A New Efficient Reliability Analysis Method for Competing Failure Systems

International Maritime Organization (IMO) implements the principles of risk management through a systematic process called Formal Safety Assessment (FSA). FSA is a structured and systematic methodology, aimed at enhancing maritime safety, including protection of life, health, the marine environment and property, by using risk analysis and cost benefit assessment. One of the most widely used hazard identification and risk analysis techniques in FSA is Fault Tree Analysis (FTA) method. However, only basic conventional methodology of the FTA technique is used in FSA. When dealing with large fault trees, the limitations of FTA in terms of accuracy and the efficiency become apparent. It is necessary for IMO to improve FTA method in FSA. In recent years, the Binary Decision Diagram (BDD) method has been developed that solves fault trees and overcomes the disadvantages of the conventional FTA approach. In this paper, the BDD method is introduced for the application in FSA, as it has never been used in FSA studies. A commonly used construction method and some basic event ordering methods of BDD are described. By applying BDD to FTA, two main issues concerned in FSA, minimal cut set and top event probability, can be obtained efficiently and accurately comparing to the analysis using a conventional FTA method.

Since their introduction in form of a canonical representation of logical functions, the Binary Decision Diagrams (BDDs) gained a wide acceptance in numerous industrial applications. This paper summarizes the properties of BDD representation of Minimal Cut Sets (MCS) of Fault Tree (FT) models most typically encountered in nuclear energetics. Cut sets from MCS are defined as paths from the top BDD node to terminal nodes in the BDD, on which a quantitative and qualitative FT analysis (FTA) is performed. The core of the FTA on the BDDs is performed with help of two fundamental algorithms, one for conditional probability evaluation and another for the selection of cut sets. The accuracy of conditional probability evaluation represents an essential feature for an unbiased quantitative analysis, such as the top event probability or the determination of event importance measures. The cut set selection algorithm is shown in a generic version introducing logical predicates for its selection criteria. As it is known, the efficiency of depicted algorithms depends only on the number of BDD nodes used for the FT representation. In order to appraise the compactness of the BDD representation of FT models, their characteristics have herein been evaluated on several real-life models from the Nuclear Power Plant Krško. The extraordinariness of the compactness of the BDD representation reflects in its ability to implement advanced dynamic analysis (i.e. what-if) of FT models. The efficiency of such an approach is recognized by commercial vendors upgrading their FT Tools to new versions by implementing BDD based algorithms.

Efficient Fault Tree Analysis of Complex Fault Tolerant Multiple-Phased Systems

Introducing Temporal Behaviour into Binary Decision Diagrams

An ordering heuristic to develop the binary decision diagram based on structural importance

Solving dynamic flowgraph methodology models using binary decision diagrams

In this paper, we propose an algorithm to construct the ordered binary decision diagram (OBDD) representing the cut function of a terminal-pair network. The algorithm recognizes isomorphic sub-problems and thus avoids redundant computations. The system reliability could be efficiently computed by the OBDD. Finally, we propose an approach to compute the importance measures for multiple components by traversing the OBDD only once. The correctness and the effectiveness of our approach are demonstrated by experiments on 30 benchmark networks. The experimental results on a 2-by-100 lattice network, which has 2/sup 99/ paths or 10,000 cuts, show an impressive improvement compared to the previous works using the sum of disjoint products method that have exponential complexity. The CPU time of our method, including the calculation of not only the reliability but also the importance measures, for a 100-stage lattice network is only about 0.24 seconds. Thus, this approach is very helpful for the reliability and sensitivity analysis of large networks.

Exact and truncated computations of prime implicants of coherent and non-coherent fault trees within Aralia

Fault trees are a key model in reliability analysis. Classical static fault trees (SFT) can best be analysed using binary decision diagrams (BDD). State-based techniques are favorable for the more expressive dynamic fault trees (DFT). This paper combines the best of both worlds by following Dugan’s approach: dynamic sub-trees are analysed via model checking Markov models and replaced by basic events capturing the obtained failure probabilities. The resulting SFT is then analysed via BDDs. We implemented this approach in the Storm model checker. Extensive experiments (a) compare our pure BDD-based analysis of SFTs to various existing SFT analysis tools, (b) indicate the benefits of our efficient calculations for multiple time points and the assessment of the mean-time-to-failure, and (c) show that our implementation of Dugan’s approach significantly outperforms pure Markovian analysis of DFTs. Our implementation Storm-dft is currently the only tool supporting efficient analysis for both SFTs and DFTs.

Based on the structure and operation mechanism of the dual-stage lithographic system, fault tree analysis for the key subsystem, wafer stage, is performed. Since the system is very complexity, the BDD (binary decision diagram) and DFTA (dynamic fault tree analysis) technique are introduced to make up the disadvantages of the traditional static FTA (fault tree analysis) method. Event “The kinematic accuracy of wafer stage can't meet the goal” is installed as the top event of the fault tree. Central factors affecting the kinematic accuracy of the wafer stage is identified through the study.

A comparison of fault trees and the Dynamic Flowgraph Methodology for the analysis of FPGA-based safety systems part 2: Theoretical investigations

While most of the research efforts on network reliability analysis have focused on networks with imperfect links but perfectly reliable nodes, binary decision diagram–based methods have recently been developed to determine reliability of networks with imperfect links and imperfect nodes. The smaller the binary decision diagram size is, the better the performance of the binary decision diagram–based algorithm will be. The binary decision diagram size heavily depends on the chosen variable ordering. As finding the optimal variable ordering is a nondeterministic polynomial time-complete problem, a heuristic is typically used. Various heuristics based on depth-first search, breadth-first search, and network-driven search have been developed for network reliability analysis. However, they often assume the networks have perfectly reliable nodes. This article advances the state-of-the-art by proposing a new ordering heuristic for the binary decision diagram–based reliability analysis of networks with imperfect links/edges and nodes. Empirical studies show that the proposed new ordering heuristic can generate significantly smaller binary decision diagram size for a wide variety of network structures than the traditional depth-first search–based, breadth-first search–based, network-driven search–based heuristics for most cases, enabling efficient binary decision diagram–based reliability analysis of large-scale networks considering both link and node failures. Robustness of the proposed heuristic is also investigated through empirical studies.

On the Boolean extension of the Birnbaum importance to non-coherent systems

This paper presents a comparative study of availability evaluation of systems modeled by a mixed fault tree (MFT). This MFT contain a static sub-trees and dynamic sub-trees. These sub-trees can be independent or dependent. To evaluate the availability of a system from its fault tree, three methods are applied here: the first uses the classic Bayesian networks (CBN) for static sub-trees and dynamic Bayesian networks (DBN) for dynamic sub-trees, the second being proposed, bases on the binary decision diagrams (BDD) for static sub-trees and dynamic Bayesian networks (DBN) for dynamic sub-trees and the third being proposed uses the binary decision diagram (BDD) for static sub-trees and Markov chains (MC) for dynamic sub-trees . The three methods are compared in both cases; independence and dependence of sub-trees.

This paper presents the computation method for the dependability measure in fault trees when the uncertainty of model parameters is considered. The propagation of uncertainty of model parameters can be estimated by regarding the model parameters as random variables. However, the computation cost of expected values is now so low in such situation. In this paper, we focus on the moment-based approximation method for uncertainty propagation in fault trees. In particular, to obtain the moment-based approximation, we discuss the computation of first and second derivatives of dependability measures in fault trees with BDD (binary decision diagram) representation.