  The present study supposes a single unit and investigates cumulative damage
and catastrophic failure models for the unit, in situations where the
interarrival times between the shocks, and the magnitudes of the shocks,
involve two different stochastic processes. In order to consider two
essentially different stochastic processes, integer gamma and Weibull
distributions are treated as distributions with two parameters and extensions
of exponential distributions. With respect to the cumulative damage models,
under the assumption that the interarrival times between shocks follow
exponential distributions, the case in which the magnitudes of the shocks
follow integer gamma distributions is analyzed. With respect to the
catastrophic failure models, the respective cases in which the interarrival
times between shocks follow integer gamma and Weibull distributions are
discussed. Finally, the study provides some characteristic values for
reliability in such models.
