Uncertainty Analysis Based on Probability Bounds (P‐Box) Approach in Probabilistic Safety Assessment

Abstract

A wide range of uncertainties will be introduced inevitably during the process of performing a safety assessment of engineering systems. The impact of all these uncertainties must be addressed if the analysis is to serve as a tool in the decision-making process. Uncertainties present in the components (input parameters of model or basic events) of model output are propagated to quantify its impact in the final results. There are several methods available in the literature, namely, method of moments, discrete probability analysis, Monte Carlo simulation, fuzzy arithmetic, and Dempster-Shafer theory. All the methods are different in terms of characterizing at the component level and also in propagating to the system level. All these methods have different desirable and undesirable features, making them more or less useful in different situations. In the probabilistic framework, which is most widely used, probability distribution is used to characterize uncertainty. However, in situations in which one cannot specify (1) parameter values for input distributions, (2) precise probability distributions (shape), and (3) dependencies between input parameters, these methods have limitations and are found to be not effective. In order to address some of these limitations, the article presents uncertainty analysis in the context of level-1 probabilistic safety assessment (PSA) based on a probability bounds (PB) approach. PB analysis combines probability theory and interval arithmetic to produce probability boxes (p-boxes), structures that allow the comprehensive propagation through calculation in a rigorous way. A practical case study is also carried out with the developed code based on the PB approach and compared with the two-phase Monte Carlo simulation results.

Advanced Methods in Uncertainty Management

“…In the first method, Monte Carlo simulation with 10 6 iterations have been carried out which gave 10 6 sample of inputs (x 1 , x 2 … x 9 ) and associated system output (y i ), where 'i' denotes iteration number. Pearson correlation coefficient has been calculated with the Eq.…”

“…To handle the propagation of uncertainties in PSA in the presence of correlations, only three of above mentioned methods are useful: (i) Method of moments [6][7][8], (ii) P-box approach [9,10] and (iii) Monte Carlo simulation. There are several strategies a Monte Carlo analyst can use to account for knowledge and uncertainty about correlations.…”

Discretization Analysis Method of Hybrid Reliability Based on Evidence Theory

“…Consequently, a kind of important random-interval hybrid reliability analysis problems is easily to obtain, and the efficient solution of this problem is of great significance for the reliability design of many complex products. Aiming at this problem, some numerical methods, including the function approximation method [22], the iterative rescaling method [23], and the probability bounds (p-box) approach [24], have been proposed for the lower and upper bounds estimation of the structural reliability in the presence of both random and interval variables. In addition, Luo et al [25] presented a combined probabilistic and set-valued description based on the multiellipsoid convex model description for grouped uncertain-but-bounded variables.…”

Hybrid Reliability Analysis for Spacecraft Docking Lock with Random and Interval Uncertainty

“…In recent years, many research studies have been carried out on the HRA methods for structure [23][24][25][26]. The following numerical methods have been proposed: the function approximation technique [27], the probabilistic transformation technique [28][29][30], the iterative rescaling method [31], the probability bounds approach [32], the mixed perturbation Monte Carlo (MC) method [33], the optimization algorithm with single-layer nesting [34,35], two-layer nesting [36,37], and the complex nesting [22], among others [38][39][40]. Nevertheless, the HRA with FORM is still in its infancy, as there are some calculating problems in the practical applications.…”