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The author reviews developments in mathematical reliability theory, especially those developments which have had or are likely to have impact on engineering reliability problems. The review to 1960 is based on a similar review whi...
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The author reviews developments in mathematical reliability theory, especially those developments which have had or are likely to have impact on engineering reliability problems. The review to 1960 is based on a similar review which appeared in the 1965 book by R.E. Barlow and F. Proschan entitled Mathematical Theory of Reliability. It is pointed out that if the 1970s were the fault tree era, the 1980s may well turn out to be the era of network reliability, principally due to the importance of computer and computer network reliability.
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Authors of this paper were educated and have spent many years in Lomonosov Moscow State University (MSU), in the Interfaculty Laboratory of Statistical Methods (ILSM). Prof. Yu. K. Belyaev was student of Kolmogorov, and for severa...
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Authors of this paper were educated and have spent many years in Lomonosov Moscow State University (MSU), in the Interfaculty Laboratory of Statistical Methods (ILSM). Prof. Yu. K. Belyaev was student of Kolmogorov, and for several years his deputy in the ILSM, created and led by the great A. N. Kolmogorov. Now Prof. Yuri Belyaev is Emeritus Professor at Umea University (Sweden). Asaf Hajiyev was a PhD student in Kolmogorov's ILSM. In this paper some unusual incidents about the legendary Kolmogorov, and people around him are presented. Some stories were taken from the books and the internet (see references) dedicated to the memory of Kolmogorov; some were told by his students, and some happened with authors of this paper. Men are cruel but Man is kind. - A. N. Kolmogorov
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Orientation is an assignment of direction to each edge of an undirected graph. When none of the directed edges is in a cycle, the orientation is called acyclic. When every directed edge is in some cycle, the orientation is called ...
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Orientation is an assignment of direction to each edge of an undirected graph. When none of the directed edges is in a cycle, the orientation is called acyclic. When every directed edge is in some cycle, the orientation is called totally cyclic. A spanning tree of an undirected graph is a connected subgraph, including all its vertices, but containing no cycles. The number of spanning trees seems to have a relationship with the numbers of acyclic and totally cyclic orientations of the graph. Yet, proof of such a relation for a general graph is still elusive.
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With the increasing interactions between natural gas systems (NGS) and power systems, component failures in one system may propagate to the other one, threatening reliable operation of the whole system. Due to neglect of such cros...
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With the increasing interactions between natural gas systems (NGS) and power systems, component failures in one system may propagate to the other one, threatening reliable operation of the whole system. Due to neglect of such cross-sectorial failure propagation in integrated electricity-gas systems (IEGSs), traditional economy-oriented reserve expansion models may lead to unreasonable planning results. In order to address this, an innovative reserve expansion model is proposed to determine the allocation of energy production components through the harmonization between costs and reliability. First, novel multifactor-influenced reliability indices are defined considering synthetic effects of multiple uncertainties, including failure propagation, load uncertainties and generation failures. In reliability index formulation, contribution of failure propagation on system reliability is analytically expressed. To avoid high computational complexity, the fuzzy set theory is combined with conventional methods, e.g., Monte-Carlo simulation technique to reduce numerous contingency states. Sampled contingency states are aggregated into several clusters represented by a fuzzy number. To effectively solve the planning model, a decomposition approach is introduced and applied to decompose the original problem into a master problem and two correlated reliability sub-problems. Numerical studies show the proposed model can plan reasonable reserves to guarantee reliability levels of IEGSs considering failure propagation.
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Evaluation must be considered a continuing necessity during every phase of the large system's life, starting with the conceptual stage and continuing through design, fabrication, test, installation, and finally maintenance and ope...
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Evaluation must be considered a continuing necessity during every phase of the large system's life, starting with the conceptual stage and continuing through design, fabrication, test, installation, and finally maintenance and operation. The object of this evaluation is everyone's concern — the greatest possible degree of reliability
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Adding parallel redundancy to different components generally yields different system reliability improvements. The effect of such parallel redundancy upon system reliability when applied at various places and in various systems is...
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Adding parallel redundancy to different components generally yields different system reliability improvements. The effect of such parallel redundancy upon system reliability when applied at various places and in various systems is investigated. The problem of how to choose components for parallel redundancy is studied, and some results are given. Some examples are presented to illustrate the approach.
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As a key enabling technology for 5G, network function virtualization abstracts services into software-based service function chains (SFCs), facilitating mission-critical services with high-reliability requirements. However, it is ...
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As a key enabling technology for 5G, network function virtualization abstracts services into software-based service function chains (SFCs), facilitating mission-critical services with high-reliability requirements. However, it is challenging to cost-effectively provide reliable SFCs in dynamic environments due to delayed rewards caused by future SFC requests, limited infrastructure resources, and heterogeneity in hardware and software reliability. Although deep reinforcement learning (DRL) can effectively capture delayed rewards in dynamic environments, its trial-and-error exploration in a vast solution space with massive infeasible solutions may lead to frequent constraint violations and traps in poor local optima. To address these challenges, we propose a RuleDRL algorithm that combines the capability of DRL to capture delayed rewards and the strength of rule-based schemes to explore high-quality solutions without violating constraints. Specifically, we first formulate the reliable SFC provision problem as an integer nonlinear programming problem, which is proven to be NP-hard. Then, we jointly design DRL and rule-based schemes that are coupled to make the final decision and establish a bounded approximation ratio in general cases. Extensive trace-driven simulations show that RuleDRL can save the total cost by up to 65.67% and improve the SFC acceptance ratio by up to 82%, compared to the state-of-the-art solution.
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Application of Boole's inequality results in a simple lower bound for system reliability in terms of reliabilities of subsystems for a k-out-of-n:G system. No assumptions regarding statistical dependence or independence of the out...
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Application of Boole's inequality results in a simple lower bound for system reliability in terms of reliabilities of subsystems for a k-out-of-n:G system. No assumptions regarding statistical dependence or independence of the outcomes (success or failure) for the subsystems are used. The no assumption lower bound for pure series or parallel systems has been previously published, but the more general case of the title has been overlooked. On the other hand, using the assumption of association of the outcomes, the lower bound in this paper can be improved upon slightly as shown in Barlow and Proschan (1981).
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The authors show that if the convolution of n HNBUE distributions is exponential, then n-1 of the distributions are degenerate at zero and the other distribution is exponential. This result is also shown to hold for the wider HNBU...
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The authors show that if the convolution of n HNBUE distributions is exponential, then n-1 of the distributions are degenerate at zero and the other distribution is exponential. This result is also shown to hold for the wider HNBUE(3) class. The result extends similar results previously published for the IFRA and NBU cases. The authors conjecture that if a monotonic system formed with independent components has exponential life, it must be essentially a series system with exponential components.
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The genesis of every complex system is an informal set of requirements. In a good development process, these are formalized as a text document. This natural language text, however, is not truly formal; it is susceptible to being m...
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The genesis of every complex system is an informal set of requirements. In a good development process, these are formalized as a text document. This natural language text, however, is not truly formal; it is susceptible to being misunderstood and is difficult to analyze for contradictions and omissions. Through a series of steps, the requirements are transformed into formal artifacts such as source code and configuration files. The most difficult and error-prone part of the development process is the transition from informal to formal descriptions of the system. The "formal specification level" of the book's title isn't new. It consists of unified modeling language (UML) or systems modeling language (SysML) models-specifically, class diagrams with object constraint language (OCL) invariants and pre-and post-conditions. What is new is the description of tools to assist the transition from natural language text into formal models, to verify that these models are consistent, and to transform them in various ways.
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