It is an undisputable fact that most systems, upon consistence usage are bound to fail in the performance of their intended functions at a point in time. When this occurs, various strategies are set in place to restore them back to a satisfactory performance. This may include replacing the failed component with a new one, swapping parts, resetting adjustable parts to mention but a few. Any such system is referred to as a repairable system. There is the need to study these systems and use statistical models to predict their failing time and be able to set modalities in place to repair them at least cost to the operator. The main objective of this paper is to analyze data collected on the projectors used for teaching and learning activities in some designated rooms at the Brigham Young University (BYU) under the auspices of the Office of Information Technology (OIT) and help to detect the failure rate of such systems, predict the optimal replacement time for the parts with the view of maximizing the reliability of the systems and finally formulate a cost model that will be used to estimate the optimal cost involve in servicing a failed projector.