  The reliability of processes with moving elastic and isotropic material
containing initial cracks is considered in terms of fracture. The material is
modelled as a moving plate which is simply supported from two of its sides and
subjected to homogeneous tension acting in the travelling direction. For
tension, two models are studied: i) tension is constant with respect to time,
and ii) tension varies temporally according to an Ornstein-Uhlenbeck process.
Cracks of random length are assumed to occur in the material according to a
stochastic counting process. For a general counting process, a representation
of the nonfracture probability of the system is obtained that exploits
conditional Monte Carlo simulation. Explicit formulae are derived for special
cases. To study the reliability of the system with temporally varying tension,
a known explicit result for the first passage time of an Ornstein-Uhlenbeck
process to a constant boundary is utilized. Numerical examples are provided for
printing presses and paper material.
