The present study deals with the performance of irrigation systems under a stochastic environment. A method is developed to calculate yield measures (relative yield and water use efficiency) using either actual or generated daily evapotranspiration and rainfall values along with soil and crop data. A methodology to generate daily evapotranspiration with periodic and stochastic components, utilizing actual daily values, has been developed. The crop yield is dependent on soil, crop and meteorological factors as well as the quantity and quality (uniformity) of the applied water. The level and the variation of yield are used to evaluate risk of failure in water delivery under certain operating conditions. An optimization method is developed to allocate the available water resources to irrigated crops. The results of the study reveal how irrigation activities should be programmed in order to optimize the efficiency of water use. It is debated here that the minimum uniformity levels as recommended in practice should not be generally accepted. A general rule should be that when there are adequate water supplies then it is better if water is applied more uniformly than in cases of low supplies. When water is limited then it is advisable that it is applied `lq proportionally to the crop's sensitivity to water deficits during the specific periods of growth. Variabilities in yield are expected from year to year and their magnitude is higher at low water inputs. High productivities are expected at high water inputs. It is further recommended that the irrigation system capacity should not exceed a certain limit since only minimal increase in output will be expected thereafter. The present analysis can be directly used in planning, design or management of irrigation systems, their distribution part and/or their source.