This paper examines maintenance planning in multi-unit, identical parallel manufacturing systems using queueing theory. It utilizes birth-death processes and M/M/m//C queueing models to understand system dynamics. The model considers units that fail independently according to a Poisson process, with a maintenance crew able to handle a limited number of units simultaneously. Equations are derived to represent the probability distribution of units in various states (operational, failed, under maintenance). Little’s laws help compute key performance metrics like the average number of failed units, maintenance waiting times, and overall system failure rates. The findings, illustrated through transition rate diagrams, are applied to real-world scenarios with two numerical examples demonstrating the model's flexibility. The paper provides a robust framework for optimizing maintenance planning in parallel manufacturing systems, offering insights for system designers, engineers, and decision-makers in manufacturing industries.
