Theoretical and Conceptual Framework - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 13

to develop the relationships between the reliability and entropy. Here, the key question is
what a given level of entropy means in terms of reliability for a given distribution system.

Table 2.3 Approaches for reliability assessment of water distribution systems (Ostfeld, 2004)

Authors Reliability Measure Methodology Applications

ANALYTICAL APPROACHES

Goulter (1987) General overview/trends Overview Overview

Jacobs and
Goulter (1988)

Enumeration of all possible
combinations of working/non-
working system components

State enumeration, filtering
and heuristic procedures

Small illustrative
example

Wagner et al.
(1988)

Connectivity and Reachability Graph theory algorithms

(Rosenthal, 1977;
Satyanarayana and Wood,
1982)

Small illustrative
example

Jacobs and
Goulter (1989)

Redundancy measures arising from
system layout

Integer goal programming AnyTown USA

(Walsky et al., 1987)

Shamsi (1990) Nodal Pair Reliability (NPR): the

probability of two nodes being
connected

Minimal path sets/minimum
cut-sets.

Small illustrative
looped network

Quimpo and
Shamsi (1991)

Idem Idem City of Norwich, state

of New-York
Hydraulic

SIMULATION APPROACHES

Su et al. (1987) Probability of satisfying nodal

demands and pressure heads for
various possible pipe failures

Minimum cut-set Small illustrative

looped network

Wagner et al.
(1987b)

List of Even-Related, Node-
Related, Link-Related and System-
Related

Stochastic (Monte Carlo)
simulation

AnyTown USA
(Walsky et al., 1987)

Bao and Mays
(1990)

Probability of satisfying nodal
demands at required pressure heads

Stochastic (Monte Carlo)
simulation

Small illustrative
looped network

Cullinane et al.
(1992)

Hydraulic availability: the
proportion of time the system
satisfactory fulfils its function -
minimum pressure at consumer
nodes

Hydraulic simulation linked
with non-linear optimisation

Small illustrative
looped network

Fujiwara and
Ganesharajan
(1992)

Expected served demand Markov chain approach Small illustrative

looped network

Xu and Goulter
(1988)

Probability of meeting nodal
demands at, or above, a minimum
prescribed pressure

Two-stage stochastic
assessment based on a
linearised hydraulic model

Small illustrative
example

Shinistine et al.
(2001)

Probability of satisfying nodal
demands and pressure heads for
various possible pipe failures

Minimum cut-set (Su et al.,
1987)

Two large-scale
municipal water
distribution networks,
Tucson Arizona

Weintrob at al.
(2001)

Required demands at acceptable
pressures

Fast stochastic simulation
(Lieber et al. 1999) + a linear
optimisation model

EPANET Example 3
(Rossman, 2000)