For each limit state, it is necessary to recognize and manage randomness and uncertainty. It isn't adequate to simply say that the average demand is less that the average capacity - the probability of failure must be less than a specified amount.
This failure probability is usually designated as x% probability of failure in y years where y is generally taken to be the service life of the structure. For example, the Load and Resistance Factor Design (LRFD) format uses load factors on the demand and resistance factors on the capacity to provide a certain probability of failure. The basic design inequality is stated as:
gDAVE < fCAVE
/ CAVE > g / f
a given probablility of failure