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From CSP models to Markov models

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3 Author(s)
Sorensen, E.V. ; Tech. Univ. of Denmark, Lyngby, Denmark ; Nordahl, J. ; Hansen, N.H.

It is shown how a probabilistic dependability model of a safety-critical system can be derived from a trace-based functional model of the system. The functional model is a communicating sequential process (CSP) that includes command, failure, and repair events. The dependability model is a time homogeneous Markov process with transitions determined by these events. The method applies to deterministic systems that can be described in terms of a finite number of states and in which all event occurrences are stochastic with exponential time distribution. The derivation is carried out in two steps. An algorithmic determination is made of a finite automaton from the specification of the CSP process. The automaton is transformed into a Markov process. The Markov model for this system is used to determine the waiting time to terminal failure. The theory is applied to a larger and more realistic example: a gas burner system operating in the on-off mode. For this system, the waiting time to terminal failure is calculated, and the number of failures per year in a large population of identical, independently operated systems is estimated

Published in:

Software Engineering, IEEE Transactions on  (Volume:19 ,  Issue: 6 )

Date of Publication:

Jun 1993

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