This research develops the availability function for a continuously demanded component which is maintained by an age replacement preventive maintenance policy. The availability function, A(t), is a function of time and is defined as the probability that the component functions at time t. The component is considered to have two states: operating and failed. In this policy, the component is repaired or replaced at time of failure. Otherwise, if the component survives T time units, a preventive maintenance service is performed. T is known as the age replacement period or preventive maintenance policy. The component is considered to be as good as new after either service action is completed. A renewal theory approach is used to develop A(t). Past research has concerned infinite time horizons letting analysis proceed with limiting values. This research considers component economic life that is finite. The lifetime, failure service time and preventive maintenance service time probability distributions are unique and independent. Laplace transforms are used to simplify model development. The age replacement period, T, is treated as a parameter during model development. The partial Laplace transform is developed to deal with truncated random time periods. A general model is developed in which the resulting availability function is dependent on both continuous time and T. An exact expression for the Laplace transform of A(t, T) is developed. Two specific cases are considered. In the first case, the lifetime, repair and preventive maintenance times are unique exponential distributions. This case is used to validate model performance. Tests are performed for t→0, t→∞ and for times in between these extremes. Results validate model performance. The second case models the lifetime as a Weibull distribution with exponential failure repair and preventive maintenance times. Results validate model performance in this case also. Exact infinite series for the partial and normal Laplace transform of the Weibull distribution and survivor function are presented. Research results show that the optimum infinite time horizon age replacement period does not maximize average availability for all finite values of component economic life. This result is critical in lifecycle maintenance planning. / Ph. D.