Abstract
AbstractFault 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 with 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). An 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 is 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 assessments 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. Copyright © 2008 John Wiley & Sons, Ltd.
Highlights
Fault trees were first developed in the 1960s and are commonly used for the qualitative and quantitative analyses of causes of system failure
The weaknesses of the L-Binary Decision Diagram (BDD) method are the introduction of the three different types of basic events and the requirement for minimisation before obtaining prime implicant sets. These results show that the ternary decision diagram (TDD) method is an efficient method to obtain prime implicant sets, when all prime implicant sets are obtained by performing the conjunction of the two branches of each node
This paper presents procedures by which non-coherent fault trees can be examined and prime implicant sets obtained
Summary
Fault trees were first developed in the 1960s and are commonly used for the qualitative and quantitative analyses of causes of system failure. The analysis of complex industrial systems may produce thousands of combinations of events (minimal cutsets/prime implicants) which can cause system failure. The determination of these failure combinations can be a time-consuming process even on modern high speed digital computers. If the fault tree has many failure modes, the determination of the exact top event probability requires lengthy calculations. For many complex fault trees this requirement may be beyond the capability of the available computers. Approximation techniques have had to be introduced which resulted in loss of accuracy
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