Semi-Markov models with an application to power-plant reliability analysis
Perman, Mihael ; Senegačnik, Andrej ; Tuma, Matija
Systems with finitely many states with random holding times in each state are often modelled using semi-Markov processes. For general holding time distributions, closed formulas for transition ...probabilities and average availability are usually not available. We derive recursion procedures to approximate these quantities for arbitrarily distributed holding times, and then use them to fit the semi-Markov model with Weibull distributed holding times to actual power-plant operating data. The results are compared to the more familiar Markov models and it is found that the semi-Markov model using Weibull holding times fits the data remarkably well. In particular comparing the transition probabilities shows that the probability of the system being in the state of refitting converges rather more quickly to its limiting value as compared to convergence in the Markov model. This may be a consequence of the fact that the distibution of the holding times in this state is rather unlike the exponential distribution. The more flexible semi-Markov model with Weibull holding times provides a more accurate description of the operating characteristics of power-plants, and produces a better fit to the actual operating data.
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