# MSA (Measurement System Analysis) - Process Tolerances

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#### s15763w

Need help on how to develop process tolerances for inline laser measuring unit that measures runout. The print spec is 0.30 mm Max runout of friction surface. Due to the inherent error in the inline laser measurement unit, how should I proceed with developing a process tolerance to ensure we dont ship parts above 0.30 mm runout? What studies do I need to conduct?

Super Moderator
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#### ncwalker

What you are asking for is the uncertainty of the gage.

The statement "My rounout gage measures to +/- X microns." You need to know what "X" is, then you can emplace a guard band the size of X and run to tighter limits than the print specification, running limits. This guarantees your parts are in specification.

Sadly, this uncertainty number is not usually calculated in an MSA/Gage R&R sheet, but the calculation is pretty straightforward.

The first way people do this is to take the 95% confidence on the variability of the gage, which is 2 standard deviations. In a typical Gage R&R study, there is a column of standard deviations, usually marked "SD". (There is ALSO a column typically marked (6*SD), you do NOT want this column. You also do not want the percentage columns. You want the first column, again, marked "SD". The row marked "Total Gage R&R" is the one you want. Double this value (2 standard deviations) and that's your 95% confidence uncertainty. So lets say you had an SD of 0.0007 for Total Gage R&R, then your uncertainty is +/- 0.0014. If your print spec is .05, you reduce this by one side of the uncertainty and run to 0.0486. (I'd probably round that DOWN to 0.048).

The second way people do this is incorporates NDC analysis. Again, you need the SD column, but this time you want the "Total Variation" row, not the "Total Gage R&R" row. You take the Total Variation number (TV) and use this equation:

Uncertainty = 3*TV/NDC

where NDC is your Number of Distinct Categories. These numbers are usually very similar. I calculate both and take the worst of the two, just to be safe.

BAM. There's your guard band width.

(To be complete, if you are using the old Xbar-R method, I have seen it said you can get uncertainty from an intermediate value using this method. But I personally don't like Xbar-R at all. It was good back in the day before computers because it estimated sigma and used lookup tables for shortcuts. But with computers today, it's silly to take a calculation shortcut. A lot of these statistical methods are from the slide rule and earlier era, where there was motivation to come up with "approximate" methods to save calculation time. That's not the case today .... In any case, if you hunt around on an Xbar-R sheet, you will find an intermediate calc called UCL_R. It's found by looking up the average range in one of the tables. You take this number and divide it by 2 and that's sometimes reported for uncertainty. Again, it follows the upper two methods closely. I don't like it, but I wanted to be complete.)

And that's all the ways I've seen people do this calculation.

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#### s15763w

In regards to Wheelers article &quot;How to Establish Manufacturing Specifications&quot;, I have a few questions. Our run-out print spec is 0.30 mm Max, which is a one sided spec. What would the watershed tolerance be? 0.305 mm ?? For 99.9% manufacturing specification, should I be subtracting the 2.70σe from 0.305 mm or 5.40σe from 0.305 mm, since it's a one sided spec? My belief is subtracting 2.70σe from 0.305..

Last edited by a moderator:

#### Miner

##### Forum Moderator
My belief is subtracting 2.70σe from 0.305..

This is correct. You do not double up just because its one-sided.

##### Starting to get Involved
Can we use the measuring instrument to collect the data for process capability which is qualifed in GRR by consider product tolerance ?
As product may have the tolerance of 30 micron .but process is having only max variation of 8 mircon then till can we use same instrument during CP and CPK calculation ?
In this case ,i think NDC will be okay for product but for process it will not.
Pls kindly give your input .
THanks

#### Miner

##### Forum Moderator
Anytime you use the gage for some type of statistical use (e.g., SPC, capability study, DOE, etc.), you need to use the metrics based on variation (i.e., %PV, %SV, ndc). If, for example, you had a very good %Tol, but a very bad ndc, your observed process variation will be inflated by the measurement variation and make your capability study results appear worse that the actually are. This is more important the more marginal your capability. If your capability is extremely good, the impact is small. That is, your observed capability (Cp) of 4.2 might actually be 4.9.

##### Starting to get Involved
for new process,where we dont know the variation then how to select the measuring instrument for CP and CPK.
If we go as per product specification , then it may givewrong result.
or it will be based on trail and error basis ,we can decide that instrument is okay (by considering logic given by you in reply )

#### Miner

##### Forum Moderator
For a new process, you will have to use your judgment as to selecting a suitable gage. Randomly select parts that should represent your process variation then perform an R&R study using %SV or ndc as your metric. If the metrics are good, you can proceed to your capability study.

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#### ncwalker

You can follow a strategy for a new process that will minimize your measuring (cost). We will assume you are about to make a 300 piece PPAP run and you are going to take 7 subgroups of 5 pieces each for your capability study throughout the run. What you do is this:

1) Set up your equipment and dial it in. SAVE ALL OF THESE PARTS, do not throw them away.

2) Once you get your process where you want it (centered, and in spec) begin your PPAP run of 300 pieces.

3) Keeping the parts IN ORDER, sequence them and identify and pull your 7 subgroups of 5 pieces and set them aside. You really want to sequence ALL the parts in the 300 piece run because the order of manufacture is key to calculating Cp/Cpk correctly. (It does not affect Pp/Ppk).

4) Run is complete, now off to the measurement lab.

5) Measure your subgroups for your capability study on your gage (which at this point, you are ASSUMING is OK).

6) Use the measurements you made for your capability study to select the subset of these parts that you will use for your Gage R&R. You want a wide variety of parts. Hand pick them out of this capability study.

7) Guess what? Because of the capability study, you have already measured them once. You can use those measurements. Repeat the measurements and complete your Gage R&R. If your Gage R&R is good, you are golden. Gage R&R done, Capability Study done.

8) If your Gage R&R fails, you need to understand why. If %Tol is OK but % Study Variation is bad, it usually means your parts are too identical. Remember those setup parts I told you to save way back in step 1? Introduce some or all of them in the Gage Study, replacing measurements with these. These setup parts will have more variation than the nominal parts. Does the Gage R&R pass now? Good. You are done.

9) If it does NOT pass, this is the losing situation. You have to improve your gage. AND all your capability measurements are invalid. That must be redone to. (You do not have to make more parts, you CAN use the same parts, but you have to remeasure AFTER you have improved your gage).

It's like validating the gage retroactively. The risk is, you do a capability study that is invalidated and you have to do it again. But the motivation for doing it this way is MOST of the time (especially if this is a core competency for your business - I mean the sort of part you make all the time) you will be OK and this minimizes the impact to your metrology lab and saves you time (cost).

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