave d.
brandy, you mentioned, " i have a detailed part-leg-to attatch to base part(welded)". i suggest that you start a new thread or search the archives for theads that discuss "inseperable assemblies". i would suspect that there are some pretty stout opinions in this forum on how the inseperable assemblies ought to be toleranced!
in the fundamental rules of the dimensioning and tolerancing standard y14.5 you'll find a statements that say that "each necessary dimension of an end-product shall be shown" and "dimentions and tolerances apply only at the level where they are specified" look carefully at paragraphs c and n.
many believe that a reference dimension must only refer to a toleranced dimension on the same drawing. others think that if a tolerance is that is stated at a sub level and restated on an "inseperable assembly" level that the feature is "duel dimensioned".
start another thread to talk about these issues this is not the "same question as above"
paul