A Production Model with History Based Random Machine Failures

  • Stephan KnappEmail author
  • Simone Göttlich
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


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.



This work has been financially supported by the BMBF project ENets (05M18VMA).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of MannheimMannheimGermany

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