In this paper, we introduce a time-continuous production model that enables random machine failures, where the failure probability depends historically on the production itself. This bidirectional relationship between historical failure probabilities and production is mathematically modeled by the theory of piecewise deterministic Markov processes (PDMPs). On this way, the system is rewritten into a Markovian system such that classical results can be applied. In addition, we present a suitable solution, taken from machine reliability theory, to connect past production and the failure rate. Finally, we investigate the behavior of the presented model numerically in examples by considering sample means of relevant quantities and relative frequencies of number of repairs.
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This work has been financially supported by the BMBF project ENets (05M18VMA).
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Knapp, S., Göttlich, S. (2019). A Production Model with History Based Random Machine Failures. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_62
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Print ISBN: 978-3-030-27549-5
Online ISBN: 978-3-030-27550-1