From CSP Models to Markov Models

  • Authors:
  • Erling Vagn Sørensen;Jens Nordahl;Niels Herman Hansen

  • Affiliations:
  • Technical Univ. of Denmark, Denmark;Technical Univ. of Denmark, Denmark;Technical Univ. of Denmark, Denmark

  • Venue:
  • IEEE Transactions on Software Engineering
  • Year:
  • 1993

Quantified Score

Hi-index 0.01

Visualization

Abstract

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.