# Root Sum Square and Statistical Tolerancing help needed

#### ScottK

##### Not out of the crisis
Staff member
Super Moderator
A customer told us that they are accepting of RSS when developing tolerances.
I've never heard of it until today.
Googled, found some equations, found some papers on the internet, dug around here for some threads but I'm still not entirely sure how it works.

Does anyone have a real life example of RSS method?

thanks.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Re: a little Root Sum Square and Statistical tolerancing help?

A customer told us that they are accepting of RSS when developing tolerances.
I've never heard of it until today.
Googled, found some equations, found some papers on the internet, dug around here for some threads but I'm still not entirely sure how it works.

Does anyone have a real life example of RSS method?

thanks.
I have a training example I use for the red bead experiment. Split the paddle into two halves, and count each half as two different sources of variation. If you average 10 red beads for the whole paddle, each half will average 5 red beads. If we assume the number of red beads in the paddle is Poisson (or you can physically do this and calculate the standard deviations), the standard deviation for each half is the square root of 5.

Let's add the two numbers together. We should average 10 with a square root of 10 as the standard deviation. Indeed, if I add the square of the square root of 5 (which is 5) to the square of the square root of 5 (which also is 5), I get 5 + 5 = 10. I then take the square root of 10 and indeed get the expected answer.

#### Paul F. Jackson

##### Quite Involved in Discussions
Re: a little Root Sum Square and Statistical tolerancing help?

Linear tolerance stacks typically are performed to verify critical clearences/interferences using a RSS value of the stacked tolerances involved but that value is typically multiplied by 1.5 (Thanks to Mr. Bender).
He wrote an SAE paper in the 60's that advised a safety factor of 1.5*RSS to predict critical stacked tolerance values.

With the modern emphasis on +/-4 or +/-5 sigma statistical capability of the individual tolerance contributors to those stacks some have abandoned the traditional safety 1.5 factor which would set the stacked value at +/-4.5sigma.

Paul

#### Chitchat

##### Registered Visitor
Is RSS the correct method for combining the calibration tolerances of two similar pieces of equipment for comparison purposes?

For example, we use an IR camera to measure the temperature of the laser beam. In order to verify the correct operation of the IR camera, the laser is set to 200 degrees and a second IR camera is aimed in the path of the laser beam and the readings from both cameras compared. If the IR camera has a calibration accuracy of ±3 degrees, what is the acceptable error in order to verify the correct operation of the IR camera? Given that the RSS would be 4.24, is 200 ±4.24 correct?

Thanks!