# Can I use Cpk to compare if one part is usable in another part?

#### QCJS

##### U can't change a person but u can change yourself
Hi,

I have raw data of 10 pieces of Metal rollers (Inner diameter specification: Ø10.7 -0.005) and 10pcs Bearings(Outer Diameter specification: Ø10.7 -0.007). The Bearings are meant to be tightly fitted into the Metal Rollers. Can I find Cpk values for the Metal rollers and Bearings, compare the values and conclude that they can be used in production? Is that even the right way?

My purpose is to convince the Engineer that they can be use in production. To convince Customer, can these calculations be used too?

Appreciate all sorts of help, no matter how small it might be.

Thanks,
QCJS

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
No. First a sample size of 10 is way too small. Requirements for the usefulness of any statistic are that the sample size is adequately large and that the sample selection is representative of the underlying distribution.

To provide useful advice we would need to understand more about the situation.

#### QCJS

##### U can't change a person but u can change yourself
No. First a sample size of 10 is way too small. Requirements for the usefulness of any statistic are that the sample size is adequately large and that the sample selection is representative of the underlying distribution.

To provide useful advice we would need to understand more about the situation.
Hi Bev D,

1. Can you explain in simple words on this statement: "sample selection is representative of the underlying distribution. "? Do you mean to say that the the specification selected is dependent on the sample size?

2. So if I increase the sample size to 30 or 50, would Cpk values tell that Roller and Bearing are compatible for use? Can you suggest a way to convince the Engineer, using data, that the bearings can be used in the rollers even when the 2 of the readings are out?
For now, I simply took the averages of each data and compare. Since I want a tight fit, if average Roller reading is equivalent or is more than 1 micron than the Bearing average, then I conclude that it can be used. But something struck me, how did I determine a tight fit? Is it through the ISO tolerance chart? How will I explain that even if it is more than 3 microns but less then 5 microns, I will Use As Is?

3. Customer complains that rollers produces a scratchy sound when rotating. Production supervisor is adamant that it's due to the dimension of the Roller and Bearing. But the QC inspector is unable to take the reading again as the Bearing is press-fit into the Roller. The ID reading of the Roller will not be accurate if we force out the Bearing to investigate the cause. Customer demands an answer from us ASAP or we will need to change the hundreds of rollers at their site. This is one of the scenario faced currently. Can you suggest a way out?

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Whoa. are you saying that 2 of the parts (out of 10) are out of spec?
are the bearings a catalog part? and 2 of them are out of your internal spec for fitting into the roller (3microns) or the bearing supplier spc of 5 microns?

#### Welshwizard

##### Involved In Discussions
Hello QCJS,

It sounds like you are trying to manage limits and fits for an interference condition of assembly. Going by what you are saying the issue surrounds the sounds coming from the bearing in service, this leads me to think of failed or faulty bearings, which, may or may not have anything to do with the condition of the pre assembled bearing.
To eliminate the dimensional condition of housing and bearing could you carry out a dimensional check of the bore of the bearing after installation and follow it up with a simple functional check e.g. assuming a ball race bearing, spin and check for lack of smoothness?

If the bearing is being crushed its a limits and fits issue, otherwise there's a failure of the bearing in service.

If its limits and fits could you demonstrate the measured values of bore and bearing pre assembly to your customer?

As for the bearings in service, isn't it just a functional check for customer protection?

Lastly, reading you post again it would seem that your fit conditions are set at extremely tight tolerances which don't follow the norm on any transition or interference fits specified by ISO.

For example, looking at a H7 s6 Interference Fit (typical for pressed bearings), the tolerances would be:

Hole - 10.7 to 10.718 mm
Bearing - 10.735 to 10.748 mm

Notice the ranges in the sizes to achieve the condition you may want i.e. 18 micron for Hole and 13 micron for the Bearing. Comparing this against your stated sizes of Hole 10.7 to 10.695 and Bearing 10.7 to 10.693 mm you can see that you could have for example more tolerance to achieve the same fit, in this case for Hole an additional 0.013 mm and for Bearing an additional of 0.006 mm.

Perhaps its worth evaluating the functionality required from the limits and fits?

Hope this helps.

#### Matt's Quality Handle

##### Involved In Discussions
For example, looking at a H7 s6 Interference Fit (typical for pressed bearings), the tolerances would be:

Hole - 10.7 to 10.718 mm
Bearing - 10.735 to 10.748 mm
This is what you need to be looking at. Interference is what keeps the roller/bearing interface from slipping. It appears from your post that the max interference per your specs is 0.005mm. In the example that Welshwizard quoted, there is 0.048 max interference.

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