Theoretical and Conceptual Framework - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 17

failure rate. This is considered acceptable when comparing a pipes lifetime measured in years
with repair times counted in hours (Watson et al., 2001).

Tobias and Trindade (1995) describe the NHPP model in two versions:

dM ( t )

b − 1

λ ( ) = = abt

(1) Power relation model: 2.7

dt

c + bt

(2) Exponential model:

λ t ) = e

2.8

In the above equations λ(t) is the pipe failure rate at time t , dM(t) is expected number of
failures between time 0 and t, and a , b , and c are empirically determined parameters from the
historical burst records.

Although the probabilistic aspect of pipe failures have been incorporated in many reliability
studies (e.g., Cullinane et al., 1992; Gargano and Pianese, 2000; Shinstine et al., 2002), the
underlying assumption was that the successive pipe failures can be modelled using HPP with
the constant failure rate, λ . Hence, the Poisson probability distribution, given by Equation 2.6
has been commonly used in reliability model of repairable systems.

2.5 SIMULATION APPROACHES USING DEMAND-DRIVEN MODELS

In the assessment of water network reliability, the simulation approaches that are applied by
manipulating the demand-driven models were firstly used, despite the inability of the
demand-driven algorithm to calculate the demand reduction resulting from the pressure drop
caused by failure. These deficiencies have been coped with by applying an alternative way of
modelling of nodes, for instance as virtual tanks that should supply the demand.

The application is based on simulations of single pipe failures throughout the system. The
effects of the failure of subsequent pipes are analysed by comparing the level of service after
each failure to the one established by setting a threshold pressure under normal operating
conditions. The hydraulic reliability and/or availability can therefore be determined based on
the pressure- or demand deficit in the system. Two of such approaches are elaborated further
in this section.

2.5.1 Reliability Approach Based on Pressure Drop Analysis

In its most rudimentary form, this approach does not quantify the reliability although it
clearly gives an idea about the magnitude of the failure; the drop of the pressure will
obviously be more significant in case of the burst of a major pipe rather than the peripheral
one. On the other hand, such kind of analysis does not require any additional information
next to standard input required for the demand-driven models, which makes it relatively
simple to apply in situations where the network information is scarce.

A method that quantifies reliability by analysing the pressure deficit in the system has been
proposed by Cullinane (1989). According to this method, the nodal reliability can be defined