Reliability Analysis of Regional Water Distributuion Systems

8/14/2019 Reliability Analysis of Regional Water Distributuion Systems

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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


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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


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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


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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.



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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.



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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.



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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.



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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.

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