# 3 SIGMA METHOD PETZL

SIGMA is an element of statistical calculations, which allows to display a products’ guaranteed strength value throughout its manufacturing process.

Therefore, it is related to product safety. During the testing process, the greater the differences between the 10 recorded values, the higher turns out the sigma value.

For example, for 10 carabiners tested, their ten recorded values are usually different and not the exact same:

24,9 | 25,9 | 26,2 | 25,6 | 25,8 | 24,7 | 25,5 | 24,7 | 26,0 | 25,7 kN

So which value to take into account to display the MBS (Minimum Breaking Strength) value?

We first calculate the average:

(24,9 + 25,9 + 26,2 + 25,6 + 25,8 + 24,7 + 25,5 + 24,7 + 26,0 + 25,7) / 10 = 25,5 kN

We then calculate the variance :

24,9 - 25,5 = - 0,6    (-0,6)2 = 0,36

25,9 - 25,5 = - 0,4    ( 0,4)2 = 0,16

...and so on for the 10 measured values.

We add those 10 results :

0,36 + 0,16 + 0,49 + 0,01 + 0,09 + 0,64 + 0,064 + 0,25 + 0,04 = 2,68

And we create the average :

2,68 / 10 = 0,268

The variance is even to : 0,268

SIGMA (standard deviation) = square root of 0,268 = 0,5176

The maximum value displayed on the carabiner would be:

average of 10 carabiners = 25,5 kN

SIGMA = - 0,5176

____________________________

Displayed Value = 24,0724 kN

## What you should know in particular about the 3 SIGMA safety margin?

Slack Inov uses the 3 SIGMA method to calculate the MBS. We multiply the SIGMA for 3 (this is why it is called “3 SIGMA”) to boost the prudency in the MBS calculation.

Taking the 10 previous carabiners as an example:

The average of those 10 carabieners is 25,5kN

3 SIGMA (3 x 0,5176) = - 1,5528

_____________________________

Displayed value = 23,0472 kN

Our choice aims to maximize the safeness of our users while using our products.

SOURCE @Petzl

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