Accurately estimating the required tritium breeding ratio (TBR) r in fusion reactor systems is necessary to guide fusion research and development and to assess the feasibility of fusion reactors as a self-sufficient energy source. This is especially true when one considers the limits imposed by the present-day breeding performance of breeder blanket candidates. Studies of this subject have been performed in the past, with particular emphasis on developing appropriate dynamic simulations of the fuel cycle. In the last few years, development of new dynamic and integrated fusion fuel cycle tritium computer codes has moved away from general residence-time models and instead incorporated more comprehensive and realistic models. Furthermore, detailed and rigorous computer codes that model the dynamic retention behavior of individual components inside the fuel cycle, in particular the torus plasma-facing components in a tokamak, have been vastly improved with uncertainties identified.  A more efficient and intuitive methodology for tritium self-sufficiency analyses is developed based on an analytical scheme that makes use of different types of tritium inventories inside the fuel cycle as calculated from detailed numerical simulations. Short-term and long-term tritium inventories are differentiated as well as tritium lost through waste material. Also, the tritium fuel cycle is split into a number of independent tritium migration paths to aid in the development of an integrated tritium balance for which r or other parameters of interest can be solved analytically. Tritium startup requirements are also examined. An important side benefit derived from using the aforementioned methodology is that the uncertainty in r for a given reactor design can easily be calculated from uncertainty ranges characterizing a number of relevant reactor operation and fuel cycle parameters. Maximum tritium inventory limits were considered from safety and operational standpoints. A wide range of parametric studies were conducted with various scenarios to forecast changes in r when the reactor design is modified. For example, it was determined that with most current estimates of the achievable TBR a, ranging from 1.04 to 1.07, a small design window for both the fuel fractional burnup and the downtime of tritium reprocessing components severely limits any proposals for a reactor operating scenario that will be valid for a reasonably paced fusion growth rate.