论文标题

量化BDMP的各种方法

Various Ways to Quantify BDMPs

论文作者

Bouissou, Marc, Khan, Shahid, Katoen, Joost-Pieter, Krcal, Pavel

论文摘要

布尔逻辑驱动的马尔可夫过程(BDMP)是一个可靠性分析模型,该模型定义了连续的马尔可夫链(CTMC)。这种形式主义具有很高的表达力,但是它仍然可以阅读,因为它的图形表示与标准故障树保持接近。 BDMP的大小与IT模型的系统尺寸成正比,而该BDMP指定的CTMC的大小则遭受了指数增长。因此,量化大型BDMP可能是一项具有挑战性的任务。量化它们的最通用方法是蒙特卡洛模拟,但这对于高度可靠的系统可能是棘手的。另一方面,可以使用更有效的方法处理一些BDMP的子类别。例如,无需维修的BDMP可以转化为动态故障树,一种被认为是风暴模型检查器的输入的形式主义,在稀疏矩阵上执行数值计算,或者可以使用FigSeq处理它们的工具,该工具探索了通往故障状态并计算其概率的路径。 BDMP具有维修的BDMP可以通过FIGSEQ(快速捕获的BDMP捕获且完全可修复的行为通过不同的算法求解),以及最近发布并实施的I&AB(发起者和所有障碍)方法,通过I&AB(发起者和所有障碍)方法来解决风险谱PSA的原型版本。该工具仅基于布尔表示,寻找并量化系统的最小切割集,即诱导系统损失的组件故障的最小组合。这允许快速量化具有可修复的组件,备用冗余和其他类型的依赖项的大型模型。所有这些量化方法都已在基准上尝试,该方法的定义是在《火星2017年的《 2017年》研讨会上发布的:核电厂的紧急电源模型。在本文中,在回顾了各种量化方法的理论原理后,我们将它们在基准上的表现进行了比较。

A Boolean logic driven Markov process (BDMP) is a dependability analysis model that defines a continuous-time Markov chain (CTMC). This formalism has high expressive power, yet it remains readable because its graphical representation stays close to standard fault trees. The size of a BDMP is roughly speaking proportional to the size of the system it models, whereas the size of the CTMC specified by this BDMP suffers from exponential growth. Thus quantifying large BDMPs can be a challenging task. The most general method to quantify them is Monte Carlo simulation, but this may be intractable for highly reliable systems. On the other hand, some subcategories of BDMPs can be processed with much more efficient methods. For example, BDMPs without repairs can be translated into dynamic fault trees, a formalism accepted as an input of the STORM model checker, that performs numerical calculations on sparse matrices, or they can be processed with the tool FIGSEQ that explores paths going to a failure state and calculates their probabilities. BDMPs with repairs can be quantified by FIGSEQ (BDMPs capturing quickly and completely repairable behaviors are solved by a different algorithm), and by the I&AB (Initiator and All Barriers) method, recently published and implemented in a prototype version of RISKSPECTRUM PSA. This tool, based exclusively on Boolean representations looks for and quantifies minimal cut sets of the system, i.e., minimal combinations of component failures that induce the loss of the system. This allows a quick quantification of large models with repairable components, standby redundancies and some other types of dependencies between omponents. All these quantification methods have been tried on a benchmark whose definition was published at the MARS 2017 workshop: the model of emergency power supplies of a nuclear power plant. In this paper, after a recall of the theoretical principles of the various quantification methods, we compare their performances on that benchmark.

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