A Markov chain-based approach to model the variance of times-to-failure and times-to-repair in manufacturing systems

The development of manufacturing systems with high level of automation is thrust by high-volume demand for heterogeneous engineered products. The paper focuses on the usage of Phase-type distributions in the description of reliability parameters, both times-to-failure (TTFs) and times-to-repair (TTRs), for a workstation with several failure modes. Differently from classical analytical models based on exponential distributions, the variance of reliability parameters can be exactly captured, allowing a sounder performance evaluation of the production system in which the workstation operates. While state-of-the-art research works adopt single-station models accounting for variance of TTR and/or TTF of a single failure mode, the presented model framework can capture the variance of TTRs and TTFs of all workstation failure modes, or only a portion of them. The formalized approach has been validated against a simulator replicating the workstation behavior, grounding on data acquired from the field. The application on an industrial case study showed the numerical impact of accounting for the actual variance on performance evaluation, exploiting an asynchronous continuous model of two machines-one buffer line, with finite buffer capacity and deterministic processing times. Further developments may concern the integration of the model in Markov chain-based analytical models of longer manufacturing lines.