Introduction to Water Infrastructure Asset Management - Global Drinking Water Management and Conservation - page 159

L1

A

Reservoir

L2

Fig. 7.4 Redundancy reduces the probability of failure

PI A ¼ PL ðÞ then PI A PL ð —

2 . Since PL ðÞ 1,

adding the loop has
reduced the probability of interruption. Therefore, Looped Redundancy is better
than No Redundancy.

7.2.3.3 Latticed Redundancy

Prior to introducing the lattice proper, the concept of a multiline loop should be
discussed. Following from the above discussion of Looped Redundancy, we con-
cluded that the probability of interruption decreased once another line was added. It
is obvious that adding a third line would further decrease the probability of inter-
ruption. In fact multiline redundancy can be expressed in generalized form as
PI A ¼ PL ðÞ

n where n represents the number of lines servicing A (see Fig. 7.5 ).
In a multiline system, service to A becomes interrupted if all the lines become
interrupted (experience a failure) regardless of the point at which this occurs. If the
multiline system is expanded to resemble a lattice, then all the lines could expe-
rience failures, yet A may not lose service. The only way that A would experience a
service interruption would be if all the lines experienced a failure at the same zone.
Let P ðÞ

n

1 represent the probability of any given section experiencing a failure.
In a latticed system with n lines of two sections each the probability of interruption
to A is PI

C , where the three stars
denote the latticed system. This probability resembles that of the single line system.
However,

A ¼ PF B þ PF C PF

\ F

B

in the single line system PF ðÞ ¼P ðÞ , and in the latticed system

L1

A Reservoir

L2

Fig. 7.5 Multiline redundancy reduces the probability of failure