On the use of Phase-Type distributions for modelling general distributed events in manufacturing systems

This thesis investigates the application of Phase-Type (PH) distributions for modeling non-exponential repair times when evaluating the performance of manufacturing lines where machines can fail in multiple modes, with analytical techniques. In fact, existing analytical methods for the performance evaluation of manufacturing systems almost always rely on the assumption of exponentially distributed failure and repair times. However, while the assumption of exponential distributions for time to failure is generally verified in real plants, the assumption of exponentially distributed times to repair is not matched, and a modeling approximation is typically introduced. In this thesis, the proper way to characterize Phase-Type distributions to match generally distributed repair times is investigated. The impact of the moments of the repair time distribution on the system throughput is investigated, showing that only the first and the second moment of the distribution have a significant impact on the system production rate. Higher impacts are negligible. This finding simplifies the Phase-Type distribution characterization drastically, since only few alternative PH distributions need to be considered for a proper characterization of all the possible repair events. The advantages of using the characterized set of PH distributions for modeling generally distributed repair times are proved through the application of a PH-compliant performance evaluation method to a real case study in the automotive industry. The results show that the analysis carried out with the use of PH distributed repair time models captures much better the dynamics of the material flow in the system, thus providing a prediction of the performance of the system that is much closer to the system historical data.