The application of constrained mathematics in probabilisticuncertainty analysis

摘要

Safety and reliability analyses often depend on Boolean logiccombinations of input variables that have uncertainty (imperfectknowledge) or variability (probabilistically described outcomes).Calculating safety and reliability probabilities with functions ofuncertain variables can yield incorrect or misleading results if someprecautions are not taken. One important consideration is theapplication of constrained mathematics for calculating probabilities forfunctions that contain repeated variables. An example of a constraint isthat an uncertain variable that appears multiple times in a Booleanexpression must always have the same value, although the value cannot beexactly specified. It has been recognized that using interval-basedcomputations such as interval arithmetic and fuzzy or possibilisticmathematics in an unconstrained mode (applied by sequentially parsingequation solutions), and even Monte Carlo analysis can significantlymisrepresent extreme values. This phenomenon, its ramifications, and asolution for the problem are discussed