Pp and Ppk indices - Is it statistically possible to have a Ppk greater than Pp?

[Greg Johnson]

Could someone please tell me if it is statistically possible to have a Ppk
greater than Pp?

My scenario is as follows: Using our CMM we have measured the true position
location of a hole in an "A" pillar. After a measurement of 30 pcs. our
outcome on the histogram shows a PP of 1.58 and a Ppk of 1.69. The Cp
calculates at 2.15 with a Cpk of 2.30. The tolerance used is: 0 as the
nominal with a unilateral tolerance of +2/-0

Your help in resolving this issue would be greatly appreciated.

Regards,

Greg Johnson
Quality Services Mgr.
AZ Automotive Corp
Direct Phone: 586-880-2147
Fax: 586-880-2285

[The Taz!]

Hi Greg. . .

To answer your question, "Not on this planet" . . not even with New Math. . .

Ppk and Cpk will never exceed Pp or Cp. . . Cp and Pp are true process potential indexes irregardless of centering. . . (Tol/6s)

Add the centering in, and the best you can be is. . . ON CENTER. . . Unlike a few of us here who are juuuust a tad off center.

Seeing you are using a unilateral tolerance to start with your predicament is actually easy to get out of. . . there is no Pp or Cp index. They do not exist for unilateral tolerances. Your software may be confused. . . and in turn confusing you.

IMHO, Your software either has to be put into a unilateral statistical mode for that measurement, needs an update. . . or wasn't thoughtout very well.

[Bev D]

but it is mathematically possible for Ppk to exceed Pp IF you have data wiht very little resolution - ordinal data, aka "chunky data" (as Dr. Wheeler refers to it) AND you estimate the standard deviations from the within subgroup RANGE values.

To prevent this, you can always use the within subgroup standard deviations (which is actually easier in Excel than the Ranges...and is typically the default of most statistical packages).

Of course with ordinal data (use of .001 gage pins with a tolerance of +/-.0025...) you also have another problem that isn't "real": your Ppk values will be less than your reality as the ordinal data will result in a standard deviation that is larger than the actual standard deviation of the processs...so, the real solution is use measurement techniques with an appropriate resolution)

There is also the slight possibility that you are usign the alternate approach for Ppk vs Cp utilized by Ford, where 30 random pieces from an initial run are collected, teh Ppk formula (total standard deviation of the 30 pieces) is used to calculate the SHORT TERM capability and then Cp - or Cpk - is later calculated from the within subgroup standard deviations to provide teh LONG TERM capability. In this case, Ppk can be greater than Cp or Cpk as they are calculated from different data sets.

[The Taz!]

The issue was unilateral specs. There is no Cp or Pp for unilateral specs.

I do agree with and acknowledge your points in theory. . . in practice it does not occur. The data you talked about (Lumpy Data) is a clear indication that mearurement resolution and/or discrimination might be improved.

[Tim Folkerts]

I'm trying to understand this for my own benefit, so I was hoping to get a clearer picture of what is happening, particularly as it relates to unilateral tolerances.

Originally Posted by Greg Johnson

... Using our CMM we have measured the true position
location of a hole in an "A" pillar. After a measurement of 30 pcs. our
outcome on the histogram shows a PP of 1.58 and a Ppk of 1.69. The Cp
calculates at 2.15 with a Cpk of 2.30. The tolerance used is: 0 as the
nominal with a unilateral tolerance of +2/-0

There are two scenarios I can think of for a unilateral tolerance like +2/-0:

1: Where you want to measurement to be at least a target value. For example, a hole should be at least 0.250", but it could be 0.002 bigger, so you write a spec as 0.250 +2/-0. This could also be written as .251 +/- 0.001.

Here, the "target" is in the middle of the range.

2: Where it is physically impossible to be beyond a target value. For example, you want a disk to be uniform thickness, but you can tolerate a variation of 0.002". The spec for the variation is 0 +2/-0.


Here the "target" is the end of the range.


To my thinking, for (1), Cp, Cpk, Pp & Ppk would make sense, because you can treat the unilaterial spec as a regular bilateral spec with a different center. For (2), you can't really do that. (Besides, the distribution is likely to be quite non-normal, which drives down the usefulness of the various calculations.)

It seems that the original situation was more like case (1), but I'm not quite sure. If it is, the some form of Cp and/or Cpk would be perfectly legitimate. I concur with Taz, however, that in any case you shouldn't get Cpk > Cp.


Do others concur? Disagree?

Tim F

[The Taz!]

Originally Posted by Tim Folkerts

I'm trying to understand this for my own benefit, so I was hoping to get a clearer picture of what is happening, particularly as it relates to unilateral tolerances.



There are two scenarios I can think of for a unilateral tolerance like +2/-0:

1: Where you want to measurement to be at least a target value. For example, a hole should be at least 0.250", but it could be 0.002 bigger, so you write a spec as 0.250 +2/-0. This could also be written as .251 +/- 0.001.

Here, the "target" is in the middle of the range.

2: Where it is physically impossible to be beyond a target value. For example, you want a disk to be uniform thickness, but you can tolerate a variation of 0.002". The spec for the variation is 0 +2/-0.


Here the "target" is the end of the range.


To my thinking, for (1), Cp, Cpk, Pp & Ppk would make sense, because you can treat the unilaterial spec as a regular bilateral spec with a different center. For (2), you can't really do that. (Besides, the distribution is likely to be quite non-normal, which drives down the usefulness of the various calculations.)

It seems that the original situation was more like case (1), but I'm not quite sure. If it is, the some form of Cp and/or Cpk would be perfectly legitimate. I concur with Taz, however, that in any case you shouldn't get Cpk > Cp.


Do others concur? Disagree?

Tim F

Tim,

Let's say you have a large ground metal plate with a flatness requirement of 0.25mm Max. This is also a unilateral tolerance. You wouldn't want to set the spec at 0.125mm +/- 0.125 mm would you?? You want the plate flat (Design intent) . . . and the only reason that we have a tolerance to start with is because we know we cannot make parts dead flat in a production environment. The economics of doing it are staggering let alone the physics involved.

Can you have less that a 0% concentration of a given gas in a mixture?


These are NATURAL limits.

Again, there IS NO Cp or Pp for a unilateral tolerance. It does not exist. Look it up in a stats book under Unilateral Capability Indices.

Unilateral Cpk and Ppk yes. You use one side of the distribution Equation. You will also, in all probability, get a truncated distribution because of the natural limit. sOME PARTS will BE FLAT. sOME PARTS WILL BE slightly NOT FLAT. MOST PARTS WILL FALL NEAR OR AT THE NATURAL LIMIT. . .IF YOU HAVE DESIGNED YOUR PROCESS CORRECTLY. oops. . .sorry. ..caps lock on. ..no yelling intended.

Hope this scenario helps. . .

[Tim Folkerts]

Taz,

Looking back, I see this has been discussed before. For example
http://elsmar.com/Forums/showthread....nilateral+spec
So perhaps I won't rehash just which of the Cx indices are appropriate in which conditions.

I still have two concerns, but I think I'll stick to one for now.

CONCERN 1:
There's unilateral, and then there's unilateral.

For gas concentration or flatness, there is an absolute limit - there is no way you can go below the target. The spec would read something like 0 +0.02/-0. I have no problem with anything you said about this.

But suppose you have point in a circuit that you want at 0 V; it would be fine with you if it was a little higher, but you don't want it lower. The spec could again read something like 0 +0.02/-0. However, now you do could restate this as 0.01 +/- 0.01. You don't really want 0.00, and it is possible to have a negative voltage.

Both are written as a "unilateral" spec, but only the first truly is a unilateral spec! For the first, the Cx indices don't work well, as you pointed out. For the second, they work just fine.

My original question to Greg was which of these two describes his process. Is "0" the center of a piece, in which case you could be off either direction? Or is "0" the edge of a peice, in which case it would be a natural limit? The answer to this might affect how to do the analysis.


Tim F

[The Taz!]

Tim,

I understand what you have stated and do agree. However, I default to the DESIGN INTENT in the circuit. The desired value is 0 v. While it is not a natural or physical limit, it is the desired (or design limit) value. In this case, I'd chart and calculate it based on unilateral rules. You will get an atrificially low Cpk or Ppk if the voltage is at 1.8v (Assuming you have a tight distribution), and conversely, a high Cpk and Ppk if you are near or at the lower design limit.

The distribution will (should) be skewed to one side (the 0v side) if the capability of the components is high.

In the case of a negative voltage, using unilateral rules, you would get an atrificially high Cpk or Ppk because you are centered farther away from the design limit of 2v.

Now, if the design cannot tolerate negative voltage in the application, then by all means, 1v +/- 1v and bilateral.

I think we are in agreement, just stating things in different ways. I am just looking at the design intent to determine how I analyze the data.