An efficient real-time method of analysis for non-coherent fault trees

Fault tree analysis is commonly used to assess the reliability of potentially hazardous industrial systems. The type of logic is usually restricted to AND and OR gates which makes the fault tree structure coherent. In non-coherent structures not only components’ failures but also components’ working states contribute to the failure of the system. The qualitative and quantitative analyses of such fault trees can present additional difficulties when compared to the coherent versions. It is shown that the Binary Decision Diagram (BDD) method can overcome some of the difficulties in the analysis of non-coherent fault trees. This paper presents the conversion process of non-coherent fault trees to BDDs. A fault tree is converted to a BDD that represents the system structure function (SFBDD). A SFBDD can then be used to quantify the system failure parameters but is not suitable for the qualitative analysis. Established methods, such as the meta-products BDD method, the zero-suppressed BDD (ZBDD) method and the labelled BDD (L-BDD) method, require an additional BDD that contains all prime implicant sets. The process using some of the methods can be time consuming and not very efficient. In addition, in real time applications the conversion process is less important and the requirement is to provide an efficient analysis. Recent uses of the BDD method are for real time system prognosis. In such situations as events happen, or failures occur the prediction of mission success is updated and used in the decision making process. Both qualitative and quantitative assessment are required for the decision making. Under these conditions fast processing and small storage requirements are essential. Fast processing is a feature of the BDD method. It would be advantageous if a single BDD structure could be used for both the qualitative and quantitative analyses. Therefore, a new method, the ternary decision diagram (TDD) method, is presented in this paper, where a fault tree is converted to a TDD that allows both qualitative and quantitative analyses and no additional BDDs are required. The efficiency of the four methods is compared using an example fault tree library

An efficient real-time method of analysis for non-coherent fault trees

Fault tree analysis is commonly used to assess the reliability of potentially hazardous industrial systems. The type of logic is usually restricted to AND and OR gates which makes the fault tree structure coherent. In non-coherent structures not only components’ failures but also components’ working states contribute to the failure of the system. The qualitative and quantitative analyses of such fault trees can present additional difficulties when compared to the coherent versions. It is shown that the Binary Decision Diagram (BDD) method can overcome some of the difficulties in the analysis of non-coherent fault trees. This paper presents the conversion process of non-coherent fault trees to BDDs. A fault tree is converted to a BDD that represents the system structure function (SFBDD). A SFBDD can then be used to quantify the system failure parameters but is not suitable for the qualitative analysis. Established methods, such as the meta-products BDD method, the zero-suppressed BDD (ZBDD) method and the labelled BDD (L-BDD) method, require an additional BDD that contains all prime implicant sets. The process using some of the methods can be time consuming and not very efficient. In addition, in real time applications the conversion process is less important and the requirement is to provide an efficient analysis. Recent uses of the BDD method are for real time system prognosis. In such situations as events happen, or failures occur the prediction of mission success is updated and used in the decision making process. Both qualitative and quantitative assessment are required for the decision making. Under these conditions fast processing and small storage requirements are essential. Fast processing is a feature of the BDD method. It would be advantageous if a single BDD structure could be used for both the qualitative and quantitative analyses. Therefore, a new method, the ternary decision diagram (TDD) method, is presented in this paper, where a fault tree is converted to a TDD that allows both qualitative and quantitative analyses and no additional BDDs are required. The efficiency of the four methods is compared using an example fault tree library

Analysis of non-coherent fault trees using ternary decision diagrams

Risk and safety assessments performed on potentially hazardous industrial systems commonly utilise Fault Tree Analysis (FTA) to forecast the probability of system failure. The type of logic for the top event is usually limited to AND and OR gates which leads to a coherent fault tree structure. In non-coherent fault trees components’ working states as well as components’ failures contribute to the failure of the system. The qualitative and quantitative analyses of non-coherent fault trees can introduce further difficulties over and above those seen in the coherent case. It is shown that the Binary Decision Diagram (BDD) method can be used for this type of assessment. The BDD approach can improve the accuracy and efficiency of the quantitative analysis of non-coherent fault trees. This article demonstrates the value of the Ternary Decision Diagram method (TDD) for the qualitative analysis of non-coherent fault trees. Such analysis can be used to provide information to a decision making process for future actions of an autonomous system and therefore it must be performed in real time. In these circumstances fast processing and small storage requirements are very important. The TDD method provides a fast processing capability and small storage is achieved when a single structure is used for both qualitative and quantitative analyses. The efficiency of the TDD method is discussed and compared to the performance of the established methods for analysis of non-coherent fault trees

Concerning a Decision-Diagram-Based Solution to the Generalized Directed Rural Postman Problem

Decision-diagram-based solutions for discrete optimization have been persistently studied. Among these is the use of the zero-suppressed binary decision diagram, a compact graph-based representation for a specified family of sets. Such a diagram may work out combinatorial problems by efficient enumeration. In brief, an extension to the frontierbased search approach for zero-suppressed binary decision diagram construction is proposed. The modification allows for the inclusion of a class-determined constraint in formulation. Variations of the generalized directed rural postman problem, proven to be nondeterministic polynomial-time hard, are solved on some rapid transit systems as illustration. Lastly, results are juxtaposed against standard integer programming in establishing the relative superiority of the new technique

Fault Tree Analysis: a survey of the state-of-the-art in modeling, analysis and tools

Fault tree analysis (FTA) is a very prominent method to analyze the risks related to safety and economically critical assets, like power plants, airplanes, data centers and web shops. FTA methods comprise of a wide variety of modelling and analysis techniques, supported by a wide range of software tools. This paper surveys over 150 papers on fault tree analysis, providing an in-depth overview of the state-of-the-art in FTA. Concretely, we review standard fault trees, as well as extensions such as dynamic FT, repairable FT, and extended FT. For these models, we review both qualitative analysis methods, like cut sets and common cause failures, and quantitative techniques, including a wide variety of stochastic methods to compute failure probabilities. Numerous examples illustrate the various approaches, and tables present a quick overview of results

JINC - A Multi-Threaded Library for Higher-Order Weighted Decision Diagram Manipulation

Ordered Binary Decision Diagrams (OBDDs) have been proven to be an efficient data structure for symbolic algorithms. The efficiency of the symbolic methods de- pends on the underlying OBDD library. Available OBDD libraries are based on the standard concepts and so far only differ in implementation details. This thesis introduces new techniques to increase run-time and space-efficiency of an OBDD library. This thesis introduces the framework of Higher-Order Weighted Decision Diagrams (HOWDDs) to combine the similarities of different OBDD variants. This frame- work pioneers the basis for the new variant Toggling Algebraic Decision Diagrams (TADDs) which has been shown to be a space-efficient HOWDD variant for sym- bolic matrix representation. The concept of HOWDDs has been use to implement the OBDD library JINC. This thesis also analyzes the usage of multi-threading techniques to speed-up OBDD manipulations. A new reordering framework ap- plies the advantages of multi-threading techniques to reordering algorithms. This approach uses an abstraction layer so that the original reordering algorithms are not touched. The challenge that arise from a straight forward algorithm is that the computed-tables and the garbage collection are not as efficient as in a single- threaded environment. We resolve this problem by developing a new multi-operand APPLY algorithm that eliminates the creation of temporary nodes which could occur during computation and thus reduces the need for caching or garbage collection. The HOWDD framework leads to an efficient library design which has been shown to be more efficient than the established OBDD library CUDD. The HOWDD instance TADD reduces the needed number of nodes by factor two compared to ordinary ADDs. The new multi-threading approaches are more efficient than single-threading approaches by several factors. In the case of the new reordering framework the speed- up almost equals the theoretical optimal speed-up. The novel multi-operand APPLY algorithm reduces the memory usage for the n-queens problem by factor 50 which enables the calculation of bigger problem instances compared to the traditional APPLY approach. The new approaches improve the performance and reduce the memory footprint. This leads to the conclusion that applications should be reviewed whether they could benefit from the new multi-threading multi-operand approaches introduced and discussed in this thesis