Determining the surge duration of a double exponential transient?
So I believe I have found the answer from some of my colleagues, they stated that the typical approach is to measure the time from the beginning of the pulse up to the point at which it has decayed back down to 50% of the peak value.

Alternatively, I came up with an alternative solution as well. Since the total power of the waveform is equivalent to the area under the curve over its entire duration, if one were to take this value and calculate the duration of a purely rectangular pulse that had the same peak value and the same total power, this pulse length would be a safe estimate as the damage potential of the rectangular pulse would be greater than a longer exponentially decaying one as the same total power is contained in a shorter duration (at least for the case of a purely resistive load with no complex impedance term).