1,052 research outputs found

    Stochastic comparisons of series and parallel systems with randomized independent components

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    Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random number of components chosen from the first batch increases in increasing convex order. As a consequence, we establish a result analogous to the Parrondo's paradox, which shows that randomness in the number of components extracted from the two batches improves the reliability of the series syste

    Comparison results for inactivity times of k-out-of-n and general coherent systems with dependent components

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    Coherent systems, i.e., multicomponent systems where every component monotonically affects the working state or failure of the whole system, are among the main objects of study in reliability analysis. Consider a coherent system with possibly dependent components having lifetime T , and assume we know that it failed before a given time t > 0. Its inactivity time t −T can be evaluated under different conditional events. In fact, one might just know that the system has failed and then consider the inactivity time (t − T |T ≤ t), or one may also know which ones of the components have failed before time t, and then consider the corresponding system’s inactivity time under this condition. For all these cases, we obtain a representation of the reliability function of system inactivity time based on the recently defined notion of distortion functions. Making use of these representations, new stochastic comparison results for inactivity times of systems under the different conditional events are provided. These results can also be applied to order statistics which can be seen as particular cases of coherent systems (k-out-of-n systems, i.e., systems which work when at least k of their n components work)

    Depth-First Event Ordering in BDD-Based Fault Tree Analysis

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    In BDD-based fault tree analysis, the size of BDD encoding fault trees heavily depends on the chosen ordering. From a theoretical point of view, finding the best ordering is an intractable task. So, heuristics are used to get good orderings. The most simple, and often one of the best heuristics is depth first left most (DFLM) heuristic. Although having been used widely, the performance of DFLM heuristic is still only vaguely understood, and not much formal work has been done. This paper starts from two different research objects: fault tree without repeated events (NRFT) and fault tree with repeated events (RFT). For NRFT, the BDD generated according to DFLM ordering is proved to be the smallest BDD with the size equal to the total number of events. For RFT, a randomized algorithm is firstly proposed to create reliable benchmarks including large number of random fault trees with different specificities. Then, these benchmarks are used to perform two types of experiments to study the performance of DFLM heuristic. For RFT with small number of repeated events, it is found that the sizes of the BDD built over DFLM orderings are only slightly larger than the sizes of the RFT with different specificities. However, with the increase of the number of repeated events, we encounter the size explosion problem, and the change of repeated event distribution patterns will have a significant impact on the sizes of the BDD built over DFLM orderings. We also find that the number of repeated events is the more important measure than some other specificities (shape, logical type of top gate and OR/AND gate distribution) to estimate the level of the difficulty in BDD-based fault tree analysis

    Quantum science and metrology with mixed-species ion chains

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    This chapter reviews recent developments in the use of mixed-species ion chains in quantum information science, frequency metrology and spectroscopy. A growing number of experiments have demonstrated new methods in this area, opening up new possibilities for quantum state generation, quantum control of previously inaccessible ions, and the ability to maintain quantum control over extended periods. I describe these methods, providing details of the techniques which are required in order to work with such systems. In addition, I present perspectives on possible future uses of quantum logic spectroscopy techniques, which have the potential to extend precision control of atomic ions to a large range of atomic and molecular species.Comment: 30 pages, 8 figures, revtex4. Review article for Adv. At. Mol. Phys.. Final fully-formatted version will appear in print. Comments welcom
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