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Quantification of Sequential Failure Logic for Fault Tree Analysis
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| Reliability Engineering and System Safety |
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Fault tree analysis (FTA) is generally accepted as an efficient method for analyzing system failures. Iit is well known that a fault tree (FT) is equivalent to a minimal cut set fault tree with all minimal cut-AND-structures. The minimal cut-AND-structure is an AND conjunction of an output and all inputs that compose a minimal cut set. For the structure, the failed state of the output becomes true when all failed states of inputs exist simultaneously. There are cases where the output of the minimal cut-AND structure depends not only on all failed states of inputs but also on the sequence of occurrences of those failures. This sequential failure logic (SFL) is equivalently expressed with Priority-AND-gates in FTA, where inputs to the gates have constant failure and repair rates. A probabilistic model for analysis of SFL was proposed and equations with multiple integration for arbitrary number of inputs were derived from the model. However, it is usually difficult to solve the multiple integration when the number of inputs exceeds a certain range. This paper presents analytical solutions of the probability that the output is in a failed state at time t and the statically expected number of failures of the output per unit time at time t for the special case where inputs are characterized by common failure and repair rates. In addition, the analysis of FT involving SFL is demonstrated by means of software Mathematica.
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