MultiVariate SPC

Question

Hello All-- I'm approaching my 4 week anniversary with JMP, so I guess it's high time I became active on the SE discussions!

I'm looking for advice on what we are calling Multi-Variate SPC.  (Maybe there's a better/different/more appropriate name.)  We have a customer who is interested in SPC on a hole center position.  He can measure the (Xmeas,Ymeas) position of the center of the hole, and he knows where the hole should be (Xspec,Yspec).

However, instead of looking at SPC of the X position and SPC of the Y position independently, he wants to look at the SPC of the radial error in placement of the center of the hole.  (As an aside, using an X-Y "box" to circumscribe the radial tolerance gives a box that is too big (i.e. passes too many parts), and circumscribing a smaller box with the radial tolerance gives a box that is too small (throws away good parts.))

This would appear to be a fairly simple script to write (i.e. RadialError=sqrt( ( Xmeas - Xspec ) ^2 + (Ymeas - Yspec) ^2 ), then do SPC against an upper limit spec.)  The customer says he has never seen a package that is set up to do this automatically.  In fact, he may have additional dimensions besides hole center that need to be included (such as hole roundness, axial parallelism, etc.) that would turn this into a multi-variate problem.

I'd be happy to look into a script like this.  (Might be fun!)  But before I go reinvent the wheel, the question is:  Has anyone seen a script or addin that already does this function?

Thanks!

Nate_Riordan · Answer

Here's a little jmp start for you Jerry on a cartesian to polar script (added a couple goodies such as that fantastic disclaimer!):

/*
Disclaimer by 
SAS Institute Inc.

License Agreement for Corrective Code or Additional Functionality

SAS INSTITUTE INC. IS PROVIDING YOU WITH THE COMPUTER SOFTWARE CODE INCLUDED WITH THIS AGREEMENT ("CODE") ON AN "AS IS" BASIS, AND AUTHORIZES YOU TO USE THE CODE SUBJECT TO THE TERMS HEREOF.  BY USING THE CODE, YOU AGREE TO THESE TERMS.  YOUR USE OF THE CODE IS AT YOUR OWN RISK.  SAS INSTITUTE INC. MAKES NO REPRESENTATION OR WARRANTY, EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, NONINFRINGEMENT AND TITLE, WITH RESPECT TO THE CODE.

The Code is intended to be used solely as part of a product ("Software") you currently have licensed from SAS or one of its subsidiaries or authorized agents ("SAS"). The Code is designed to either correct an error in the Software or to add functionality to the Software, but has not necessarily been tested.  Accordingly, SAS makes no representation or warranty that the Code will operate error-free.  SAS is under no obligation to maintain or support the Code.

Neither SAS nor its licensors shall be liable to you or any third party for any general, special, direct, indirect, consequential, incidental or other damages whatsoever arising out of or related to your use or inability to use the Code, even if SAS has been advised of the possibility of such damages.

Except as otherwise provided above, the Code is governed by the same agreement that governs the Software.  If you do not have an existing agreement with SAS governing the Software, you may not use the Code.

(SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are registered trademarks or trademarks of their respective companies.)

*/

Names Default To Here( 1 );
dt = Current Data Table();

cd_out = Column Dialog(
	xcol =
	ColList( "X",
		Min Col( 1 ),
		Max Col( 1 ),
		Data Type( "Numeric" )
	)
	,ycol =
	ColList( "Y",
		Min Col( 1 ),
		Max Col( 1 ),
		Data Type( "Numeric" )
	)
);
x = cd_out["xcol"][1];
y = cd_out["ycol"][1];
/*
	FORMULA creates a live value column
	SET EACH VALUE creates static values
*/
dt << New Column("Radius"
	,Numeric
	,Continuous
	//,Formula( Root( x ^ 2 + y ^ 2 ) )
	, Set Each Value( Root( x ^ 2 + y ^ 2 ) )
);

/* 
	default arctan results in -180 to 180
	adding the conditional converts to standard of 0 to 360 
	https://en.wikipedia.org/wiki/Polar_coordinate_system
*/
dt << New Column("ϕ"
	,Numeric
	,Continuous
	,Set Each Value( 
		If(	y >= 0, 	180/pi()* ATan(y,x)
		/* else */ ,	360 + 180/pi()* ATan(y,x)
		)
	)
);

/*
Disclaimer by 
SAS Institute Inc.

License Agreement for Corrective Code or Additional Functionality

SAS INSTITUTE INC. IS PROVIDING YOU WITH THE COMPUTER SOFTWARE CODE INCLUDED WITH THIS AGREEMENT ("CODE") ON AN "AS IS" BASIS, AND AUTHORIZES YOU TO USE THE CODE SUBJECT TO THE TERMS HEREOF.  BY USING THE CODE, YOU AGREE TO THESE TERMS.  YOUR USE OF THE CODE IS AT YOUR OWN RISK.  SAS INSTITUTE INC. MAKES NO REPRESENTATION OR WARRANTY, EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, NONINFRINGEMENT AND TITLE, WITH RESPECT TO THE CODE.

The Code is intended to be used solely as part of a product ("Software") you currently have licensed from SAS or one of its subsidiaries or authorized agents ("SAS"). The Code is designed to either correct an error in the Software or to add functionality to the Software, but has not necessarily been tested.  Accordingly, SAS makes no representation or warranty that the Code will operate error-free.  SAS is under no obligation to maintain or support the Code.

Neither SAS nor its licensors shall be liable to you or any third party for any general, special, direct, indirect, consequential, incidental or other damages whatsoever arising out of or related to your use or inability to use the Code, even if SAS has been advised of the possibility of such damages.

Except as otherwise provided above, the Code is governed by the same agreement that governs the Software.  If you do not have an existing agreement with SAS governing the Software, you may not use the Code.

(SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. ® indicates USA registration. Other brand and product names are registered trademarks or trademarks of their respective companies.)

*/

I tested it out on the wafer stacked data, the computation took a couple seconds on the 177k rows, not noticable if you summarize to pure x,y values.

JerryFish · Answer

Peter, thank you for your reply.  Your example is near and dear to my heart.  Coming from the printing industry, I know exactly what DeltaE means, and it is perfectly analagous to the hole center tolerance problem.

It does seem relatively straightforward conceptually.  For the hole problem:

* Calculate radial error of hole placement re: target location via formula in new column.
* Set USL on new formula (assuming LSL=0 in this case)
* Use Distribution Platform to:* Run a transform if needed
* Look at capability analysis

The customer just wanted to see this analysis done automatically.  I'll put an addin together for him.  That should be all he needs.

Thanks for the input!

Jerry

JerryFish · Answer

Nick, thanks very much for the reply.  I learned a lot looking into this.  I don't think MultiVariate Control Charts (MVCC's) are quite what I had in mind for this customer.  If I understand correctly, MVCC's are normally used where there is some correlation between the X and Y variables, and essentially look for outliers from the trend between the variables.  I'm guessing it could also work if the 2 variables are completely uncorrelated (as in the case of the example).  But it is a true control chart in the sense that it tells if a process is in control or not.  It doesn't really use product specs to look at things like Cpk and Ppk, which my customer wants.

If I'm off base on this, by all means let me know.  Also see the reply to Peter Bartell that I'm now composing.

Thanks a bunch!