Few aircraft engine manufacturers are able to consistently achieve high levels of performance reliability in newly manufactured engines. Much of the variation in performance reliability is due to the combined effect of tolerances of key engine components, including tip clearances of rotating components and flow areas in turbine nozzles. This research presents system analysis methods for determining the maximum possible tolerances of these key components that will allow a turbine engine to pass a number of specified performance constraints at a selected level of reliability. Through the combined use of a state-of-the-art engine performance code, component clearance loss models, and stochastic simulations, regions of feasible design space can be explored that allow for a pre-determined level of engine reliability. As expected, constraints such as spool speed and fuel consumption that are highly sensitive to certain component tolerances can significantly limit the feasible design space of the component in question. Discussed are methods for determining the bounds of any components feasible design space and for selecting the most economical combinations of component tolerances. Unique to this research is the method that determines the tolerances of engine components as a system while maintaining the geometric constraints of individual components. The methods presented in this work allow for any number of component tolerances to be varied or held fixed while providing solutions that satisfy all performance criteria. The algorithms presented in this research also allow for an individual specification of reliability on any number of performance parameters and geometric constraints. This work also serves as a foundation for an even larger algorithm that can include stochastic simulations and reliability prediction of an engine over its entire life cycle. By incorporating information such as time dependent performance data, known mission profiles, and the influence of maintenance into the component models, it would be possible to predict the reliability of an engine over time. Ultimately, a time-variant simulation such as this could help predict the timing and levels of maintenance that will maximize the life of an engine for a minimum cost. / Master of Science