Semi-Markov models with an application to power-plant reliability analysis

Systems with, (1) a finite number of states, and (2) random holding times in each state, are often modeled using semi-Markov processes. For general holding-time distributions, closed formulas for transition probabilities and average availability are usually not available. Recursion procedures are derived to approximate these quantities for arbitrarily distributed holding-times; these recursion procedures are then used 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; 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 more quickly to its limiting value as compared to convergence in the Markov model. This could be because the distribution of the holding-times in this state is rather unlike the exponential distribution. The more flexible semi-Markov model with Weibull holding-times describes more accurately the operating characteristics of power-plants, and produces a better fit to the actual operating data.