Date of Award


Document Type


Degree Name

Master of Science


Department of Mathematics and Statistics

First Advisor

James D. Cordeiro, PhD.


This research will examine the optimal maintenance and replacement policies for a generic machine with periodic inspection intervals. The considered reliability models consist of a single machine that can fail during operation or else may be found to be inoperative during regularly-scheduled maintenance inspections. A distinction will be made between spontaneously-occurring failures during operation and those that are discovered during inspections. Since the elapsed time between inspections is constant, the resulting stochastic reliability process becomes non-Markovian, and thus a Semi-Markov Decision Process (SMDP) framework must be employed in order to determine the cost-optimal stationary policy consisting of repair and replace decisions and inspection intervals. Using the methodology developed here, a system controller will be able to readily develop an inspection-based strategy to optimize the overall costs of maintaining systems with a variety of failure characteristics over a finite time horizon

AFIT Designator


DTIC Accession Number


Included in

Mathematics Commons