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From CSP Models to Markov Models
June 1993 (vol. 19 no. 6)
pp. 554-570

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.

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Index Terms:
probabilistic dependability model; safety-critical system; trace-based functional model; communicating sequential process; time homogeneous Markov process; deterministic systems; event occurrences; stochastic; exponential time distribution; finite automaton; specification; waiting time; terminal failure; gas burner system; communicating sequential processes; fault tolerant computing; finite automata; Markov processes
E.V. Sorensen, J. Nordahl, M.H. Hansen, "From CSP Models to Markov Models," IEEE Transactions on Software Engineering, vol. 19, no. 6, pp. 554-570, June 1993, doi:10.1109/32.232021
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