Optimal repair and replacement policy for a system with multiple components

Abstract

This thesis formulates and solves a Markov decision problem to find the optimal repair and replacement policy for a system of multiple components whose failure rates are age-dependent. We assume that the failure rate for an old component is higher than for that of a new component. When a component fails, it can either be replaced, making it new, or repaired, making it functional but old. An old component can also be replaced proactively. We formulate the model for a single component as a linear program, and perform parametric analysis on the transition probabilities and system rewards to understand when different policies are optimal. We extend the model to include multiple, independent components, and apply the model to a notional infrastructure network whose performance depends on the state of its network links.