Increased positional tol. due to departure from MMC (Bonus)and calculation of Ppk/Cpk


Dura Guy

We are in a bit of a dilema. Engineering and Quality are arguing about the use of "bonus" tolerance when calculating Ppk/Cpk values. One subcommittee member of ASME Y14.5M-1994 said that this is used only for building functional gages or in individual layouts, not for capability studies. I'm seeking a second opinion. I have been unable to find any basis for this in the standard. The closest I have come is on page 85 on the note after section, but this is vague.


Dura Guy
Manufacturing Engineer
Elsmar Forum Sponsor

smith man

Wow that is tough! there is two sides to this.

What about tolerance don't they understand? Bonus smonus bolonus, IT IS STILL TOLERANCE IS IT NOT?

However, feature amy change and that is not what you are testing, you are testing POSITION not feature capability.

what a conumdrum!!!!!!!

Spaceman Spiff

Quality Joe, I had to disagree with you. There is a method to calculate capability with of true positions that I found. In an article published in 1991 by Glenn Gruner in Quality Engineering Magazine, he illustrated how to perform such calculation. This method is the combination of feature size and feature location that is critical, not the separate components.
TPa = TPm - (Bonus Tolerance)
TPa = TPm - (MMC-Xf)
TPa = TPM - MMC + Xf
TPa = Adjusted true position
TPm = Measured true position
Xf = Measured feature size

The procedure is, for example, a 100 piece sample size:
1) Calculate TPa for each of the 100 samples
2) Take the average of TPa (or XbarTPa)
3) Use conventional Cpk formula,
Cpk = (USL - XbarTPa)/3*s

According to the author, similar application could be made for tolerances specified at the LMC of the feature and when bonus tolerance is gained as one or more datum depart from MMC (or LMC).

Anyway, it was an interesting article. Hope this helps, Dura Guy.

quality joe

In general, you can not use "bonus" tolerance in calculating capability. The reason for this is the feature that is varying from MMC is what is giving you the bonus tolerance. Therefore, unless you can guarantee that the feature size will never result in less bonus tolerance than when you did the capability assessment, you MAY NOT use bonus tolerance.

However, if you can put in controls to insure that the size of the feature will never vary to take away bonus tolerance (i.e. making sure a punch is nominal or higher or a drill bit can never be below a certain exact size) you may use bonus tolerance.

I would say that a manufacturer of product that needs to use bonus tolerance to validate a positional Cpk study is playing with fire. You should either see if relief can be given from design or get a manufacturing engineer that knows what he or she is doing. The ME has be astute enough to ensure that the correct processes are in place without using the bonus tolerance as a crutch. That "crutch" will burn ya every time!

Joe Quality

Steven Truchon

Spaceman, I tried a couple of models using what you presented and I am having trouble getting it to produce a valid result. Did you write it as it was originally written or is my coconut just being too thick on this subject? (LOL)


We need to hear from "Batman" here (forum contributor). I used to work with Batman & he had a neat little formula to report capabilty on a MMC / LMC features. He reported it as "percent tolerance used". I really need him to explain it!!! All I know is, we worked for an automotive supplier (tier 1 & 2) and used this many, many times. It usually involved a call to our SQA to explain how the numbers were derived, but never a problem! Sorry I'm of no help in explaining the "hows". I always relied on "Batman". Now I'm without an action hero!


Instead of adding the bonus to the tolerance, which could result in 20 different tolerances if measuring 20 parts, subtract the bonus from the measurment. One ends up with a fixed tolerance zone, although some never get over the negative lower limit for position which is a consequence of maximum possible bonus and perfect position. I presented a paper on the technique a number of years back at a conference.

David McGan

I'm finding a lot of interesting information here, but I'm still confused! Before capability can be determined, we first must know that the process is in control. Is there any special consideration for characteristics associated with bonus tolerances? (I know "specifications" don't have anything to do with "control"). So, if I'm plotting a measurement, do I chart only the actual measurement result without any consideration for potential "bonus" values?

Paul F. Jackson

Quite Involved in Discussions
Process control for positional specifications can be separated into the X,Y,&Z components of the measurement. It can be very beneficial to the process owner to identify the source of variation. Especially if the ratio of tolerance consumed to tolerance specified is high. Monitoring the resultant diameter of position deviation adds little value to the process owner when one process delivers a position deviation that is scattered in all four quadrants and another with an equivalent magnitude of deviation emminates from a single point in one quadrant. If the ratio of tolerance consumed to tolerance available is low it may not be worth the effort to monitor the coordinates separately.

To measure process capability of geometric specifications with variable tolerances (MMC-bonus) one can monitor the residual or remaining unused value of tolerance rather than the amount consumed. For each measured feature just add the bonus to the tolerance specified and subtract the amount of positional tolerance consumed. Rather than comparing the mean and standard deviation to a "variable USL" the mean and stdev of the residual is compared to zero. Cpk of the residual is derived from the Cpl. The variation in feature size when merged with that of position changes the distribution. The standard deviation typically increases but so does the separation of the mean of the residual from zero (consistent with the magnitude of the bonus). It is important that feature size is "in-control" as well as the coordinates of feature position when predicting capability from the residual.

One enormous benefit of doing process capability from the residual is the realization the dynamic relationship between size and position. One should not necessarily target feature size at its specification midpoint! A positional tolerance that is specified as "Zero @ MMC" where the amount of tolerance is fully dependent upon size probably demonstrates that relationship the best.

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