<p>This study aims to enhance the power and efficiency of an axial gas turbine operating in non-deterministic conditions. Additionally, it investigates the influence of randomness stemming from geometrical and operational factors on the turbine’s overall performance. To achieve this, the streamline curvature method is employed to predict and analyze the turbine’s behavior. The geometrical uncertainties include the distribution of stagger angles and the thickness of the trailing edge, both of which affect the blade throat. Additionally, the turbine inlet temperature distribution is regarded as a non-deterministic condition. To model geometrical uncertainties, a beta distribution is employed with the mean and standard deviation in accordance with experimental studies in the literature. The performance map of the gas turbine considering these uncertainties reveals that mass flow rate is the most sensitive parameter, and neglecting the stochastic behavior of the turbine in the cyclic design could result in significant errors in performance prediction. To explore the possibility of eliminating unimportant non-deterministic parameters from robust optimization, sensitivity analysis is performed to calculate the influence of each stochastic parameter on the system randomness using polynomial chaos expansion. It is demonstrated that neglecting even the less significant parameters can inadvertently lead to misleading outcomes in robust optimization. Finally, the combination of the Monte Carlo method and a neural network is used for robust optimization. A novel criterion for robust optimization is introduced, enabling the utilization of the positive effects of uncertainties while mitigating their harmful impact. The performance of this criterion is validated against several existing mathematical benchmarks. Using this novel criterion, robust optimization of turbines results in approximately a 2% increase in the expected power value while decreasing the standard deviation by 7.5%.</p>