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Do you have a reference for this?
To be more precise, I am only partly right. NFPA 70E does not specifically recommend any particular arc flash hazard calculation method. Annex D in the 2012 edition references several of them, and there are more that are available but not referenced. The general consensus to date is that IEEE 1584 is the most accurate and has the backing of actual test data (a feature missing in many others) but has limited application since it is an empirical method.
I don't have my copy of IEEE 1584 with me but please bear with me as this should be pretty obvious. The references requested are ASTM 1959 and IEEE 1584.
IEEE 1584 is an empirical method to calculate the amount of incident energy at a given distance from an arcing fault. Other arc flash formulas are similar in that they all aim to predict the same threshold. The standard distance that is used in IEEE 1584 is called the "working distance". It is based on the distance from the bus bars at the back of the cabinet (the source of the worst case possible arcing fualt) to the face/chest area of the worker. Note: arms and hands are not considered at all. The focus is on the face/chest. No protection for the hands and arms is predicted or anticipated. The complete IEEE 1584 standard gives a lot more detail on this but a good summary is given in Annex D of NFPA 70E. So if you don't want to pay several hundred dollars you can use that one.
Second, Alicia Stoll subjected several sailors to a test to determine the exact threshold at which a heat source could cause a second degree burn. She equated this back to a copper calorimeter sensor so that today, we don't have to subject anyone to second degree burns to measure the second degree burn threshold. The threshold is given in cal/cm^2. This is indirect information that is used next. The Stoll curve is widely documented on the internet (google it).
The PPE is generally selected via ASTM 1959 for cloth (rainwear and face shields use different standards). The test method suspends a piece of cloth which would be used in manufacturing PPE and subjects it to an arc. A calculation is run to determine the threshold value where the PPE fails to meet the Stoll curve...the point of onset of a second degree burn. The complete standard is kind of dry but explains this in detail. ASTM 1959 does not test "PPE". It tests material samples.
IEEE 1584 contains a numerical calculation that was done where PPE meeting the ASTM 1959 standard was numerically compared to arcing faults with the incident energy calculated according to the IEEE 1584 empirical method. The percentage of failures (to prevent a second degree burn) were determined. 95% of the time, PPE selected according to ASTM 1959 will protect against a second degree or greater burn. Note that this is simply a numerical simulation...it does not represent real world results. Nothing about IEEE 1584 or ASTM 1959 represents real world results directly.
This informatio has to be translated into fatality statistics. There is a method called the "Baux" scoring method that predicts survivability from a burn that is used for triage purposes. The Baux score is equal to the total body surface area burned plus the victim's age. If this score exceeds 100, there is a high likelihood of a fatality. Arms and hands count for about 18% of total body surface area. Once a burn extends to the face/chest area, an additional 17 points is added to account for burns to the lungs, and since the bulk of the body is in the torso area, the likelihood of a fatality goes up dramatically. The Baux score is frequently given in books on arc flash as a chart relating % burned and age. You can find it all over the internet and in Jim Phillips book. So if only arms and hands are involved, a fatality due to burns is not very likely.
Finally, so far there has not been a reported case of a fatality while wearing the proper PPE in the proper manner as calculated by IEEE 1584. There have been reported injuries by either not wearing sufficient PPE or wearing it improperly. See:
"Update of field analysis of arc flash incidents, PPE protective performance and related worker injuries", by Doan, Hoagland, and Neal.
Does this mean that IEEE 1584 and ASTM 1959 guarantee "no injury"? No. Injuries were reported in the study listed above, just not fatal ones. In addition, IEEE 1584 and ASTM 1959 give the 95% performance measure only right at the very threshold. This means that 1 out of 20 cases might fail to be protected, and the above paper only located 30 cases. Arc flash incidents are even more rare than shock incidents (by a 2:1 margin according to BLS statistics analyzed by ESFI). This rarely actually occurs in practice in the real world. For instance if PPE is selected to protect against incident energy from 4 to 8 cal/cm^2, numerically most cases are not going to be 7.9 cal/cm^2. If one looks at an actual ASTM 1959 report, PPE passes 100% of the time if the incident energy is between 0.5 and 1.0 cal/cm^2 below the threshold (sharpness of the line is material dependent). Thus with such low incident rates it might be decades before the 95% performance threshold can be tested in the real world.