Another slight variation of
Case (2) (Section 10.7.1.2) is a series system with nonidentical subsystems,
in which each subsystem's
li/mi < 0.1
The availability of such a system with subsystems whose failures
and repair are statistically independent is:
where:

a_{i} = l_{i}/m_{i} with all a_{i}
<
0.1 n =
number of subsystems in series a_{(system)} = a_{1}
+
a_{2} + ... + a_{n} 
(10.95)

To design such a system, one merely allocates the subsystem
ai’s according to some weighting
scheme. For example, there may be a requirement to design a new system with
higher availability which is similar in design to the old system, where the
relative weighting factors are the same for each new subsystem.
Example 17:
A system consisting of two statistically independent subsystems
has an availability of 0.90. Subsystem 1 has an availability of 0.97, and
subsystem 2 has an availability of 0.93. A new system, similar in design to
this one, must meet a required 0.95 availability. What are the new subsystem
availabilities and ratios of failuretorepair rate?
Since the allocated ratios are known, additional tradeoff
studies can be performed to optimize l_{i}
and m_{i}
for each subsystem.