The exploratory research addressed by this project focuses upon development of a theory of imprecise risk that is consistent with well-established engineering design mathematics, yet allows subjectively specified probability measure. Engineering design activity often requires the a priori subjective assignment of a probability measure to all uncertain design inputs. While subjective a priori assignment of probability measure eliminates imprecision in the characterization of risk, experience with such exercises shows that decision makers are not necessarily self-consistent and often do not satisfy the axioms of probability measure and/or utility theory when attempting to assign probabilities. The objectives of this research activity are: (1) to investigate imprecise risk associated with decision making in engineering design using measure theoretic principles; (2) to develop, from measure-based principles probability bounds on risk using subjectively assigned probability measure. Should this research effort prove successful, it will provide an analytical framework for quantifying imprecise risk arising from often inconsistent, subjectively assigned event probabilities. This will enable substantially improved decision making in virtually all engineering design.
