Quantification of margins and uncertainties using multiple gates and conditional probabilities

A methodology to perform the Quantification of Margins and Uncertainties (QMU) is introduced to enable the assessment of the safety associated with the operating conditions of complex engineering devices consisting of multiple subcomponents or coupled multi-physics processes. One of the key components of the approach is the possibility of decomposing the system into subcomponents characterized by critical metrics - gates - that collectively describe the reliability of the whole system. In the present study we formalize the process of constructing conditional probabilities for system performance and illustrate it with two applications: the evaluation of the test-time in a shock-tube experimental facility and the assessment of the unstart limit in the combustion chamber of a supersonic propulsion engine. In both cases, multiple uncertainties are considered and the gates are used as a mechanism to reduce the complexity of the resulting stochastic problem.