Building Reliability Bounds in Stochastic Binary Systems

Cancela, Héctor; Ferreira, Graciela; Guerberoff, Gustavo; Robledo, Franco; Romero, Pablo

doi:10.1109/rndm.2018.8489823

Cited by 5 publications

(7 citation statements)

References 17 publications

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“…In this section, the combinatorics of SMBS is revisited. The interested reader can consult further details in Cancela et al (2018) and Romero (2016Romero ( , 2019. For completeness, here we briefly explain the interplay between SBS and propositional logic.…”

Section: Computational Complexitymentioning

confidence: 99%

“…(2014, 2015a), represent our point of departure for this work; other papers, such as Cancela et al. (2018) and Romero (2016, 2019), can be useful as SBMS methodological background.…”

Section: Introductionmentioning

confidence: 99%

“…Our goal is to extend the success of well-known reliability estimation methods previously applied to network models to arbitrary stochastic monotone binary systems (SMBS). Some of our previous works, such as s Canale et al (2014Canale et al ( , 2015a, represent our point of departure for this work; other papers, such as Cancela et al (2018) and Romero (2016Romero ( , 2019, can be useful as SBMS methodological background.…”

Section: Introductionmentioning

confidence: 99%

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On the reliability estimation of stochastic binary systems

Cancela

Murray

Robledo

et al. 2021

Int Trans Operational Res

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A stochastic binary system (SBS) is a multicomponent on‐off system subject to random independent failures on its components. After potential failures, the state of the subsystem is ruled by a logical function (called structure function) that determines whether the system is operational or not. A SBS serves as a natural generalization of network reliability analysis, where the goal is to find the probability of correct operation of the system (in terms of connectivity, network diameter, or different measures of success). A particular subclass of interest is stochastic monotone binary systems (SMBS), which are characterized by nondecreasing structure. We explore the combinatorics of SBS, which provide building blocks for system reliability estimation, looking at minimal nonoperational subsystems, called mincuts. One key concept to understand the underlying combinatorics of SBS is duality. As methods for exact evaluation take exponential time, we discuss the use of Monte Carlo algorithms. In particular, we discuss the F‐Monte Carlo method for estimating the reliability polynomial for homogeneous SBS, the recursive variance reduction for SMBS, which builds upon the efficient determination of mincuts, and three additional methods that combine in different ways the well‐known techniques of permutation Monte Carlo and splitting. These last three methods are based on a stochastic process called the creation process, a temporal evolution of the SBS which is static by definition. All the methods are compared using different topologies, showing large efficiency gains over the basic Monte Carlo scheme.

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Section: Computational Complexitymentioning

confidence: 99%

“…(2014, 2015a), represent our point of departure for this work; other papers, such as Cancela et al. (2018) and Romero (2016, 2019), can be useful as SBMS methodological background.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the reliability estimation of stochastic binary systems

Cancela

Murray

Robledo

et al. 2021

Int Trans Operational Res

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“…We enumerate a number of relevant results about separable SMBS presented in our previous conference paper [4], which will be useful in the remainder of the paper.…”

Section: Definition 4 (Separable Systemmentioning

confidence: 99%

“…This fact promotes the need of distinguished sub-classes, and the development of novel approximative techniques. In [4] the concept of separability in stochastic binary systems was introduced. As discussed below, separable systems are those whose structure function can be characterized by a hyperplane separating operational from failure states.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Reliability of Separable Systems

Cancela¹,

Guerberoff²,

Robledo³

et al. 2020

Preprint

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The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems, where the components are subject to probabilistic failures. Our goal is to understand the reliability of the global system.The reliability evaluation of an SBS belongs to the class of NP-Hard problems, and the combinatorics of SBS imposes several challenges. In a previous work by the same authors, a special sub-class of SBSs called separable systems was introduced. These systems accept an efficient representation by a linear inequality on the binary states of the components. However, the reliability evaluation of separable systems is still hard.A theoretical contribution in the understanding of separable systems is given. We fully characterize separable systems under the all-terminal reliability model, finding that they admit efficient reliability evaluation in this relevant context.

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On the Reliability of Dynamical Stochastic Binary Systems

Lagos

Romero

2020

Machine Learning, Optimization, and Data Science

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Building Reliability Bounds in Stochastic Binary Systems

Cited by 5 publications

References 17 publications

On the reliability estimation of stochastic binary systems

On the reliability estimation of stochastic binary systems

Analysis and Reliability of Separable Systems

On the Reliability of Dynamical Stochastic Binary Systems

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