The behavior of repairable equipment is often modeled under assumptions such as perfect repair, minimal repair, or negligible repair. However the majority of equipment behavior does not fall into any of these categories. Rather, repair actions do take time and the condition of equipment following repair is not strictly "as good as new" or "as bad as it was" prior to repair. Non-homogeneous processes that reflect this type of behavior are not studied nearly as much as the minimal repair case, but they far more realistic in many situations. For this reason, the quasi-renewal process provides an appealing alternative to many existing models for describing a non-homogeneous process. A quasi-renewal process is characterized by a parameter that indicates process deterioration or improvement by falling in the interval [0,1) or (1,Infinity) respectively. This parameter is the amount by which subsequent operation or repair intervals are scaled in terms of the immediately previous operation or repair interval. Two equivalent expressions for the point availability of a system with operation intervals and repair intervals that deteriorate according to a quasi-renewal process are constructed. In addition to general expressions for the point availability, several theoretical distributions on the operation and repair intervals are considered and specific forms of the quasi-renewal and point availability functions are developed. The two point availability expressions are used to provide upper and lower bounds on the approximated point availability. Numerical results and general behavior of the point availability and quasi-renewal functions are examined. The framework provided here allows for the description and prediction of the time-dependent behavior of a non-homogeneous process without the assumption of limiting behavior, a specific cost structure, or minimal repair. / Ph. D.