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Network reliability analysis: Matrix-exponential approach

机译：网络可靠性分析：矩阵指数方法

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摘要

An exact method for analyzing the reliability of networks whose components' lifetimes have matrix-based distributions is proposed. The method produces an add-on algorithm for the available sum of disjoint products (SDP) algorithms so that they can be utilized to calculate the parameters of the network reliability function directly from the parameters of the component reliability functions. Until now, SDP algorithms have only been used to calculate a network reliability value from the reliability values of its components. The advantage is that once the network reliability function is obtained, other reliability measures, such as the network's hazard function, the mean time to failure (MTTF), and the coefficient of variation of the time to failure (CVTTF), can be obtained using only matrix algebra. An extension to general systems containing basic structures that cannot be expressed as an SDP is given. The method is applicable for both phase-type (PH) and matrix-exponential (ME) distributions. The applicability of the method for other distributions is made possible by using PH distributions as their approximation. An application and comparison with a method based on the state-space model are presented to show the superiority of the proposed method, alongside a strategy to reduce its computation time.
机译：提出了一种分析组件寿命的网络可靠性的精确方法，其是具有基于矩阵的分布。该方法产生用于可用的不相交产品（SDP）算法的附加算法（SDP）算法，使得它们可以被用来直接从组件可靠性函数的参数计算网络可靠性函数的参数。到目前为止，SDP算法仅用于计算来自其组件的可靠性值的网络可靠性值。优点在于，一旦获得了网络可靠性函数，可以使用其他可靠性措施，例如网络的危险功能，平均故障（MTTF）和失败时间的变化系数（CVTTF）。只有矩阵代数。给出了包含不能表示为SDP的基本结构的通用系统的扩展。该方法适用于相型（pH）和矩阵指数（ME）分布。通过使用pH分布作为其近似来实现方法的适用性。提出了一种基于状态空间模型的方法的应用和比较来示出所提出的方法的优越性，以及降低其计算时间的策略。

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