We often get asked about the strength of rope rescue and rope access equipment. When seeing a new piece of equipment the first question is often, “How strong is this?” This sounds like a simple question but the answer is more complicated.

It is common to think all products are manufactured the exact same. In reality all manufactured products have variances. They are all a little different. These differences are managed through quality control. These differences can be made very small through better manufacturing processes but this effects the price of the product. The key is to find a balance between a product that does what it is supposed to do but is also affordable. In other words to find a product that is ‘good enough’.

If only one sample of a product is tested, it only gives information on that one item. It is impossible to determine the quality of the manufacturing process. If more samples of the same item are tested, this gives information about the quality of manufacturing. The more samples tested, the more accurate the information.

If a large number of samples are tested, how is this information compared? One way to compare these samples is to use a statistical formula known as standard deviation and using that to compute a ‘3 Sigma’ value. This number can then be used to assure the quality of the product to the end user.

**What is 3 Sigma?**

3 Sigma is a statistical formula used to calculate probability. It is commonly used for computing the minimum breaking strength (MBS) of Climbing, Rope Rescue, and Rope Access equipment. Using the 3 Sigma formula provides a way to determine a safe minimum breaking strength from a range of numbers gathered during testing. When used to calculate the minimum breaking strength it gives confidence that the minimum breaking strength is higher than 99.86% of samples tested.

The simplest way to explain 3 Sigma is to show how it is computed. For this example we broke Figure 8 knots tied in **Teufelberger 6mm Nodus Accessory Cord** and recorded the results on a **Rock Exotica Enforcer Load Cell**.

Ten tests were conducted with the following results recorded in KiloNewtons (kN):

- Test #1: 7.20 kN
- Test #2: 7.97 kN
- Test #3: 6.57 kN
- Test #4: 6.84 kN
- Test #5: 6.44 kN
- Test #6: 7.49 kN
- Test #7: 6.92 kN
- Test #8: 7.38 kN
- Test #9: 6.51 kN
- Test #10: 6.96 kN

These tests resulted in the knot breaking within the range of **6.44 kN – 7.97 kN**.

The first step in computing the 3 Sigma value is to compute the mean breaking strength which comes out to 7.03 kN.

The next step is to compute the standard deviation. The standard deviation is the amount of variation in a set of values. If all the numbers are very close to the mean then the standard deviation will be a small number. If there is a wide range of numbers further away from the mean then the standard deviation will be a larger number. The smaller the standard deviation in a set of values the higher the quality of manufacturing.

*The standard deviation can easily be computed in Microsoft Excel by using the =STDEV function.*

For the results of this test the standard deviation is computed as 0.49 kN. Since we are computing a 3 Sigma value we multiply the standard deviation by 3 resulting in 1.47 kN (0.49 kN * 3).

This value is then subtracted from the mean resulting in a final **3 Sigma value for this test of 5.56 kN** (7.03kN – 1.47 kN).

Using 3 Sigma gives confidence that although there is still a 0.14% chance of the knot breaking lower than 5.56 kN the chance is very small. This number can be made more accurate by increasing the sample size. Instead of 10 tests, 20 or even 50 could have been performed. The more tests that are performed, the more confidence we have that this number is truly representative.

**How was the MBS on your equipment computed?**

Note that the 3 Sigma number computed for this test, 5.56 kN, is 13.66% lower than the lowest recorded value, 6.44 kN. What if the lowest obtained value, 6.44 kN was used instead for the minimum breaking strength? In this case, we would expect 11.35% of values to fall below 6.44 kN. More than 1 out of 10 would be below the rated strength. When the 3 Sigma number is used instead, only 1 out of 715 will fail below the rated strength.

What if this was a carabiner instead of a knot tied in rope? Would you use this equipment knowing the number on the label was unrealistically high? This is what might happen when equipment is purchased without knowing how these numbers were calculated. Being certified to international standards provides a way to guarantee the meaning of these numbers.

What do we mean by international standards? To be sold in Europe, life safety equipment must be manufactured to European Union (EU) directives. This manufacturing is independently verified and tested resulting in a CE mark. Likewise equipment manufactured to meet **NFPA 1983 Standard on Life Safety Rope and Equipment for Emergency Services** must also be independently tested. Other countries and regions have their own standards.

For equipment manufactured using international best practices, the minimum breaking strength printed on the equipment has an established meaning. This can be verified by checking with the laboratories that independently certified the equipment. The number following a CE label, for example CE 0194, is the Notified Body. This is the organization that performed the independent quality assurance on the product. If there are doubts about the equipment, the Notified Body can be contacted to verify the product’s compliance with the appropriate standard. Similarly NFPA certified equipment tested by Underwriters Laboratories (UL) can be verified in their online database.

We have contacted Notified Bodies before marked on some equipment and were told there was no record of testing the product in question. If this information is fraudulent, what about the other markings on the equipment? Should it be trusted? In this case, what do the numbers mean? Are the numbers the result of a 3 Sigma tests or simply the lowest test value recorded? Was the equipment even tested? We don’t know and do not wish to find out by the possibility of having it fail when in use.

This is why we choose to only use equipment from well known manufacturers with a proven record of safety. The strength of the equipment is only as good as the standards used by the manufacturer.