# Geometric Tolerancing and SPC - Calculating position upper and lower control limits

L

#### lee01

I have a problem,

I am trying to calculate the upper and lower control limits for a hole position with a size as follows:
1mm diameter +0.10. Please note this is a geometric tolerance and as a result equates to nominal plus 0.10. Standard control limit rules only allow for linear values. A hole position can be out of position through 360'. Similar to the appearance of a scatter graph.

Control Limits I think do not allow for this? Or do they?

The way I'm thinking is that you have a value of say. . 10.00+/-0.1. The values can only fall from 9.9 to 10.1 in a linear manner. Whilst a hole position can fall anywhere around a single point not just above, below, left and right? Or am I making no sense whatsoever?

Lee Moffatt confused: )

#### Geoff Cotton

##### Quite Involved in Discussions
Can you run SPC in both the x and y axis?

Geoff

L

#### lee01

No,

All I have is a value at the present time.

I have been investigating it further and understand that I do not need a lower cntrol limit because is there is none! There is an upper control limit obviously but the lower is in fact the target.

Therefore the cp value is reduntant but this still does not help in my quest for understanding if I can apply the ucl limit to this type of characteristic

Lee Moffatt

R

#### Russ Kochis

Lee,
You may want to check out an article from Quality Mag from February 2001 called "Simple Process Capability?". It is at qualitymag.com go to the article archives. I think this is what you want.
Russ

#### Marc

##### Hunkered Down for the Duration
Staff member
I received this in an e-mail:

Forgive my intrusion,

I have been reading your replies to spc & GD&T and would like to view the file as named above in the subject bar, if you still have that file.

I have posted a new thread entailed GD&T And SPC that describes the same type of problem.

I have this old file of Marty Ambrose's. It's dated 1999. I don't know what ever happened to ol' Marty, but he was one of the 'pioneers' here at the Cove in the old forums.

I believe Don Winton also wrote a paper on this which was in the old pdf_files directory at one time. I will look for it this weekend and if I find it I'll post it in this thread as well.

That said, this file is, and has been, available in the Members and Premium directories. You might want to be nice and consider donating to 'the cause' --> http://Elsmar.com/join.html (plug intended...).

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#### Darius

##### Quite Involved in Discussions
The article is excellent, about hole drilling I found an article about ussing "A PROCESS CAPABILITY INDEX
SENSITIVE TO SKEWNESS" by Peter A. Wright, I tink it could complement it.

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#### Paul F. Jackson

##### Quite Involved in Discussions
Lee,

I've got a couple of questions. What is the tolerance for feature size and what is the geometric tolerance for position? Is the position tolerance constant or variable (does it have a MMC modifier attached to the tolerance)?

I don't suppose that you are questioning about the upper and lower control limits for feature size.

Process control examination for the position tolerance (I think) is best accomplished by monitoring the X,Y,Z coordinates of the feature location separately. It provides two important benefits, It helps to distinguish whether the individual coordinates are accurate (mean centered on the basic location) or not and it helps to discover how precise each axial deviation is and how much each is contributing to process variation.

You commented about the position tolerance being non-linear scattered about 360 degrees. The position tolerance describes the zone that the axis, median plane, center, etc. of the feature must reside within. The zones can be described in a number of ways (spherical, circular, cylindrical, rectangular, square, cubic, etc.) all determined by the symbols used in (or absent from) the feature control frame and from the way the tolerance "leader lines" are depicted on the specification.

The individual coordinates can be normally distributed when examined separately but when they are combined to determine the displacement from the basic location the resultant radial separation (or doubled "diametrical deviation") is typically a skewed distribution that is 'nearer to' and 'truncated by' zero and tailed toward the USL. Monitoring the derived position deviation for process control is not good for a couple of reasons. The position deviation does not distinguish between process parameters "X, Y, & Z" that are accurate but not precise where mean-shifts are no help and ones that are precise but not accurate where mean-shifts may improve. The other reason is that the deviation is not typically a normal distribution.

The control limits for the coordinates are established by the process variability so there is no relation to the drawing specification for position. Process control can be done effectively
by monitoring the X Y & Z of geometric deviations.

To predict the process capability for the true position deviation one must first establish that the process is "in-control" and that can be done with the individual coordinates. If the geometric tolerance is constant one can predict capability by applying the appropriate distribution function that best fits the skewed true position deviations and transforming the data. If the geometric tolerance is variable you can use a method that compares the (USL plus the Mean variable tolerance "bonus tolerance" minus the Mean geometric deviation) to (three times the square root of the combined variances for size and geometric deviation). It assumes normality for both but it demonstrates prediction error margins comparable to predicting the capability of a constant tolerance with the Weibull Method.

I would not recommend using: the residual tolerance method described in "Simple Process Capability" Quality Magazine by me, the percent of tolerance method described in "Calculating MMC Cpk" by Marty Ambrose, or the adjusted true position method "Calculation of Cpk under conditions of Variable tolerances" Quality Engineering by Glen Gruner because each one of those methods uses an individual pair of variables for size and geometric deviation to produce a surrogate variable the can be compared to a constant limit. In so doing the underlying variation from the independent sources can either be amplified or moderated in the surrogate.

I will be publishing another paper soon.

R

#### Ravi Khare

Both, Upper as well as lower Control Limits will exist whether you have geometric tolerances or the traditional ones.

Geometric tolerances will define circular tolerance zones for location of a round feature, and will have a one sided tolerance. Cpk will be defined as Cpk(upper) and Cp will be undefined.

As for Control Charts, it will pay to plot separate control charts for tolerance of size and tolerance on location.

In case there is a bonus tolerance allowable, by a modifier applied to the location tolerance, the method sited above by Marty Ambrose will tell you how much of the allowable tolerance is 'eaten up' by your process and give you a very good estimate of the proess capability, after compensating for the bonus tolerance.

It will however help to plot the control charts for location, without giving any consideration to the bonus tolerance. Control Charts can be used to monitor the inherent stability of the process, without paying heed to the tolerance (bonus or otherwise).

#### Paul F. Jackson

##### Quite Involved in Discussions
Geometric tolerances of round features will commonly be round but not always. In the American national standard the shape of the zone is defined by the symbol preceeding the tolerance or by the way leader lines are attached to the features. See page #140 of ASME Y14.5M-1994 for an example of how the tolerance zone could be defined to allow extra rotational freedom about the secondary axis (possibly for an application such as the position of a pinion shaft in a planetary gear assembly).

As for control charts for position specifications, it will pay plot separate charts for the X, Y, and Z coordinates. To reduce the variation of a geometric position distribution one would first have to detect from the individual XYZ coordinate locations whether the position deviation can be reduced with mean-shifts to X,Y,Z or not. Since the charted variable of computed position deviation commonly includes the magnitude without its direction, the radial deviations of a group of clustered in the first quadrant of a Cartesian coordinate system at the maximum radius can have the same mean and variation as a group scattered on the perimeter at the maximum radius if the polar that direction is ignored. The computed radius or diameter of geometric deviation does not indicate whether there are potential process improvement opportunities to reduce variation via mean-shifts or not. A process that is accurate but not precise can only be improved by a reduction in common cause variation. A process that is precise but not accurate can benefit from shifting the means of the coordinates to their target values but the two distributions are indistinguishable when only the radius or diameter of true position is the charted value.

In the case where the tolerance itself is variable (by permitting bonus geometric tolerance relative to feature size) I personally don't reccomend the method sited by Marty Ambrose with what I know of the shortcomings of various methods predicting the capability of processes with variable tolerances. Attached is a response that I wrote to Todd Minnick after I examined his work with variable tolerances.

Let me say that I am indebted to all of those that have and are
attempting to find methods to predict conformance with variable tolerances. Glen, Marty, Todd and others are pioneers in this stuff.

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#### poong

Re: Geometric Tolerancing and SPC - Calculating position upper and lower control limi

Can you run SPC in both the x and y axis?

Geoff
Hello sir
I want to plot the control chart,range chart & calculate the cp,cpk,for flateness required within 0.1mm.pls. help me how can i draw the above becouse there no LSL.
Ranjeet Singh
Chandigarh

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