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Monte Carlo Simulation of Markov, Semi-Markov, and Generalized Semi- Markov Processes in Probabilistic Risk AssessmentA standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.
Document ID
20050202015
Acquisition Source
Johnson Space Center
Document Type
Other
Authors
English, Thomas
(College of the Mainland Texas City, TX, United States)
Date Acquired
September 7, 2013
Publication Date
August 1, 2005
Publication Information
Publication: NASA Summer Faculty Fellowship Program 2004, Volumes 1 and 2
Subject Category
Numerical Analysis
Funding Number(s)
CONTRACT_GRANT: NAG9-1526
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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