A Search Algorithm for Calculating Validated Reliability Bounds

The search algorithm presented allows the CDF of a dependent variable to be bounded with 100% confidence, and allows for a guaranteed evaluation of the error involved. These reliability bounds are often enough to make decisions, and require a minimal number of function calls. The procedure is not intrusive, i.e. it can be equally applied when the function is a complex computer model (black box). The proposed procedure can handle input information consisting of probabilistic, interval-valued, set-valued, or random-set-valued information, as well as any combination thereof. The function as well as the joint pdf of the input variables can be of any type.