Maintenance decision-making has emerged as an important area of industrial research. Over the past two decades, maintenance policies have evolved from simple reactive maintenance to complex versions of condition-based maintenance (CBM). A quantitative description of a machine’s health, as found in CBM, is essential to plan maintenance effectively as it helps avoid excessive or insufficient maintenance. In spite of several advancements in the degradation monitoring techniques, most CBM decision-making methods still focus on a single machine system. Maintenance analysis of a single machine provides good insights, but lacks practical applications. In this paper, we develop a continuous time Markov chain degradation model and a cost model to quantify the effects of maintenance on a multiple machine system. An optimal maintenance policy for a multiple machine system in the absence of resource constraints is obtained. In the presence of resource constraints, two prioritization methods are proposed to obtain effective maintenance policies for a multiple machine system. A case study focusing on a section of an automotive assembly line is used to illustrate the effectiveness of the proposed method.