Uncertainty Theory Based Partitioning for Cyber-Physical Systems with Uncertain Reliability Analysis

Reasonable partitioning is a critical issue for cyber-physical system (CPS) design. Traditional CPS partitioning methods run in a determined context and depend on the parameter pre-estimations, but they ignore the uncertainty of parameters and hardly consider reliability. The state-of-the-art work proposed an uncertainty theory based CPS partitioning method, which includes parameter uncertainty and reliability analysis, but it only considers linear uncertainty distributions for variables and ignores the uncertainty of reliability. In this paper, we propose an uncertainty theory based CPS partitioning method with uncertain reliability analysis. We convert the uncertain objective and constraint into determined forms; such conversion methods can be applied to all forms of uncertain variables, not just for linear. By applying uncertain reliability analysis in the uncertainty model, we for the first time include the uncertainty of reliability into the CPS partitioning, where the reliability enhancement algorithm is proposed. We study the performance of the reliability obtained through uncertain reliability analysis, and experimental results show that the system reliability with uncertainty does not change significantly with the growth of task module numbers.

Structural and System Reliability

Based on material taught at the University of California, Berkeley, this textbook offers a modern, rigorous and comprehensive treatment of the methods of structural and system reliability analysis. It covers the first- and second-order reliability methods for components and systems, simulation methods, time- and space-variant reliability, and Bayesian parameter estimation and reliability updating. It also presents more advanced, state-of-the-art topics such as finite-element reliability methods, stochastic structural dynamics, reliability-based optimal design, and Bayesian networks. A wealth of well-designed examples connect theory with practice, with simple examples demonstrating mathematical concepts and larger examples demonstrating their applications. End-of-chapter homework problems are included throughout. Including all necessary background material from probability theory, and accompanied online by a solutions manual and PowerPoint slides for instructors, this is the ideal text for senior undergraduate and graduate students taking courses on structural and system reliability in departments of civil, environmental and mechanical engineering.

Using a Chen-Stein identity to obtain low variance simulation estimators

This paper is concerned with developing low variance simulation estimators of probabilities related to the sum of Bernoulli random variables. It shows how to utilize an identity used in the Chen-Stein approach to bounding Poisson approximations to obtain low variance estimators. Applications and numerical examples in such areas as pattern occurrences, generalized coupon collecting, system reliability, and multivariate normals are presented. We also consider the problem of estimating the probability that a positive linear combination of Bernoulli random variables is greater than some specified value, and present a simulation estimator that is always less than the Markov inequality bound on that probability.