reliability analysis of regional water distributuion systems
TRANSCRIPT
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
1/8
Reliability analysis of regional water distribution systems
Avi Ostfeld *,1
Civil Engineering Department, Technion Israel Institute of Technology, Haifa 32000, Israel
Received 13 July 2000; received in revised form 14 March 2001; accepted 11 May 2001
Abstract
Reliability analysis of water distribution systems is a complex task. A review of the literature reveals that there is currently no
universally acceptable denition or measure for the reliability of water distribution systems as it requires both the quantication of
reliability measures and criteria that are meaningful and appropriate, while still computationally feasible. This paper focuses on a
tailor-made reliability methodology for the reliability assessment of regional water distribution systems in general, and its appli-cation to the regional water supply system of Nazareth, in particular. The methodology is comprised of two interconnected stages:
(1) analysis of the storageconveyance properties of the system, and (2) implementation of stochastic simulation through use of the
US Air Force Rapid Availability Prototyping for Testing Operational Readiness (RAPTOR) software. 2001 Elsevier Science Ltd.
All rights reserved.
Keywords: Analysis; Network; RAPTOR; Regional; Reliability; Stochastic simulation; Water distribution systems
1. Introduction
This paper focuses on a tailor-made reliability
methodology for the assessment of regional water dis-
tribution systems in general, and on its application to
the regional water distribution system of Nazareth, in
particular.
A water distribution system is an interconnected
collection of sources, pipes, and hydraulic control ele-
ments (e.g., pumps, valves, regulators, and tanks)
aimed at delivering water to consumers in prescribed
quantities and at desired pressures. Such systems are
often described in terms of a graph, with links repre-
senting the pipes, and nodes representing connections
between pipes, hydraulic control elements, consumers,
and sources. The behavior of a water distribution
system is governed by: (1) physical laws that describethe ow relationships in the pipes and hydraulic con-
trol elements, (2) consumer demand, and (3) system
layout.
Reliability in general, and that of a water distribution
system in particular, is a measure of performance. A
system is said to be reliable if it functions properly for a
specied time interval under prescribed environmental
conditions. While the question: ``Is the system reliable?''
is usually understood and easy to answer, the question
``Is it reliable enough?'' does not have a straightforward
response as it requires both the quantication and cal-
culation of reliability measures.
No system is perfectly reliable. In every system un-
desirable events failures can cause a decline or in-
terruption in system performance. Failures are of a
stochastic nature, and are the result of unpredictable
events that occur in the system itself and/or in its envi-
rons.
Reliability considerations for water distribution
systems are an integral part of all decisions regarding
the planning, design, and operation phases. A major
problem in reliability analysis of water distribution
systems is to dene reliability measures that aremeaningful and appropriate, while still being compu-
tationally feasible. Traditionally, reliability is provided
by following certain heuristic guidelines, like ensuring
two alternative paths to each demand node from at
least one source, or having all the pipe diameters
greater than a minimum prescribed value. By using
these guidelines it is implicitly assumed that reliability
is assured, but the level of reliability provided is not
quantied or measured. Therefore only limited con-
dence can be placed in these guidelines, since reliability
is not considered explicitly.
Urban Water 3 (2001) 253260
www.elsevier.com/locate/urbwat
* Tel.: +972-4-8292-782; fax: +972-4-822-8898.
E-mail address: [email protected] (A. Ostfeld).1 D.Sc., Project Manager, TAHAL Consulting Engineers Ltd.
1462-0758/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.
PII: S 1 4 6 2 - 0 7 5 8 ( 0 1 ) 0 0 0 3 5 - 8
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
2/8
2. Water distribution system reliability
Quantitatively, the reliability of a water distribution
system can be dened as the complement of the proba-
bility that the system will fail, a failure being dened
as the inability of the system to supply its consumers'
demand.
Reliability analysis involves three interconnected
stages: (1) identication of measures and criteria to as-
sess system reliability, (2) quantication of the proba-
bilistic nature of the behavior of system components and
consumer demand, and (3) determining the proper en-
vironmental conditions under which the system is de-
signed to operate.
Two distinct types of events can cause a water dis-
tribution system to fail: (1) system components going
out of service (e.g., pipes and/or hydraulic control ele-
ments), and/or (2) consumers' demand (i.e., ow rates at
minimum pressures) exceeding design values.
Three issues are involved in assessing the reliability ofa water distribution system:
(1) Denition of reliability measures. These must be
determined from the consumers' point of view, and
should specify a required level of service (e.g., duration
and frequency of supply interruptions, expected un-
served demand, damage incurred when failure occurs).
(2) Denition of the possible failures considered. Fail-
ure is an event in which the reliability measures dened
in (1) above are not met. Failure can occur either if a
system component fails (e.g., a pipe, valve, pump, tank),
if consumer demand exceeds design demand, or a
combination of both. When analyzing the reliability of a
water distribution system these two types of events and
their possible mutual dependencies should be taken into
account.
(3) Construction of a mathematical model that com-
bines (1) and (2) above. The mathematical model is used
to evaluate the level of system reliability subject to the
measures dened in (1), and the failure distributions
dened in (2).
However, dening reliability measures which are
meaningful and appropriate, while still being of a form
that can be computed eciently, is not an easy task, as
stated by Tanimboh and Templeman (1993, p. 77):
The reliability of a water supply network is a partic-
ularly dicult entity to dene precisely and to mea-
sure. Many dierent denitions have been proposed
in the research literature in the past decade. An un-
fortunate feature of most of the candidate deni-
tions is that the more satisfying and generally
useful the denition is, the more dicult and time
consuming it is to measure quantitatively. Those re-
liability measures which can be calculated easily
seem not to contain the essence of an intuitively
sensible denition of reliability.
Thus, there is no universal measure or method for
calculating the reliability of water distribution systems.
2.1. Literature review
Reliability assessment of water distribution systems,
as in the research literature, can be classied into two
main categories: topological, and hydraulic. Following
is a brief review.
2.2. Topological reliability
Topological reliability refers to the probability that a
given network is physically connected, given its com-
ponents' mechanical reliabilities (i.e., the components'
probabilities to remain operational over a specied time
interval under specied environmental conditions).
Wagner, Shamir, and Marks (1988a) used reachabil-
ity and connectivity to assess the reliability of a water
distribution system, where reachability is dened as theprobability that a given demand node is connected to at
least one source, and connectivity as the probability that
all demand nodes are connected to at least one source.
Shamsi (1990), and Quimpo and Shamsi (1991) used
node pair reliability (NPR), where the NPR measure is
dened as the probability that a specied source node is
connected to a specied demand node.
Measures used within this category consider only the
connectivity between nodes (as in transportation or
telecommunication network reliability models), and
therefore do not take into account the level of service
provided to the consumers during a failure. The exis-
tence of a path between a source and a consumer node,
in a non-failure or once a failure occurred, is only a
necessary condition for supplying required demands.
2.3. Hydraulic reliability
Hydraulic reliability is the probability that a water
distribution system can supply its consumers' demand
over a specied time interval under specied environ-
mental conditions. As such, hydraulic reliability refers
directly to the basic function of a water distribution
system: conveyance of desired water quantities at de-
sired pressures to desired appropriate locations at de-sired appropriate times.
The straightforward way to evaluate the hydraulic
reliability of a water distribution system is through
stochastic simulation (e.g., Bao & Mays, 1990; Fujiwara
& Ganesharajah, 1993; Ostfeld, Shamir, & Kogan, 1996;
Su, Mays, Duan, & Lansey, 1987; Wagner, Shamir, &
Marks, 1988b). A typical stochastic (or Monte Carlo)
simulation procedure, involves generation of random
events out of the mechanical component reliabilities
through random number generators, evaluation of the
resulted events on the system performance, and accu-
254 A. Ostfeld / Urban Water 3 (2001) 253260
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
3/8
mulation of performance statistics (e.g., frequency of
component failures, reduction of pressure at consumer
nodes). The statistics collected depends on what reli-
ability measures are desired. In theory, any index can be
calculated, as long as the appropriate needed data of the
system is available. While stochastic simulation is the
most ``accurate'' way to evaluate the ``true'' reliability of
a system, it is the most expensive and dicult to ex-
trapolate (i.e., a ``black box'') method.
An excellent additional reference summarizing the
state-of-the-art methods for assessing the reliability of
water distribution systems was published by the ASCE
Task Committee on Risk and Reliability Analysis of
Water Distribution Systems (Mays, 1989).
The methodology and application presented here-
after, is a hybrid method of the two: topological and
hydraulic reliability concepts, tailor-made to regional
water distribution systems.
3. Methodology
Regional water distribution systems serve as the hy-
draulic connections (supplying quantities of water at
minimum pressures) between sources (wells, reservoirs),
and inlets to municipal regions. As such, these systems
usually consist of just a few hydraulic control elements,
and may be categorized as ``lumped supplylumped
demand'' models (Wagner, Shamir, & Marks, 1988a). A
lumped supplylumped demand model is comprised of a
single aggregated consumer fed by a single aggregated
storage reservoir and a single aggregated source. The
ability to model a given regional water distribution
system as lumped supplylumped demand is the core of
the methodology presented below.
The methodology consists of two interconnected
stages: (1) storageconveyance analysis of the trade-o
between storage capacity, water delivery capacity, and
annual durations of shortfall, and (2) stochastic simu-
lation using the outcome of (1) through use of the US
Air Force Rapid Availability Prototyping for Testing
Operational Readiness (RAPTOR) software (Carter,
Jacobs, Ochao, & Murphy, 1997).
3.1. Stage 1: Storage conveyance analysis
Damelin, Shamir, and Arad (1972) were the rst to
use the storageconveyance analysis for shortfall esti-
mations of pumping equipment in a lumped supply
lumped demand model.
The basic idea is rather simple: for a given water
delivery capacity and storage pair (either an existing or
design point), a sequence of consumer demands is aimed
to be met from the aggregated source and the aggregated
storage. If at a specic time, the consumer demand is
fully met by the water delivery capacity, then the dif-
ference between the water delivery capacity and the
consumer demand feeds the aggregated storage; if the
water delivery capacity is less than the consumer de-
mand, then the dierence needed to fulll the consumer
demand is supplied from the aggregated storage; if the
aggregated storage plus the water delivery capacity fail
to meet the consumer demand, then a shortfall (and its
duration) is recorded.
Running the consumer demand sequence (historical
or design values) through a grid of storage capacity vs.
water delivery capacity pairs, results in a graph of iso-
reliability lines (or isolines of shortfall durations) for the
system considered. Such a graph for the Nazareth re-
gional water distribution system is shown in Fig. 1.
Point A in Fig. 1 shows the normal water delivery
capacity vs. storage (i.e., no component failure), and
point B, the water delivery capacity vs. storage after a
failure has occurred, that is approximately at an isoline
of four hours of annual shortfall.
The storage conveyance analysis is accomplished as-suming that all system components are functioning, and
therefore constitutes an expression of the ability of the
system to satisfy the consumers' demand, where the only
constraining factor being the required consumption
quantities.
Furthermore, the storage conveyance analysis maps
the present situation (and the future situation if future
demands are considered) of the system on the plane of
water delivery capacity vs. storage, and thus gives only a
deterministic indication of the reliability level of the
system, as the only cause of shortfall is the system's
hydraulic ability and/or the consumers' demand re-
quirements.
Storage conveyance analysis thus does not dene the
``probability distance'' from a given storage conveyance
design point, to a given isoline of shortfall duration
(e.g., the zero line, in Fig. 1), once failures are consid-
ered.
This ``probability distance'', which is a function of the
system redundancy, the system component reliabilities,
and the system maintenance level, is the reliability
quantication of the system. It is ``measured'' using
stochastic simulation based on RAPTOR. This is stage
two of the methodology.
3.2. Stage 2: Stochastic simulation using RAPTOR
RAPTOR (Carter, Jacobs, Ochao & Murphy, 1997) is
a product of the RAPTOR Quality Team within Head-
quarters (HQ) Air Force Operational Test and Evalua-
tion Center (AFOTEC) Logistics Studies and Analysis
Team (SAL). Standing for Rapid Availability Proto-
typing for Testing Operational Readiness, it is a public-
domain stochastic modeling simulation environment for
creation of reliability, availability, and maintainability
(RAM) models. The user models his system graphically
A. Ostfeld / Urban Water 3 (2001) 253260 255
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
4/8
by drawing a reliability block diagram (RBD), com-
prised of reliability blocks connected through ``k-out-of-
n'' intermediate nodes, by answering questions about the
way blocks fail and are repaired, and by dening the k-
out-of-n nodes. As the blocks fail and are repaired during
the simulation time, system-level reliability, maintain-
ability and availability parameters are determined.
A reliability block, the basic unit with which the en-
tire RBD model is established, can be either an oper-
ating reliability block or an event reliability block. An
operating reliability block (in the current model, a pipe,
a pumping unit, a tank, etc.) represents an operating
unit of the system that can fail at any time according to
a time-based failure probability distribution. A random
number is drawn from the entered failure probability
distribution to determine how long such a block will run
before failing. When a block fails, repairs will begin for
that block if a spare unit is available, according to atime-based probability of repair distribution. The block
will resume running when repairs are completed. An
event reliability block is a component that is not time-
dependent. Based on a given success probability, the
block will be determined to be either a success or a
failure at the beginning of each simulation, and remain
in that state for the entire run.
The reliability blocks are connected through k-out-of-
n nodes, a k-out-of-n node being a node where k (out of
n) inlet paths are required in order for the node to be
considered ``up'' (i.e., not in a state of failure).
The denitions of the reliability blocks and the con-
necting k-out-of-n nodes comprise the RBD. The RBD
is the model representation of the system, used for
``measuring'' the ``probability distance'' between an ex-
isting (or planned) water delivery capacitystorage
point, and an iso shortfall line. The ``probability dis-
tance'' is thus the reliability quantication of the system.
3.3. Application
Figs. 17 show the application of the methodology to
the regional water distribution system of Nazareth. Fig.
8 is a sensitivity analysis to the Nazareth water distri-
bution system reliability results, through enlarging of
the mean time to repair (MTTR) data.
Fig. 1 is the shortages analysis diagram (i.e., stage 1
of the methodology), showing the iso shortfall lines for
dierent pairs of water delivery capacity vs. storage forthe monthly ow, peak ow data, and daily consump-
tion pattern (assumed) of the system. Point A in Fig. 1 is
the existing (as of August 1994) water delivery capacity
vs. storage pair, and point B corresponds to about a
four-hour annual shortage recorded after a failure event
occurred in the system.
Fig. 2 is a schematic representation of the Nazareth
regional water distribution system, showing its status as
of August 1994, and expansions as of May 1998. The
sources of the system are the National Water Carrier
and regional wells (e.g., Tel-Adashim wells, Iksal wells).
Fig. 1. Shortages analysis storage vs. water delivery capacity.
256 A. Ostfeld / Urban Water 3 (2001) 253260
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
5/8
The system discharges to the elevated storage tanks of
Nazareth (tanks #1, 2, and 3), from which water is
supplied to the consumers.
Fig. 3 is the RBD schematic for the Nazareth regional
water distribution system, including its design nal stage
expansions. Fig. 3 shows three layers: the rst is
the source layer, the second is the conveyance layer,
and the third is the storage layer. At each node of the
system the k-out-of-n status is dened such that the entire
system is ``up'' for a state of zero annual shortfall. For
Fig. 2. Nazareth regional water distribution system.
Fig. 3. RBD schematic for Nazareth regional water distribution system.
A. Ostfeld / Urban Water 3 (2001) 253260 257
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
6/8
Fig. 5. Snapshot from RAPTOR at a ``Yellow'' run state during stochastic simulation.
Fig. 4. Snapshot from RAPTOR at a ``Green'' run state during stochastic simulation.
258 A. Ostfeld / Urban Water 3 (2001) 253260
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
7/8
example, all three Tel-Adashim wells need to function for
the system to be ``up'', but only three out of the Netofa
and Kana wells. The entire storage of the Nazareth tanks
can be supplied from either the wells or through the
National Water Carrier through Shimshit pumping sta-
tion, making the Nazareth tanks a node of ``1 of 2''.
Fig. 4 is a snapshot from RAPTOR at a ``Green'' run
state during stochastic simulation, where a ``Green''
state is dened as a state in which no blocks in the RBD
are in a failed status.
Fig. 5 is a snapshot from RAPTOR at a ``Yellow''
run state during stochastic simulation, where a ``Yel-
Fig. 6. Snapshot from RAPTOR at a ``Red'' run state during stochastic simulation.
Fig. 8. Sensitivity analysis to the Nazareth water distribution system
reliability results, through enlarging the MTTR data (SA stands for
sensitivity analysis, BR for base run).
Fig. 7. Cost vs. reliability for the Nazareth regional water distribution
system.
A. Ostfeld / Urban Water 3 (2001) 253260 259
-
8/14/2019 Reliability Analysis of Regional Water Distributuion Systems
8/8
low'' state is dened as a state in which some of the
blocks in the RBD are failed, but the overall system is
``up'' (e.g., one of the Netofa wells is down, but since
only three out of four of the Netofa and Kana wells
need to be operational, the entire system is ``up'').
Fig. 6 is a snapshot from RAPTOR at a ``Red''
run state during stochastic simulation, where a ``Red''
state is dened as a state in which some blocks on
the critical path in the RBD are failed, causing the
overall system to be ``down'' (i.e., being in a failure
mode).
Fig. 7 shows the results of running RAPTOR with the
schematic shown in Figs. 46. The system reliabilities
obtained (i.e., the probabilities of zero annual shortfalls)
are: 0.864 as of August 1994, 0.923 for the expansions as
of May 1998, and 0.993 for the nal design stage. The
additional costs for obtaining those reliabilities are: 7.53
million New Israeli Shekels (NIS) (NIS 1US$0.25) for
May 1998, and 43.61 million NIS for the nal design
stage.Fig. 8 shows a sensitivity analysis to the Nazareth
water distribution system reliability results, through en-
larging the MTTR data. The top part of Fig. 8 shows the
time to repair accumulated probability density functions
used: an MTTR of 0.142 days for the base run (BR) (i.e.,
for the original analysis as in Fig. 7), 0.284 days (i.e.,
twice the MTTR compared to the BR), 0.426 and 0.568
days. The bottom part of Fig. 8 shows the results: 0.923
for the BR (i.e., the reference: the reliability of the
Nazareth system as of May 98, see Fig. 7), 0.864 for twice
the MTTR compared to the base run, 0.828 and 0.787 for
MTTR data that are three and four times greater than
that of the BR. As expected, as the MTTR is enlarged,
the reliability of the entire system is reduced.
4. Conclusions
A tailor-made reliability methodology for the reli-
ability assessment of regional water distribution systems
in general, and its application to the regional water
supply system of Nazareth, in particular, was developed
and demonstrated through a base run and sensitivity
analysis.
The methodology is comprised of two interconnectedstages: (1) analysis of the storageconveyance properties
of the system, and (2) implementation of stochastic
simulation through use of the US Air Force RAPTOR
software.
The method contribution is in combining topological
and hydraulic reliability in a single simple straightfor-
ward framework.
As the methodology is basically for water distribution
systems that can be modeled as lumped supplylumped
demand, additional research is needed for extending the
method for more complex cases.
Acknowledgements
This paper is the outcome of a project funded by
the Israeli Water Commission, entitled ``Reliability of
Municipal Water Distribution Systems Theory and
Application'', whose funded support is gratefully ac-
knowledged. The data for the Regional Water Distri-
bution System of Nazareth were obtained by courtesy
of Mekorot Israel National Water Company Co.
References
Bao, Y., & Mays, L. W. (1990). Model for water distribution system
reliability. Journal of Hydraulic Engineering, ASCE, 116(9), 1119
1137.
Carter, Jacobs, J., Ochao, L., & Murphy, K. E. (1997). Rapid
availability prototyping for testing operational readiness (RAP-
TOR). Version 2.99, US Air force, http://www.barringer1.com/
raptor.htm.
Damelin, E., Shamir, U., & Arad, N. (1972). Engineering and
economic evaluation of the reliability of water supply. Water
Resources Research, 8(4), 861877.
Fujiwara, O., & Ganesharajah, T. (1993). Reliability assessment of
water supply systems with storage and distribution networks.
Water Resources Research, 29(8), 29172924.
Mays, L. W. (Ed.) (1989). Reliability analysis of water distribution
systems. In Congress cataloging-in-publication data (pp. 532).American Society of Civil Engineers.
Ostfeld, A., Shamir, U., & Kogan, D. (1996). Reliability assessment of
single and multiquality water distribution systems (pp. 44). Final
Report 015-056. Haifa: The Water Research Institute, Technion.
Quimpo, R. G., & Shamsi, U. M. (1991). Reliability based distribution
system maintenance. Journal of Water Resources Planning and
Management Division, ASCE, 117(3), 321339.
Shamsi, U. (1990). Computerized evaluation of water supply
reliability. IEEE Transaction on Reliability, 39(1), 3541.
Su, Y. C., Mays, L. W., Duan, N., & Lansey, K. E. (1987). Reliability-
based optimization model for water distribution systems. Journal of
Hydraulic Engineering, ASCE, 114(12), 15391556.
Tanimboh, T. T., & Templeman, A. B. (1993). Using entropy in water
distribution networks. In: Coulbeck, B. (Ed.), Integrated computer
applications in water supply (Vol. 1, pp. 7780).Wagner, M. J., Shamir, U., & Marks, D. H. (1988a). Water
distribution reliability: analytical methods. Journal of Water
Resources Planning and Management Division, ASCE, 114(3),
253275.
Wagner, J. M., Shamir, U., & Marks, D. H. (1988b). Water
distribution reliability: simulation methods. Journal of Water
Resources Planning and Management Division, ASCE, 114(3),
276294.
260 A. Ostfeld / Urban Water 3 (2001) 253260