Machine failure is often an important source of variability and so it is essential to model breakdowns in manufacturing simulation models accurately. This thesis describes the modelling of machine breakdown durations in simulation models of engine assembly lines. To simplify the inputs to the simulation models for complex machining and assembly lines, the Arrows classification method has been derived to group machines with similar distributions of breakdown durations, where the Two-Sample Cram´er-von Mises statistic and bootstrap resampling are used to measure the similarity of two sets of data. We use finite mixture distributions fitted to the breakdown durations data of groups of machines as the input models for the simulation models. We evaluate the complete modelling methodology that involves the use of the Arrows classification method and finite mixture distributions, by analysing the outputs of the simulation models using different input distributions for describing the machine breakdown durations. Details of the methods and results of the grouping processes will be presented, and will be demonstrated using examples.