When a series system consists of N units (with independent unit
availabilities) separately repairable or replaceable whenever the system fails
because of any one unit failing, the steady state availability is given
by:

A = (1 + S
ai)^{1} 
(10.30) 
Caution is necessary in computing a_{i} , since Eq. (10.30) applies
to the availability of the whole system. Thus, when the units are replaceable
as line replaceable units or system replaceable units, the MTTR_{i} is
the mean time required to replace the unit with a good one at the system
maintenance level and is not the mean
repair time of the failed removed unit. On the other hand, if failed units are
not replaced but are repaired at the system level, MTTR_{i} is the
meantimetorepair of the unit, which becomes also the downtime for the
system. Thus, when computing the A_{s} of the
units and the availability As
of the system, all MTTRs must be those
repair times that the system experiences as its own downtime. The
MTTR_{i} of the i^{th} unit is thus the system mean
repair time when the i^{th}
unit fails.
If we compare Eq. (10.30) with Eq.
(10.20) in Model A we find that they are identical. The system maintenance
time ratio (MTR) is: