
Discrete-Time Instantaneous Availability Models ◾ 205
where A
j
is the approximate instantaneous availability in case t
j
= jh for the system
instantaneous availability A(t):
g
u
[(i–v)h] = g
u(i–v)
.
7.6.2 Discrete Model
Suppose the system consists of n units in a series, among which the failure time of
ith unit X
i
follows the geometric distribution, whereas the repair time after fail-
ure Y
i
follows the general probability distribution. e failure rate function and
repair rate function of every unit are λ(k) = λ and μ(k), respectively. Generally,
in the discrete-time repairable system, the failure can occur in multiple units at
the same time. B ...