Stochastic analytical approaches are particularly suitable to design and study engineering systems based on aleatory information, as wind systems are. The present paper provides a stochastic analytical model to evaluate the performance of a wind power plant. The model has been applied to a small isolated wind system. The results obtained indicate a strong influence of wind speed stochastic variability on the minimum production costs turbine size. The results also point out the economic advantage in the use of a stochastic analytical approach in wind system design compared with a design procedure based on system average performances evaluated according to a determinist approach.