Boolean Logic Driven Markov Processes Research Articles

A Compositional Semantics of Boolean-Logic Driven Markov Processes

Boolean-logic driven Markov processes (BDMPs) is a prominent dynamic extension of static fault trees to model repairable and complex dynamic systems. While BDMPs are intensively used in an industrial context for dependability analysis of energy systems, its formal semantics has not been systematically treated. To date, BDMPs are defined as a library of the domain-specific dependability-modelling language Figaro, a library that is neither open source nor publicly available. A rigorous semantic underpinning of BDMPs is indispensable for (1) developing BDMP analysis tools and (2) comparing its expressive power to other related reliability modelling languages. This paper presents a formal semantics to BDMPs using Markov automata (MA), an extension of continuous-time Markov chains (CTMCs) with action transitions that can be used to compose complex MA from smaller MA. This enables us to provide a compositional semantics. That is, we express the semantics of each individual BDMP element as an MA and obtain the MA for the entire BDMP by combining the MA of its elements. This makes the semantics comprehensible, for those who are familiar with automata theory, and easily extensible with new BDMP elements, e.g., to model security aspects. After the entire BDMP is considered, the actions in its MA that were used to “glue” the MA of BDMP elements, are ignored. This results in a CTMC that is amenable to exact numerical analysis by, e.g., efficient probabilistic model-checking techniques. We report on a prototypical implementation of our semantics and empirically show that our semantics yields dependability metrics that correspond to the interpretation by the Figaro knowledge base of BDMPs.

Finding the minimal cut sequences of dynamic, repairable, and reconfigurable systems from Generalized Boolean logic Driven Markov Process models

Minimal cut sequences computation is the main objective of qualitative safety analysis of dynamic systems. This article shows first that the existing definitions of minimal cut sequences are not suitable when these systems are both repairable and reconfigurable. A new definition for this class of systems as well as an algorithm to compute these sequences from a safety analysis model, in the form of a Generalized Boolean logic Driven Markov Processes model, are then proposed. These contributions are illustrated on a case study from power industry. Comparison of the obtained minimal cut sequences to those which are yielded by algorithms based on the previous definitions permits to highlight the relevance of the approach.

A Benchmark on Reliability of Complex Discrete Systems: Emergency Power Supply of a Nuclear Power Plant

This paper contains two parts: the description of a real electrical system, with many redundancies, reconfigurations and repairs, then the description of a reliability model of this system, based on the BDMP (Boolean logic Driven Markov Processes) formalism and partial results of a reliability and availability calculation made from this model.

Generalized Boolean logic Driven Markov Processes: A powerful modeling framework for Model-Based Safety Analysis of dynamic repairable and reconfigurable systems

This paper presents a modeling framework that permits to describe in an integrated manner the structure of the critical system to analyze, by using an enriched fault tree, the dysfunctional behavior of its components, by means of Markov processes, and the reconfiguration strategies that have been planned to ensure safety and availability, with Moore machines. This framework has been developed from BDMP (Boolean logic Driven Markov Processes), a previous framework for dynamic repairable systems. First, the contribution is motivated by pinpointing the limitations of BDMP to model complex reconfiguration strategies and the failures of the control of these strategies. The syntax and semantics of GBDMP (Generalized Boolean logic Driven Markov Processes) are then formally defined; in particular, an algorithm to analyze the dynamic behavior of a GBDMP model is developed. The modeling capabilities of this framework are illustrated on three representative examples. Last, qualitative and quantitative analysis of GDBMP models highlight the benefits of the approach.

Modeling standby redundancies in repairable systems as guarded preemption mechanisms

Abstract: This paper proposes an extension of the BDMP (Boolean logic Driven Markov Processes) formalism for enriching its capabilities to model replacement and resumption mechanisms in repairable systems. The implicit assumptions made by the classical BDMP to describe these mechanisms are first highlighted. An analogy between standby redundancies management in critical systems and preemption mechanisms in concurrent systems is then proposed. This permits to formally define an extension of BDMP that allows several replacement and resumption mechanisms be specified. A case study illustrates the benefits of this proposal.

A new formalism that combines advantages of fault-trees and Markov models: Boolean logic driven Markov processes

Abstract This paper introduces a modeling formalism that enables the analyst to combine concepts inherited from fault trees and Markov models in a new way. We call this formalism Boolean logic Driven Markov Processes (BDMP). It has two advantages over conventional models used in dependability assessment: it allows the definition of complex dynamic models while remaining nearly as readable and easy to build as fault-trees, and it offers interesting mathematical properties, which enable an efficient processing for BDMP that are equivalent to Markov processes with huge state spaces. We give a mathematical definition of BDMP, the demonstration of their properties, and several examples to illustrate how powerful and easy to use they are. From a mathematical point of view, a BDMP is nothing more than a certain way to define a global Markov process, as the result of several elementary processes which can interact in a given manner. An extreme case is when the processes are independent. Then we simply have a fault-tree, the leaves of which are associated to independent Markov processes.