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Constructing Dynamic Event Trees from Markov Models (PSAM-0369)

Excerpt

In the probabilistic risk assessment (PRA) of process plants, Markov models can be used to model accurately the complex dynamic interactions between plant physical process variables (e.g., temperature, pressure, etc.) and the instrumentation and control system that monitors and manages the process. One limitation of this approach that has prevented its use in nuclear power plant PRAs is the difficulty of integrating the results of a Markov analysis into an existing PRA.

In this paper, we explore a new approach to the generation of failure scenarios and their compilation into dynamic event trees from a Markov model of the system. These event trees can be integrated into an existing PRA using software tools such as SAPHIRE.

To implement our approach, we first construct a discrete-time Markov chain modeling the system of interest by: a) partitioning the process variable state space into magnitude intervals (cells), b) using analytical equations or a system simulator to determine the transition probabilities between the cells through the cell-to-cell mapping technique, and, c) using given failure/repair data for all the components of interest. The Markov transition matrix thus generated can be thought of as a process model describing the stochastic dynamic behavior of the finite-state system. We can therefore search the state space starting from a set of initial states to explore all possible paths to failure (scenarios) with associated probabilities. We can also construct event trees of arbitrary depth by tracing paths from a chosen initiating event and recording the following events while keeping track of the probabilities associated with each branch in the tree.

As an example of our approach, we use the simple level control system often used as benchmark in the literature with one process variable (liquid level in a tank), and three control units: a drain unit and two supply units. Each unit includes a separate level sensor to observe the liquid level in the tank and can be in one of three states: operational, failed on, and failed off. We present the results of our analysis of this system.

  • Summary/Abstract
  • Introduction
  • Construction of the Markov Model: The Cell-To-Cell Mapping Technique (CCMT)
  • The Example System
  • The Dynamic Event Tree Generation Algorithm
  • Implementation
  • Conclusion
  • Acknowledgments
  • References

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