I am afraid it becomes too difficult to understand if I talk about the real problem, which is related to structural and earthquake engineering but here is a shot:

I have a computer model that simulates a building under a suite of ground motion records. In this simulation,the material characteristics are fixed at median values. From this model, I get the probability distribution of structural failure for various intensities of ground motion. In another model, I study the effects of the variability of material characteristics. Therefore, I also have the probability distribution of structural failure due to the variation of concrete strength and other material characteristics. I manage to have the same "x" axis for both distribution functions (say for example, roof displacement). Now, a real structure has both types of uncertainties: those related to the seismic action and those related to its characteristics (materials, etc). How do I calculate the probability pf failure considering both types of uncertainty?