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研究由两个部件串联组成的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态. 当部件发生故障后进行故障维修, 因为各种原因可能会延迟修理. 部件在每次故障维修后的工作时间形成随机递减的几何过程, 且每次故障后的维修时间形成随机递增的几何过程. 以部件进行预防维修的间隔T和更换前的故障次数N组成的二维策略(T,N)为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析. 相似文献
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本文研究的是由两个部件串联组成且有两种故障状态的系统的预防维修策略, 当系统的工作时间达到T时进行预防维修, 预防维修使部件恢复到上一次故障维修后的状态。每个部件发生故障都有两种状态, 可维修和不可维修。当部件的故障为可维修故障时, 修理工对其进行故障维修, 且每次故障维修后的工作时间形成随机递减的几何过程, 每次故障后的维修时间形成随机递增的几何过程。当部件发生N次可维修故障或一次不可维修故障时进行更换。以部件进行预防维修的间隔和更换前的可维修故障次数N组成的二维策略(T, N) 为策略, 利用更新过程和几何过程理论求出了系统经长期运行单位时间内期望费用的表达式, 并给出了具体例子和数值分析。 相似文献
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本文研究了一类Poisson冲击下的$k/n(G)$系统(即$k$-out-of-$n$: $G$系统). 假定冲击的到达数形成一个参数为$\lambda$的Poisson过程, 且冲击的量服从某一分布. 当每次冲击到达时, 对系统中工作的部件独立地产生影响. 进而假定每一部件以一定的概率故障, 概率值是冲击量的函数. 且各次冲击独立地对系统造成损失, 直到工作部件数少于$k$系统故障为止. 在这些假定下, 我们获得了系统的可靠度函数和系统的平均工作时间. 进一步, 假定系统是可修的, 系统中有一个维修工, 并根据``先坏先修’’的维修规则对故障部件进行维修. 在维修时间服从指数分布的假设下, 系统状态转移服从Markov过程. 对该系统我们建立了状态转移方程, 并求得了系统可用度、稳态下的平均工作时间、平均停工时间和系统失效频率等可靠性指标. 最后, 我们还给出了一个简单例子来演示讨论的模型. 相似文献
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《数学的实践与认识》2020,(9)
主要研究一类常见的可修多状态退化系统模型,且针对系统的可靠性优化和服务台的有效利用,提出了维修优于保养的的系统优化策略.假定系统随在退化过程中,选择不完全预防性保养,当系统发生故障时,服务台停止保养而转向维修故障.在整个退化、保养、维修等过程中,根据模型实际假设和状态转移图,结合广义马尔可夫过程理论,建立状态概率转移微分方程组,根据可用度的定义,利用极限思想得到稳态可用度的计算方式和结果.最后利用数值算例得到维修优先于保养的多状态系统的稳态可靠度,以及保养率和维修率对可用度的影响,从而体现维修优于保养的优化策略对可靠性设计具有重要意义和实际价值. 相似文献
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考虑不完全检测的冲击模型最优维修策略 总被引:1,自引:0,他引:1
针对制造系统中设备检测不完全的情形,研究基于不完全检测的冲击模型的周期检测、维修联合策略.通过定期检测获知系统的劣化状态以进行必要的预防性维修.在假设系统是退化的且有k个不同故障状态的条件下,以最小化系统运行成本为目标,以检测周期T、系统更换前故障次数Ⅳ为联合决策变量,利用更新过程理论建立了系统平均费用率C(T,N)的数学模型,并且给出最优联合策略的数值算法.最后借助数值例子演示了该模型,分析了检测水平对系统运行成本的影响. 相似文献
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针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性. 相似文献
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Ciprian Foias Luan Hoang Jean-Claude Saut 《Journal of Applied Analysis & Computation》2018,8(3):727-763
This paper surveys various precise (long-time) asymptotic results for the solutions of the Navier-Stokes equations with potential forces in bounded domains. It turns out that the asymptotic expansion leads surprisingly to a kind of Poincare-Dulac normal form of the Navier-Stokes equations. We will also discuss some related results and a few open issues. 相似文献
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利用Lebesgue测度的等测内核和等测外包讨论内外测度的一系列性质,给出外测度有限可加的一个充要条件,该条件改进了原有外测度有限可加性相关问题的结果. 相似文献
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In this paper, we solve dual and triple sequences involving q-orthogonal polynomials. We also introduce and solve a system of dual series equations when the kernel is the q-Laguerre polynomials. Examples are included. 相似文献
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L. A. B. Cortez 《International Journal of Mathematical Education in Science & Technology》2017,48(4):630-641
Considering the important role played by mathematical derivatives in the study of physical–chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact differentials associated with path functions. As an application, we discuss the equation of state associated with a gas. 相似文献
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This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to some numeraire (‘cash’). As a main result, for any function f, we find the greatest closed convex monotone and cash-invariant function majorized by f. We then apply our results to some well-known risk measures and problems arising in connection with insurance regulation. 相似文献
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Gerald Dunn 《K-Theory》1989,3(2):141-161
We associate to the singular chains of the Moore loop space Y two dihedral chain complexes. The dihedral homology of these complexes is shown to be isomorphic to the O(2)-equivariant homology of the mapping spaces Y
o(2) and
. We also construct simple homotopy theoretic models of EO(2) x O2 (Y)G/BO(2) for G = O(2) or S1, where denotes suspension. Quaternionic analogues of these results are also established. 相似文献
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控制图与过程能力指数Cp(Cpk)都是用来进行质量分析与处理的重要工具。文 [1]谈及控制图的两类错误 (其概率分别为α、β) ,文 [2 ]讨论了Cpk与α的关系 ,但涉及Cpk与控制图检出力 (1- β)关系的文章却不多。本文以 X控制图为例 ,讨论了α、β、1- β、与Cpk的关系 ,得出了联合应用它们会对工序状态有较好的了解 ,对其适当的调整有助於提高产品质量 相似文献
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We show that the class of trapezoid orders in which no trapezoid strictly contains any other trapezoid strictly contains the class of trapezoid orders in which every trapezoid can be drawn with unit area. This is different from the case of interval orders, where the class of proper interval orders is exactly the same as the class of unit interval orders. 相似文献
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Endre Boros 《Discrete Mathematics》2009,309(12):3853-321
Given a family of graphs , a graph is called edge-minimal (vertex-minimal) if for every subgraph (induced subgraph) G′ of G; furthermore, G is called locally edge-minimal (locally vertex-minimal) if whenever G′ is obtained from G by deleting an edge (a vertex). Similarly, the concepts of minimality and local minimality are introduced for directed graphs (digraphs) and, more generally, for partially ordered sets.For example, by the Strong Perfect Graph Theorem, the only vertex-minimal graphs with χ>ω are odd holes and anti-holes. In contrast, the only locally vertex-minimal graphs with χ>ω are partitionable graphs. Somewhat surprisingly, there are infinitely many non-trivial perfect graphs that are locally edge-minimal and -maximal simultaneously. In other words, such a graph is perfect but it becomes imperfect after any edge is deleted from or added to it.In this paper we consider vertex- and edge-minimal and locally minimal graphs in the following families: (i) perfect and imperfect graphs, (ii) graphs with χ=ω and with χ>ω, (iii) digraphs that have a kernel and kernel-free digraphs, and finally, (iv) vertex-minimal complementary connected d-graphs. 相似文献
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William Y. C. Chen Eva Y. P. Deng Rosena R. X. Du Richard P. Stanley Catherine H. Yan 《Transactions of the American Mathematical Society》2007,359(4):1555-1575
We present results on the enumeration of crossings and nestings for matchings and set partitions. Using a bijection between partitions and vacillating tableaux, we show that if we fix the sets of minimal block elements and maximal block elements, the crossing number and the nesting number of partitions have a symmetric joint distribution. It follows that the crossing numbers and the nesting numbers are distributed symmetrically over all partitions of , as well as over all matchings on . As a corollary, the number of -noncrossing partitions is equal to the number of -nonnesting partitions. The same is also true for matchings. An application is given to the enumeration of matchings with no -crossing (or with no -nesting).