  This paper analyses a system subject to multiple dependent degradation
processes. Degradation processes start at random times following a non
homogeneous Poisson process and next dependently propagate. The growth of these
degradation processes is modeled using gamma increments. We assume that the
arrival of a new process to the system triggers the degradation rate of the
processes present in the system. Under this framework, the analytic expression
of the system reliability is obtained and bounds of the system reliability are
also analyzed. Furthermore, the system is inspected at certain times.
Information on the system health is recorded at these inspection times and the
decision on performing maintenance actions on the system is taken at these
times. We consider in this paper a dynamic inspection policy since the
information that becomes available in an inspection time is taken into account
to schedule the next inspection time. The maintenance cost for this system is
dealt with the use of semi-regenerative process. Numerical examples are
performed to illustrate the analytic expressions.
