Process Capability Calculation 3

[weisusu]

Say I have a tolerance feature frame that calls out true position of 0.000 (M)|A. Each part measured has a different IDs and its allowable true position tolerance depending on the deviation from the max material condition. How do I calculate the process capability index for the true position tolerance?

 

[PaulJackson]

Read thru the attached powerpoint presentation. It explains how to examine "variable tolerance limits" with "position deviations in a histogram. It then shows how to predict or estimate capability of the sample data and offers relevant parameter adjustments for process optimization.

I also have spreadsheets that perform the calculations and I will try to post them up but there are macros in them that may prevent that.

I zipped the excel spreadsheets so you will have to unzip to use them.

Paul

http://files.engineering.com/getfil...ae44-926f95c8a5b9&file=ExpandingLimitsSPC.pdf

http://files.engineering.com/getfil...9208-49d2-bec8-5e21805fd25a&file=PpkMMCXY.zip

http://files.engineering.com/getfil...8-d221-4545-9f51-4ba079a3b8a9&file=PpkMMC.zip

 

[dingy2]

Paul:

You still believe that the method that you have presented still meets ALL the requirements simultaneously?

The simultaneous requirements are:
Location from the secondary & tertiary
Perpendicularity to the primary datum
Shape of the feature superseding centres
Straightness of each feature of size
Diametrical tolerance zones converted into proportions using X & Y co-ordinates
Calculated bonus tolerances from the smallest inscribed diameter of a hole rather than its average size

I won't even get into secondary and tertiary datums at MMC.

What do you think?

Dave D.

http://www.qmsi.ca

 

[dingy2]

wiesusu:

Please go to the following web page to review why capability of positional tolerances only take into account some of the requirements. It is not the distribution itself but the full requirements of positional tolerances that are being questioned.

http://www.qmsi.ca/capabilityindex.html

Hope this helps.

Dave D.

http://www.qmsi.ca

 

[PaulJackson]

Weisusu,

I apologize for having to explain in such detail but there is considerable controversy among us who offer advice in predicting statistical “capability” with regard to positional tolerances. Your question has ignited this controversy once again. If you search previous threads here and elsewhere for key words (Cpk, Ppk, MMC, Capability, Position) you will discover many spirited discussions.

David Delong “dingy2”,

Weisusu asked, “How do I calculate the process capability index for the true position tolerance?”

Your advice… from your web page is, “Let’s call all positional tolerances “Major Functional Characteristics” and then perform an statistical attribute study on the its checking fixture using Kappa (AIAG Measurement System Analysis 3rd edition). This does make sense.”

“This does make sense”? I say NO, it does not make sense, unless you cannot acquire objective variables data from the measured features. Statistical attribute studies require huge sample sizes to predict the % defective at common levels of expected risk… The attribute sample size required (Defect Free) for a capability prediction of 1.33 @ a confidence level of 95% would mean that there can be no more than 1 defective occurrence in approximately 94,588 measurements (even at a confidence level of 50% it would be 21,886) ….for 1.67 @ 95% confidence no more than 1 in 10,450,779 (@ 50% 1 in 2,418,083).

Many customers insist that the capability ratios be calculated for positional tolerances and if that tolerance is variable (meaning @ MMC or @LMC) the variable portion is unfortunately ignored in the capability equation which penalizes the producer greatly. Predicting positional tolerance capability of 0 @ MMC like this is ludicrous since all of the tolerance is variable with respect to size… the result will always be negative.

My papers detail how to predict capability with “variable tolerances X.X@MMC or 0@MMC” and they show how to monitor and optimize processes by targeting the feature size for optimum capability using the variability size and position simultaneously. When X and Y coordinates for the features can be monitored for process control (not capability) individually the method suggests that the “means” of their variation may also be adjusted to further optimize the process. These process optimization parameters are not apparent when an attribute inspection strategy is employed.

You asked, “You still believe that the method that you have presented still meets ALL the requirements simultaneously?”

Of course not! Statistical predictions are “inferences” based upon observed variation. Only samples of the data are required to make the predictions… but the power is… that you do not need to check every part to have some confidence that the rest are similar. Capability predictions are much more economical than % defective predictions from attribute measurements… consider the difference in sample sizes, $ and time… to make process changes, man hours measuring and relevant feedback to production for optimization, yada, yada, yada.

The simultaneous requirements are:[/color]

“Location from the secondary & tertiary”
Ignore “MMC datum shift” in the variables measurement and sacrifice the miniscule portion of acceptable product that could be attained with it! It is still far more economical to figure the capability without “datum shift” than it is to employ an attribute measurement strategy! You can include the variation from datum shift in the variables data measurement strategy but it is tedious and involves monitoring the coordinate and rotation displacement variations of datum shift using a “best fit coordinate system routine” too high level for this discussion. If CMM programming for this is available and is comprehensive enough to include all simultaneous requirements employ it… few are!

“Perpendicularity to the primary datum”
As I said before in other thread responses Dave… (if you don’t know check for it), If the hole depths are significant and variation is expected then you can do a circle and location at both the top and bottom and include both in the variation… that will insure that the orientation variation is baked in the position prediction. If it is insignificant “Ignore it” most variables data inspections do so now.

“Shape of the feature superseding centres”
This is a statement that appears as an addendum to paragraph 5.3.2.1 EXPLANATION OF POSITION TOLERANCES AT MMC and explains that the feature surface supersedes that of its axis in extreme cases, however the entire discourse of position tolerance rests in determining the axis except for this exception. For what it is worth, I agree with you, all position requirements MMC and RFS should pertain to feature surfaces rather than axis (derived by some means from surfaces) but that is not what the standard commonly states. I could go on a dissertation on this one!

“Straightness of each feature of size”
I think that I covered this one in “Perpendicularity to the primary datum”.

“Diametrical tolerance zones converted into proportions using X & Y co-ordinates”
This whole discussion is a “red herring” on your web page! You (as others have) explain that coordinates in various quadrants may have the same resultant radial or diametrical deviation and therefore exhibit the same resultant without variation. The solution some suggest is to constrain the coordinates to the “square within the circle” therefore proportioning the diametrical tolerance X 0.707 within a square. Nonsense!!!! Only those who do not understand what the prediction of process capability is would suggest this.

Capability predictions are predicated on random variation! Process Control (not process capability). You monitor and “control” the individual coordinates, size, and as you know I am sure from your knowledge “control limits” are not related to “specification limits”. Therefore one can detect that the X, Y, or size is exhibiting non-random behavior and question the capability prediction until that behavior exhibits randomness.

The point is the encroachment of the computed deviation (with its variation) on the upper limit boundary whether constant or variable from whatever quadrant reveals the probability of a defect to that circular boundary. In the case of a variable tolerance that boundary has a mean and variance itself and the probability of intersection of those distributions can be estimated statistically. My stuff does so!

Calculated bonus tolerances from the smallest inscribed diameter of a hole rather than its average size
Let it go Dave… you are grabbing at straws!

I won't even get into secondary and tertiary datums at MMC.
I think I covered this in “Location from the secondary & tertiary”


It is not the distribution itself but the full requirements of positional tolerances that are being questioned.
What do you mean? The distribution for the position deviation (if well centered on its basic coordinates will be skewed toward the boundary zero and the distribution for size (depending upon the processing method)… drill, ream, punch, edm, cast, laser, etc. will be as it is… skewed or not. If the tolerance is variable… the capability for the hole location will depend upon the hole’s variability for size and location simultaneously. There are relevant parameters which can be monitored to improve the process or condemn it!
Your web page Dave states: “Performing capability studies on Positional tolerances is bogus or “make believe” but we do attempt it to please the Customer.” That is bogus

Your Pal Paul

 

[dingy2]

Hi Paul:

Wow - you really had some spare time and I know we have discussed this so many times.

In a nut shell, your information in the distribution is only related to X & Y co-ordinates or the secondary and tertiary datums and that is not the full requirement of positional tolerances at MMC.

PS - straightness is a component of perpendicularity and is not confirmed by checking the top and bottom of the feature. If a long hole is bent, the bend would most like occur in the centre. A checking pin would catch this condition.

I have been in the quality game a long time and have seen the automotive companies (big 3 but not the transplants)ask for some pretty dumb things that are extremely costly to perform. Capability studies on positional tolerances is at the top of the list. It is possible that one could have spent a lot of $$ on capability studies reflecting a great Ppk (from X & Y co-ordinates) and one of the sample parts could be out of specification. No wonder GM, Ford and Chrysler and their suppliers are in trouble.

Dave D.

http://www.qmsi.ca

 

[PaulJackson]

Dave,

I give up trying to graciously convince you that you are wrong on this issue.

Many of us have been "in the quality game" a long time but there is always something to learn from one another. Give it a try!

Paul

 

[dingy2]

Paul:

I do agree that confirming the location of holes relative to the secondary and tertiary datums (X & Y co-ordinates) is beneficial to Process Engineering for relative location to the true position. It happens all the time. We can also provide ongoing statistical studies using control limits for process control, if required, but NOT CAPABILITY.

You also pointed out in your quite elaborate answer that the data collected does not confirm all the requirements of positional tolerances. In that case, Ppk derived from X & Y co-ordinates is not valid for positionial tolerances at MMC referencing datums B & C at MMC.

I guess it is like confirming flatness on a surface and one only uses 60% of the surfaces for the data. Don't worry about the other 40% since it probably is good anyway. ???

We remain apart on this one but I do respect your opinion.

Until our next discussion.

Dave D.

http://www.qmsi.ca

 

[weisusu]

Hi Paul:

I don't really understand the formula in the presentation slides to estimate Ppk for true position call out. Can you please elaborate? Thank you.

 

[PaulJackson]

weisusu,

To understand the method I propose for predicting capability with variable tolerances you should first familiarize yourself with the common method for predicting the capability of one sided geometric tolerances. You can review that in the NIST ENGINEERING STATISTICS HANDBOOK, It explains under Capability how to evaluate One-sided specifications and the corresponding capability indices. See:

http://www.itl.nist.gov/div898/handbook/toolaids/pff/6-pmc.pdf

You should also understand that the distributions for these geometric position locations are typically skewed toward the target boundary "zero" when the coordinate distributions are fairly well centered on their basic displacements and are therefore "non-normal". I think that my presentation explains that in detail. If your specification limit was not variable "didn't have a MMC modifier" you would typically need to transform the "skewed" distribution using a BoxCox transformation or use a fitted non-normal curve function "Weibull" to do the capability analysis.

Since all commercially available statistical software products, analysis tools, and topic explanations assume that tolerance limits are "constant"... you will not find resources to explain or analyze your variable tolerance limit "ZERO@MMC". I included two spreadsheets in the previous post that you can use to perform the analysis. If you carefully read the instructions on the spreadsheet, copy and paste the measurement data on the first sheet, insert the specification values on the analysis sheet, and choose the appropriate “radio buttons” to reflect the specification…then you will see histograms for both the position deviation distribution and the feature size distribution on the same graph. You will also see the suggested value to adjust feature size in the process to improve the predicted PPM defective and if you inputted the coordinate values… the suggested corrections necessary to move the means of the X and Y distributions to their basic targets in the process.

You shouldn’t perform any of these capability analysis predictions until you first check the size and coordinate data to see if it is random normal. Naturally the data for the computed position will be “non-normal” if the coordinate distributions are on target, so if you cannot get the individual coordinate data to check for normality and all you have is the computed position deviation values you can and should view the histogram to check for outliers, bi-modalities, and any other unexpected distribution attributes.

If, after you read the instructions and try the spreadsheet, you still cannot comprehend the analysis you can send your measurement data and specification parameters to me and I will help to configure it and explain the analysis outcomes. mailto:spcandgdtman@yahoo.com

Paul