Evaluation of highly dependable systems requires estimating the probability of a significant rare event under which the system fails to meet the requirement. To improve the estimation accuracy, advanced Monte Carlo simulation techniques such as importance sampling (IS) are commonly used. However, IS is known to misbehave under high dimension. As a result, the IS estimator can have a large relative error and underestimate the rare event probability. In this paper, we propose a novel IS method based on the idea of maximum weight minimization (MWM). Our method works by finding the sampling distribution that minimizes the maximum weight of a rare event sample. To alleviate the curse of dimensionality, we develop further heuristics based on two problem-specific structures, namely, monotonicity and symmetry. Using extensive examples from network reliability, stochastic flow analysis, cyber-security risk assessment, and fault tree analysis, we evaluate the performance of MWM, demonstrate its accuracy and scalability, and highlight applications where it outperforms state-of-the-art techniques.

Network reliability studies properties of networks subjected to random failures of their components. It has been widely adopted to modeling and analyzing real-world problems across different domains, such as circuit design, genomics, databases, information propagation, network security, and many others. Two practical situations that usually arise from such problems are (i) the correlation between component failures and (ii) the uncertainty in failure probabilities. Previous work captured correlations by modeling component reliability using general Boolean expression of Bernoulli random variables. This paper extends such a model to address the second problem, where we investigate the use of Beta distributions to capture the variance of uncertainty. We call this new formalism the Beta uncertain graph. We study the reliability polynomials of Beta uncertain graphs as multivariate polynomials of Beta random variables and demonstrate the use of the model on two realistic examples. We also observe that the reliability distribution of a monotone Beta uncertain graph can be approximated by a Beta distribution, usually with high accuracy. Numerical results from Monte Carlo simulation of an approximation scheme and from two case studies strongly support this observation.

One of the major challenges confronting the widespread adoption of solar energy is the uncertainty of production. The energy generated by photo-voltaic systems is a function of the received solar irradiance which varies due to atmospheric and weather conditions. A key component required for forecasting irradiance accurately is the clear sky model which estimates the average irradiance at a location at a given time in the absence of clouds. Current methods for modelling clear sky irradiance are either inaccurate or require extensive atmospheric data, which tends to vary with location and is often unavailable. In this paper, we present a data-driven methodology, Blue Skies, for modelling clear sky irradiance solely based on historical irradiance measurements. Using machine learning techniques, Blue Skies is able to generate clear sky models that are more accurate spatio-temporally compared to the state of the art, reducing errors by almost 50%.