Theoretical and Conceptual Framework - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 12

The final outcome of the reliability assessment will be a coefficient that, for given level of
demand, takes the values between 0 and 1. As a consequence, the availability index of a
distribution system will always be higher than its reliability index, as Figure 2.2 shows
(adapted from Tung, 1996). Parallel to the mechanical availability, some researchers express
the hydraulic reliability as the hydraulic availability , pointing to the availability of
(sufficient) demands and pressures in the system.

Next to the concept of availability, several other measures have been proposed as reliability
surrogates at the early stage of computer modelling applications in water distribution, but
none of them sufficiently complete to be universally accepted for reliability analysis. For
instance, the concepts of nodal connectivity and reachability were first applied by Wagner et
al. (1988a) using the algorithms of Satyanarayana and Wood (1982). The nodal connectivity
is defined by the probability that every demand node in the network is connected to at least
one source, while the nodal reachability is the probability that a specified demand node is

connected to at least one source. The corresponding reliability indices consider the pipe
connection and failure rate without running a hydraulic simulation. In reality, a particular
node may not receive any water, due to low supplying heads and/or high energy losses,
although a fully operational path may exist to the water source. For that reason, both methods
lack practical validity and can only be used for initial screening of network geometry.
Furthermore, a concept of network redundancy was discussed by Morgan and Goulter (1985)
and Goulter (1987), which evaluates network reliability by looking for a presence of
independent, hydraulically adequate paths between the source and demand node, which may
be used in case of a failure of the standard supply path. Finally, Goulter et al. (2000),
proposed reliability index referred to as network vulnerability , which is based on economic
consequences of the shortages, related to the frequency, duration, and severity of failure
events.

2.3 CLASSIFICATION OF METHODS FOR RELIABILITY ASSESSMENT

Ostfeld (2004) has classified the approaches to the reliability assessment of water distribution
systems in three groups: (1) analytical- (connectivity/topological), (2) simulation- (hydraulic)
and (3) heuristic (entropy) approaches; these arer summarised in Table 2.3.

Analytical approaches deal with the layout of water distribution network, which is associated
with the probability that a given network keeps physically connected, given its component
reliabilities. These are the approaches linked to the above-mentioned concepts of connectivity
and reachability that are not based on hydraulic simulations.

Simulation approaches deal with the hydraulic reliability and availability. Thus, they analyse
the hydraulic performance of the network, i.e. a conveyance of desired quantities and
qualities of water at required pressure to the appropriate locations at any given time.
Therefore these approaches rely heavily on hydraulic models and require very good
information about the network layout and operation, including the records related to the
component failures. Owing to the availability of powerful computers and software, these are
the most widely explored approaches, nowadays.

Heuristic approaches reflect the redundancy using entropy measure, as a surrogate for
network reliability. Tanyimboh and Templeman (2000) suggested algorithms for maximizing
the entropy of flows for single-source networks and they summarized the existing approaches