A semi-Markov model in continuous state and time to study the daily running of turbine has been presented in this paper. The model was used to determine the optimal performance of turbines of Shirorohydro generation station Niger State, Nigeria for a period of 4 years. The result shows that there is no transition from state 1 to state 4, state 2 to state 4 and The result also shows that the graphs of interval transition probabilities from one state to another are gradually increasing. From the virtual transition probabilities, the graph is gradually decreasing and after has the percentages of 99%, 96%, 92% and 99% , which shows that when turbine is in any of the state it stay there for a longer period before transition was made to another state. These results are important information to the engineers and utility staffs to plan against the failure of the turbines.

Keywords : Semi-Markov Process, Continuous Time, Probability, Interval Transition probability, Waiting Time, Holding Time, Turbine, Virtual Transition probability.