A quasi-renewal process is more realistic in modeling the behavior of a repairable system than traditional models such as perfect repair and minimal repair since it reflects the deterioration process of the system over time while traditional models do not. The quasi-renewal parameter is set to a value between 0 and 1 to indicate the rate of deterioration. Moreover, a quasi-renewal process can also be used to model the increasing time of maintenance actions due to the increasing difficulty of maintaining an aging system by setting the parameter to a value larger than 1. We construct a model where the operating times follow a quasi-renewal process and the corrective/preventive maintenance times follow another quasi-renewal process. A quasi-renewal function and two equivalent point availability expressions are developed for the model described by a quasi-renewal process with and age-dependent preventive maintenance policy. In addition, numerical results from various theoretical distributions are obtained to illustrate the behavior of the models. The two equivalent point availability functions each contains an infinite sum and must be truncated to obtain a numerical approximation. The two approximated point availability functions form upper and lower bounds on the real value. The bounds are useful for determining the result accuracy, which can be arbitrarily increased by adding more terms to the truncated summation. Our framework provides a new time-dependent availability model for a non-stationary process with a preventive maintenance policy without any cost structure or optimization problem. / Ph. D.