In engineering, typically we design structures to withstand a certain load. Given that there are uncertainties in both, we apply a factor of safety to give a "buffer" between the computed capacity and the load. Here's my question:
If the load has a certain probability distribution and if the capacity has a certain probability distribution, what is the probability that the load may exceed capacity? Is there some first principals way to calculate this probability? For example, if both were normally distributed and had a region where they overlap (tail end of one overlaps the tail end of the other) what would be the probability that both the load and the capacity are in this region?
If the load has a certain probability distribution and if the capacity has a certain probability distribution, what is the probability that the load may exceed capacity? Is there some first principals way to calculate this probability? For example, if both were normally distributed and had a region where they overlap (tail end of one overlaps the tail end of the other) what would be the probability that both the load and the capacity are in this region?