Maintenance accounts for approximately 20% of the operational cost of aircraft; a margin higher than cost associated with fuel, crew, navigation, and landing fees. A significant percentage of maintenance cost is attributed to failures of aircraft components and systems. These failures are random and provide a database which can further be analyzed to aid decision-making for maintenance optimization. In this paper, stochastic mathematical models which can potentially be used to optimize maintenance task intervals of aircraft systems are developed. The initial data for this research are diagnostic variables and reliability parameters which formed the basis for selecting the probability density function for time between failures according to the exponential and Erlang models. Based on the probability density functions, the efficiency of the maintenance processes was calculated using average operational cost per unit time. The results of the analysis were further tested using the Monte Carlo simulation method and the findings are highlighted in this paper. The simulation results compared favorably with analytical results obtained using already existing Monte Carlo techniques to about 82% accuracy. The proposed mathematical optimization models determine the optimal aircraft maintenance task interval which is cost effective while considering safety and reliability requirements; our results can also be applied during the development, design, and operation phases of aircraft systems.