Therefore, if there are four channels in parallel, with F ¼ 0.1, we have
F SYST ¼ 10
À4 .
and R SYST ¼ 1 À F SYST gives R SYST ¼ 1 À 0:0001 ¼ 0:9999
The result, therefore, indicates that increasing the number of individual systems
or components in a parallel system increases the overall system reliability, here from
0.9 to 0.9999.
Typically, parallel circuits are used for pumping arrangements to water reservoirs.
In aeroplanes, where it is necessary for landing gear or brakes to operate by all means
(or at all costs, as the expression goes), it not unknown to have more than two circuits
in parallel.
9.6.4 General Series-Parallel System
Figure 9.5 depicts a general series-parallel system, consisting of n identical subsystems in parallel, and each subsystem comprising m elements in series. If R ji is the
reliability of the i
th component in the j
th subsystem, then from Eq. 9.2, the reliability
of the j
th subsystem is
R j ¼ R j1 R j2 . . . R ji . . . R jm ¼
Y i¼m
i¼1
R ji
ð9:7Þ
The corresponding unreliability of the j
th system is
F j ¼ 1 À
Y i¼m
i¼1
R ji
ð9:8Þ
From Eq. 9.5, the overall system unreliability is
R 11
R n1
R 21
R j1
R 12
R 1i
R 1m
R 2m
R 2i
R 22
R n2
R ni
R nm
R j2
R ji
R jm
Fig. 9.5 Reliability of a series-parallel system
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9 Quality and Reliability of Infrastructure