How to calculate a True Position toleranced at MMC - Capability of True Position

Is there anybody having information of how to calculate a True Position toleranced at MMC (Maximum Material Condition).

Some have answered me to calculate it using the distance from the center. I do not agree with that since the true position is a two dimensional feature.
Also what about the MMC issue, which will change your tolerance depending on each piece.

S.

[Paul F. Jackson]

Last spring my article on the "Residual Tolerance Process Capability Model" got published in Quality magazine and I figured that the problem of including the geometric bonus tolerance in a capability evaluation had been solved. It has, I think, but not with the Residual Model and not with the "Adjusted True Position" that Glen Gruner published in Quality Engineering magazine in 1991 and also not with the "Percent-of-Tolerance" method that Marty Ambrose disclosed in the paper titled "Calculating MMC Cpk."

This summer I studied the three methods and discovered that they are all flawed. Each method creates a new value for variation by manipulating and combining variables for bonus amount and geometric deviation. I found that the variation of the resulting combination does not equal the combined separate variations. That led me to a new discovery.

All three of the methods tend to over-estimate the capability from a given data set by masking actual individual variations due bonus and geometric deviation. A big bonus value combined with a big geometric deviation can yield the same resultant "Adjusted True Position, Residual Tolerance, or Percent-of-Tolerance" as a smaller bonus value combined with a smaller geometric deviation. Glen Gruner's and my method yielded identical results for Ppk-Cpk. Marty Ambrose's method was different because it expanded each ratio to a common scale.

The problem statistically is "how to retain the actual variation of each variable in the equation for Ppk or Cpk." The answer is actually quite simple.

Ppk of a variable unilateral tolerance in excel format equals:

((USL+"Bonus" Xbar-"Geometric deviation" Xbar)/ 3(SQRT(VAR("Bonus")+ VAR("Geometric deviation"))).

For Cpk use "Bonus" Xbarbar, "Geometric deviation" Xbarbar and divide them by three times the square root of the sum of the squared estimated standard deviations derived by Rbar over d2 for both "Bonus" and "Geometric deviation."

Sorry that I couldn't just show the formulas. They wouldn't paste to this reply.

I am going to present this discovery at the "Applied Measurement & Inspection Technology" conference sponsored by the SME on October 23-25, 2001 in Detroit, MI. ***DEAD LINK REMOVED***

Unfortunately the conference publication states that I will present "The Residual Tolerance Process Capability Model." I hadn't discovered its flaw until after the conference was set up in May, 2001.

Very interesting stuff, Paul.

This started me thinking in the the direction of using Cpm's. Also I feel we need to be thinking two dimensional (since .002" in the 1st quadrant is not not the same as .002" in the 3rd one -- averaging these two will be .000" if the are perfectly in the opposite direction, while if we don't assume the 2 dimensions, the average will be .002").

So calculating a Cpm-X and Cpm-Y (Cpm for each of the axisses), would be:

Cpm(x)= (USL+"Bonus(x)" Xbar)-"Geometric deviation(x)" Xbar)/ 3 Std.dev.(x) from Target.
Same for Cpm(y)

Aggregated Cpm for both axisses would be
Cpm=SQRT(Cpm(x)²+Cpm(y)²)

Just wanted to throw this at you. Feel free to critisize any flaw in my thinking.

Steven

Correction. Formula should have been:

Cpm(x)= 2*(SL+"Bonus(x)" Xbar)/ 6* Std.dev.(x) from Target

[Paul F. Jackson]

When the capability of the geometric tolerance is dependent upon feature size, it will become readily apparent to the process owner (using a variable tolerance capability equation) that targeting feature size at the center of its specification to maximize its capability indiscriminately is not a good strategy.

Targeting static-fits, clearance sizes, and boundary conditions (where the function is not influenced by varying sizes) toward the opposite material condition that is specified in the feature control frame will provide additional tolerance for the geometric specification. Of course the distribution for feature size will determine where that target will be. So if there were ever a reasonable use for Cpm it would be with feature sizes related to variable geometric tolerances.

Using Cpm for the variable unilateral geometric tolerance is not a strategic move since the target is always Zero.

If the ratio of consumed geometric deviation to available tolerance is relativley high, a better strategy would be to monitor and control the x and y coordinates of the geometric specification separately.

You would do this to distinguish between:

A process that is accurate (where the means of X and Y coordinate deviations are centered well at their basic dimensions but the associated distributions for X and Y are large or perhaps just one is large).

A process that is precise ( where the distributions for X and Y are small but the means are off-target, or perhaps just one is off target).

Since computing the resultant geometric deviation obscures the distributions for the separate coordinates, monitor and control the coordinates separately rather that attempting to monitor and control the resultant geometric deviation. If the individual coordinates are "in control" so will the resultant geometric deviation. Use the resultant geometric deviation to predict the process capability with respect to the geometric specification.

If the ratio of consumed geometric deviation to available tolerance is low, it isn't necessary to do the extra work.