# Combining two sources of uncertainty

#### BIal

##### New Member
I will use an imperfect dice for simplicity. Let's assume there are two factors that influence the probability of the results obtained from throwing a dice: 1) the way the dice is thrown and 2) imperfections of the dice. Let's assume that we know what is the probability distribution of the results for median values of the imperfections. We also know the probability distribution of the results assuming "normal" (i.e., known) techniques of throwing the dice. What is the probability distribution of the results considering both uncertainties? I came across the term "convolution" in my research, but it doesn't seem to make any sense in my case? What do you think? Any idea how to solve the problem without a Monte Carlo simulation?

#### Dason

##### Ambassador to the humans
Can you give a concrete example of what you're looking at? It's not completely clear to me.

#### BIal

##### New Member
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?