![](bg5.png)
Similarly the WSP with two spares does not
necessarily have a lower unreliability than the WSP
with only one spare or even no spare due to the
propagation of global failure. An extreme case is
that the primary is perfect and spare components
only fail globally. Even in case when two spares are
preferred, the system unreliability is influenced by
the order of the two spares and the primary
component. Parameters of component costs, failure
time distributions, and global failure rate should be
estimated. Sensitivity analysis is also required in real
applications.
5 CONCLUSIONS
This paper studies the reliability of a smart grid
system with warm standby spares and the existence
of imperfect fault coverage. For warm standby
sparing, the standby units have different failure rates
before and after they are used to replace the on-line
faulty units. Furthermore a component failure may
propagate through the grid system and cause the
whole system to fail if the failure is uncovered. It is
a challenging task to incorporate imperfect fault
coverage into systems with warm standby spares.
The existing approaches are restricted to special
cases, such as assuming exponential failure
distribution for all the system components or
limiting the number of spares to be one. A BDD-
based approach is proposed and procedures for BDD
construction and system unreliability evaluation are
presented and illustrated. It can work well for warm
standby systems with n-spares having any arbitrary
type of time-to-failure distributions.
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