  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.
