Bayesian Integrated Global Uncertainty & Sensitivity Analysis of System’s Availability

The purpose of this manuscript is to introduce a novel conceptual design of a method that allows integration of Bayesian Uncertainty Analysis (BUA) with Bayesian Sensitivity Analysis (BSA) for event-driven indicators of system's availability. Such Bayesian Integrated Global Uncertainty and Sensitivity Analysis (BIGUSA) procedure integrates the previously independently developed global UA and SA methods. The discussed approach is based on global exploration of parameters' space, which allows to capture higher-order interactions between correlated variables, thus avoiding common pitfalls of methods based on local state space explorations. The method is developed for a generic industrial facility characterized by the following input-output signals: (i) inputs - the stochastic events causing failures of individual assets; (ii) outputs - the availability, which is measured with suitable quantitative indicators of the facility. The objectives of the proposed BIGUSA are twofold: (i) description of the uncertainty profile of the availability of the analyzed facility (system) given the uncertainty profiles of the building blocks of the system (assets); (ii) assessment of how sensitive the availability of the facility is to individual failure events that might occur at the assets level. This is done by adopting the Bayesian approach, in which, at the higher level, the failure rates (FRs) are sampled from Bayesian priors which are fed to the stochastic simulation engine at the lower level of the algorithm. Stochastic realizations produced by such simulation engine are used to describe uncertainty profiles of the outputs (UA stage) and their sensitivity to variations in the input variables (SA stage). The former is performed by nonparametric density estimation, while the latter is assessed with Sobol indices, which measure how much of the output variance is due to variance in inputs.