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

ASTRA 3.0: Logical and Probabilistic Analysis Methods

This report contains the description of the main methods, implemented in ASTRA 3.0, to analyse coherent and non-coherent fault trees. ASTRA 3.0 is fully based on the Binary Decision Diagrams (BDD) approach. In case of non-coherent fault trees ASTRA 3.0 dynamically assigns to each node of the graph a label that identifies the type of the associated variable in order to drive the application of the most suitable analysis algorithms. The resulting BDD is referred to as Labelled BDD (LBDD). Exact values of the unavailability, expected number of failure and repair are calculated; the unreliability upper bound is automatically determined under given conditions. Five different importance measures of basic events are also provided. From the LBDD a ZBDD embedding all the MCS is obtained from which a subset of Significant Minimal Cut Sets (SMCS) is determined through the application of the cut-off techniques. With very complex trees it may happen that the working memory is not sufficient to store the large LBDD structure. In these cases ASTRA 3.0 completes the analysis by constructing a Reduced ZBDD embedding the SMCS - using cut-off techniques - thus by-passing the construction of the LBDD. The report also contains few tutorials on the usefulness of non-coherent fault trees, on the BDD approach, and on the determination of failure and repair frequencies.JRC.DG.G.7-Traceability and vulnerability assessmen

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

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

Binary decision diagrams for fault tree analysis

This thesis develops a new approach to fault tree analysis, namely the Binary Decision Diagram (BDD) method. Conventional qualitative fault tree analysis techniques such as the "top-down" or "bottom-up" approaches are now so well developed that further refinement is unlikely to result in vast improvements in terms of their computational capability. The BDD method has exhibited potential gains to be made in terms of speed and efficiency in determining the minimal cut sets. Further, the nature of the binary decision diagram is such that it is more suited to Boolean manipulation. The BDD method has been programmed and successfully applied to a number of benchmark fault trees. The analysis capabilities of the technique have been extended such that all quantitative fault tree top event parameters, which can be determined by conventional Kinetic Tree Theory, can now be derived directly from the BDD. Parameters such as the top event probability, frequency of occurrence and expected number of occurrences can be calculated exactly using this method, removing the need for the approximations previously required. Thus the BDD method is proven to have advantages in terms of both accuracy and efficiency. Initiator/enabler event analysis and importance measures have been incorporated to extend this method into a full analysis procedure

Applications on fault tree analysis in railway power supply systems

Fault tree analysis (FTA) is presented to model the reliability of a railway traction power system in this paper. First, the construction of fault tree is introduced to integrate components in traction power systems into a fault tree; then the binary decision diagram (BDD) method is used to evaluate fault trees qualitatively and quantitatively. The components contributing to the reliability of overall system are identified with their relative importance through sensitivity analysis. Finally, an AC traction power system is evaluated by the proposed methods

Efficient fault tree analysis using binary decision diagrams

The Binary Decision Diagram (BDD) method has emerged as an alternative to conventional techniques for performing both qualitative and quantitative analysis of fault trees. BDDs are already proving to be of considerable use in reliability analysis, providing a more efficient means of analysing a system, without the need for the approximations previously used in the traditional approach of Kinetic Tree Theory. In order to implement this technique, a BDD must be constructed from the fault tree, according to some ordering of the fault tree variables. The selected variable ordering has a crucial effect on the resulting BDD size and the number of calculations required for its construction; a bad choice of ordering can lead to excessive calculations and a BDD many orders of magnitude larger than one obtained using an ordering more suited to the tree. Within this thesis a comparison is made of the effectiveness of several ordering schemes, some of which have not previously been investigated. Techniques are then developed for the efficient construction of BDDs from fault trees. The method of Faunet reduction is applied to a set of fault trees and is shown to significantly reduce the size of the resulting BDDs. The technique is then extended to incorporate an additional stage that results in further improvements in BDD size. A fault tree analysis strategy is proposed that increases the likelihood of obtaining a BDD for any given fault tree. This method implements simplification techniques, which are applied to the fault tree to obtain a set of concise and independent subtrees, equivalent to the original fault tree structure. BDDs are constructed for each subtree and the quantitative analysis is developed for the set of BDDs to obtain the top event parameters and the event criticality functions

Using reliability analysis to support decision making in phased mission systems

Due to the environments in which they will operate, future autonomous systems must be capable of reconfiguring quickly and safely following faults or environmental changes. Past research has shown how, by considering autonomous systems to perform phased missions, reliability analysis can support decision making by allowing comparison of the probability of success of different missions following reconfiguration. Binary Decision Diagrams (BDDs) offer fast, accurate reliability analysis that could contribute to real-time decision making. However, phased mission analysis using existing BDD models is too slow to contribute to the instant decisions needed in time-critical situations. This paper investigates two aspects of BDD models that affect analysis speed: variable ordering and quantification efficiency. Variable ordering affects BDD size, which directly affects analysis speed. Here, a new ordering scheme is proposed for use in the context of a decision making process. Variables are ordered before a mission and reordering is unnecessary no matter how the mission configuration changes. Three BDD models are proposed to address the efficiency and accuracy of existing models. The advantages of the developed ordering scheme and BDD models are demonstrated in the context of their application within a reliability analysis methodology used to support decision making in an Unmanned Aerial Vehicle

Phased mission analysis using the cause–consequence diagram method

Most reliability analysis techniques and tools assume that a system used for a mission consists of a single phase. However, multiple phases are natural in many missions. A system that can be modelled as a mission consisting of a sequence of phases is called a phased mission system. In this case, for successful completion of each phase the system may have to meet different requirements. System failure during any phase will result in mission failure. Fault tree analysis, binary decision diagrams and Markov techniques have been used to model phased missions. The cause–consequence diagram method is an alternative technique capable of modelling all system outcomes (success and failure) in one logic diagram. [Continues.