# Reducing variation through multiple readings

B

#### Black arrow

Hello,
We made a MSA recently and the tolerance is "one sided" and the tolerance limit is 0.020 mm. I can see that the variation of the present measurement system is not acceptable so if we measure parts that are close to upper tolerance limit we can have some problems to know if the parts are within spec are not. I would like to determine a sorting limit based on the variation from the measurement system.
The data from the MSA are:
6 standarddeviations: 0.008 mm => 3 standarddeviations 0.004 mm
My approach to this is to decrease the tolerance limit by 3 times standarddeviations => 0.020 -0.004= 0.016 mm.

If we measure the detail and gets 0.016 mm, the part should be ok.
BUT if we get 0.018 mm?
I know that we can reduce the variation by measure it once again, (6s)/√.
Do someone have some good guidelines to follow when it becomes multiple readings when a result is above the sorting limits such in my case above?

Thanks for your support here.

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#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
in these cases I usually use 3 measurements when the part falls between the guardband limit and the specification (on the inner side; if the first measurement falls out or specification I leave it as out). I have found that 3 measurements typically gives me a reasonable confidence in the actual value. I don't take the average of the 3 readings I use the median (the middle value of the 3). if its out, the part is out.

But, I also use this only as a short term containment action until I can either:
• improve the measurement system
• improve the part quality, reducing the variation
• or change the specification to the correct limits - specs are often not engineered and may be wrong

#### Miner

##### Forum Moderator
Staff member
Admin
You could calculate new sorting limits based on using the mean of multiple measurements. For example, using the mean of 4 measurements reduces the standard deviation by half, so you can calculate the new sorting limit using the reduced standard deviation.

B

#### Black arrow

You could calculate new sorting limits based on using the mean of multiple measurements. For example, using the mean of 4 measurements reduces the standard deviation by half, so you can calculate the new sorting limit using the reduced standard deviation.

Yes that's correct, i reduce the standard deviation by half if i measure 4 times. So in my case, new sorting limit is then 0.018 mm.

So if i understood you correctly, if the mean is after 4 measurements:

-0.018 the part is ok.
-0.019 the part is not ok.

#### Miner

##### Forum Moderator
Staff member
Admin
So if i understood you correctly, if the mean is after 4 measurements:

-0.018 the part is ok.
-0.019 the part is not ok.
That is correct.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
for small sample sizes the median is a better estimate of the central tendency - or 'true' value. it isn't effected by an extreme value, which can have a huge effect on the average of a small sample.

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