Reliability of 2-out-of-N:G systems with NHPP failure flows and fixed repair times
DwyerVincent M.
GoodallRoger M.
DixonRoger
2012
It is commonplace to replicate critical components in order to increase system lifetimes
and reduce failure rates. The case of a general N-plexed system, whose failures are
modeled as N identical, independent nonhomogeneous Poisson process (NHPP) flows,
each with rocof (rate of occurrence of failure) equal to λ(t), is considered here. Such
situations may arise if either there is a time-dependent factor accelerating failures or
if minimal repair maintenance is appropriate. We further assume that system logic for
the redundant block is 2-out-of-N:G. Reliability measures are obtained as functions of
τ which represents a fixed time after which Maintenance Teams must have replaced any
failed component. Such measures are determined for small λ(t)τ, which is the parameter
range of most interest. The triplex version, which often occurs in practice, is treated in
some detail where the system reliability is determined from the solution of a first order
differential-delay equation (DDE). This is solved exactly in the case of constant λ(t),
but must be solved numerically in general. A general means of numerical solution for the
triplex system is given, and an example case is solved for a rocof resembling a bathtub
curve.