Zhuwaki Application 2017
Zhuwaki Application 2017
Zhuwaki Application 2017
Thesis presented in partial fulfilment of the requirements for the degree of Master of Engineering
in Engineering Management in the Faculty of Engineering at Stellenbosch University
March 2017
Stellenbosch University https://scholar.sun.ac.za
Declaration
By submitting this thesis electronically, I declare that the entirety of the work contained therein
is my own original work, that I am the authorship owner thereof (unless to the extent explicitly
otherwise stated) and that I have not previously in its entirety or in part submitted it for obtaining
any qualification.
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Abstract
Reliable railway infrastructure systems guarantee the safety of operations and the availability of
train services. With an increase in mobility demands, it is increasingly becoming a challenge to
deliver railway infrastructure systems with a sustainable functionality that meets the various
dependability attributes such as reliability, availability, and maintainability. Decisions related to
infrastructure asset management in the railway industry focus on the maintenance, enhancement,
and renewal of assets. This is to ensure that the infrastructure assets meet the required level of
dependability and quality of service at the lowest life cycle costs. The success of these decisions
depends on the effective management of individual assets over their lifetime from the perspective
of a whole systems approach. A whole systems approach offers greater advantages over the
traditional silo approach which lacks integration and coordination in the maintenance and
management of complex cross-functional multi-asset systems. Reliability, when applied to
infrastructure asset management, is a mathematical concept associated with dependability in
which engineering knowledge is applied to identify and reduce the likelihood or frequency of
failures within a system. In addition, it enables a systematic analysis to be performed at various
levels of the railway network to quantify the various dependability attributes of individual
infrastructure assets and their impact on the overall performance of the infrastructure system.
The objective of this study is to develop a scientific approach to model and evaluate the reliability
performance of railway infrastructure systems. This paper presents the development and
application of a holistic reliability model for multi-asset systems that can facilitate and improve
infrastructure maintenance management processes in railway environments. The model is
applied and validated using a practical case study in the context of the Passenger Rail Agency of
South Africa (PRASA). The case study applied to PRASA`s Metrorail network concluded that a
holistic performance assessment method using reliability analysis can assist in improving the
maintenance and management of railway infrastructure assets to guarantee high quality of
service.
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Opsomming
Spoorweg infrastruktuurstelsels waarborg die veiligheid van werksaamhede/bedrywighede
asook die beskikbaarheid van treindienste. Met ’n toename in mobiliteitsvereistes raak dit ‘n al
groter problem/uitdaging om spoorweg infrastruktuur met ‘n volhoubaarhieds-funksionaliteit te
lewer wat die verskeie afhanklikheidskenmerke, soos betroubaarheid, beskikbaarheid en
onderhoudbaarheid. Besluite rakende infrastruktuur batebestuur in die spoorweg-industrie
fokus op instandhouding, versterking en vernuwing van bates. Dit is om te verseker dat die
infrastruktuur se bates die vereiste vlak van betroubaarheid en kwaliteitsdiens by die laagste
moontlike lewensikluskostes handhaaf. Die sukses van hierdie besluite hang af van die effektiewe
bestuur van individuele bates tydens hulle leeftyd van die perspektief van die volledige stelsel-
aanslag. ’n Volledige stelsel-aanslag bied groter voordele in vergelyking met die tradisionele silo-
aanslag waar integriteit en koördinasie ontbreek in die onderhoud en bestuur van komplekse
kruis-funksionele multi-bate stelsels. Daarby is dit moontlik om ’n sistemiese analise uit te voer
by verskillende vlakke van die spoornetwerk om die verskillende betroubaarheidseienskappe van
die individuele infrastruktuur bates en hulle impak op die algehele werksverrigting van die
infrastruktuurstelsel te kwantifiseer. Waar dit infrastruktuur batebestuur aangaan, is
betroubaarheid ’n wiskundige konsep wat geassosieer word met betroubaarheid in die
ingenieurskennis wat toegepas word om die waarksynlikheid en frekwensie van falings binne die
stelsel te identifiseer en te verminder. Die doel van hierdie tesis is om ’n wetenskaplike
benadering te ontwikkel om die betroubaarheidsnakoming van die spoorweg-
infrastruktuurstelsels te modelleer en te evalueer. Hierdie tesis stel die ontwikkeling en
toepassing van ’n holistiese betroubaarheidsmodel voor vir ’n multi-bate stelsel wat die
infrastruktuur instandhoudingsbestuurprosesse in spoorweg-omgewings kan fasiliteer en
verbeter. Die model word toegepas en geldig verklaar deur gebruik te maak van ’n praktiese
gevallestudie in die konteks van Passasier Spoor Agentskap van Suid-Afrika (Passenger Rail
Agency of South Africa (PRASA)). Die gevallestudie wat toegepas is op PRASA se Metrorail
netwerk het tot die gevolgtrekking gekom dat ’n holistiese werksverrigting assesseringsmetode
nodig is wat betroubaarheidsanalises gebruik wat kan bydra tot die verbetering van die
instandhouding en bestuur van spoorweg-infrastruktuurbates om hoë kwaliteit diens te verseker.
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Acknowledgements
Firstly I would like to express my sincere gratitude to my thesis advisor Professor C.J Fourie who
has supported me throughout my thesis with his patience, knowledge, and invaluable guidance.
He consistently allowed this paper to be my own work by providing me with the room to work in
my own way and guiding me in the right the direction whenever he thought I needed it. Without
his efforts, this thesis would not have been successful. I would also like to thank my co-supervisor
Joubert Van Eeden for his invaluable input in my results and constructive suggestions which
contributed immensely to the quality of the work.
I would like to thank the staff at PRASA Western Cape Depot for the support and timeous
assistance in providing the necessary information and feedback that has contributed to the
success of this thesis. To Robert Venter, I thank you for your support in ensuring I connected with
Ayanda Bani, Jaco Cupido, John Mollet, Raymond Maseko and Jaime Mabota from the Engineering
services department. Without their passionate participation and input, this thesis could not have
been successfully completed.
I am particularity grateful to Pieter Conradie from the PRASA Engineering Research Chair at
Stellenbosch University for his continuous encouragement and suggestions throughout the course
of my thesis. To Olabanji Asekun, I thank you for the invaluable support in ensuring that my
academic experience within the research chair was rewarding and fulfilling.
Finally, I must express my very profound gratitude to my parents for providing me with unfailing
support. They have been an important and indispensable source of spiritual support throughout
my years of study and through the process of researching and writing this thesis. This
accomplishment would not have been possible without them.
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Contents
Declaration............................................................................................................................................................................ii
Opsomming..........................................................................................................................................................................iv
Acknowledgements ........................................................................................................................................................... v
Contents ................................................................................................................................................................................vi
1 Introduction................................................................................................................................................................ 1
2 Transportation systems......................................................................................................................................... 7
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8.4 Limitations...................................................................................................................................................... 95
9.2 Recommendations....................................................................................................................................... 97
10 References ........................................................................................................................................................... 99
11.6 Map of Metrorail network for the Western Cape region .......................................................... 116
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List of Figures
Figure 1-1 : Research design and methodology .................................................................................................... 4
Figure 1-2 : Process of model development and validation [27] ...................................................................5
Figure 1-3 : Structure of thesis layout ...................................................................................................................... 6
Figure 2-1 : Railway system structure [30]............................................................................................................. 8
Figure 2-2 : Elements of a railway perway system .............................................................................................. 9
Figure 2-3 : The structure of a point machine [30] ........................................................................................... 10
Figure 2-4 : Elements of an electrified railway system ................................................................................... 11
Figure 2-5 : Generic asset management system components [35]............................................................. 13
Figure 2-6 : Reliability profiles under different maintenance regimes [37]. ......................................... 14
Figure 2-7 : Classification of maintenance processes[39] ............................................................................. 15
Figure 2-8 : General maintenance management process for RFI [5]. ........................................................ 16
Figure 2-9 : Factors influencing maintenance management......................................................................... 16
Figure 2-10 : Components of reliability centred maintenance program [43] ....................................... 17
Figure 2-11 : Conceptual hierarchy for achieving high performance ....................................................... 20
Figure 2-12 : Generic structure of railway infrastructure PIs [46] ............................................................ 21
Figure 2-13 : Interrelationship of RAMS elements[42] ................................................................................... 23
Figure 2-14 : Simplified RAMS analysis according to EN50126 .................................................................. 24
Figure 2-15 : Input and output factors of infrastructure performance [11] .......................................... 25
Figure 3-1 : Basic steps in a system analysis ....................................................................................................... 27
Figure 3-2 : Indenture levels for maintenance analysis for continuous improvement[53]............. 28
Figure 3-3 : Modelling paradigms ............................................................................................................................ 29
Figure 3-4 : Design Structure Matrix (DSM) Example ..................................................................................... 30
Figure 3-5 : An example of a Structural Self-interaction Matrix (SSIM)................................................... 31
Figure 3-6 : Dependability procedures .................................................................................................................. 32
Figure 4-1 : Modelling component to system failure[50]............................................................................... 34
Figure 4-2 : Functional diagram (adapted from Risk Analysis in Engineering: 2006) [51]............. 35
Figure 4-3 : Reliability block diagram showing the two main classes of configuring systems....... 36
Figure 4-4 : Framework for decision support in infrastructure asset management[2] .................... 37
Figure 4-5 : Family-based approach to modelling reliability[5] ................................................................. 38
Figure 4-6 : Reliability and failure rate forecasting procedure (adapted from Pereira [12]) ......... 40
Figure 4-7 : Causes effects and modes of failure ................................................................................................ 40
Figure 4-8 : Bathtub curve for failure studies ..................................................................................................... 43
Figure 4-9 : Stochastic process .................................................................................................................................. 45
Figure 4-10 : Framework for analysis of failure data for reliability evaluations ................................. 50
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Figure 11-4 : Cumulative distribution function for the Weibull distribution and observed values
............................................................................................................................................................................................. 112
Figure 11-5 : Arrival times for the Nyanga-Phillipi corridor ..................................................................... 113
Figure 11-6 : Cumulative failures for the observed and Weibull approximations ........................... 114
Figure 11-7 : Observed vs NHPP power law parameter estimation ....................................................... 114
Figure 11-8 : Cumulative graph of observed vs Weibull for electrical subsystem ........................... 115
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List of Tables
Table 4-1 : Steps in a reliability assessment [69] .............................................................................................. 34
Table 4-2 : Failure categorisation ............................................................................................................................ 39
Table 4-3: Interpretation of the LTT value U [25] ............................................................................................. 52
Table 5-1 : Daily failure logging for signal failures ........................................................................................... 64
Table 5-2 : Classification of infrastructure failure modes.............................................................................. 65
Table 5-3 : Probability of occurrence of the infrastructure failure modes ............................................. 66
Table 5-4 : Matrix to evaluate criticality ............................................................................................................... 66
Table 5-5 : Relationship between level of risk and mitigation measures................................................ 66
Table 6-1: Summary of the test statistic and the recommended modelling distributions. .............. 77
Table 6-2 : Summary of parameter estimation and K-S test ......................................................................... 78
Table 6-3 : Reliability of the railway infrastructure system in the first 14 days of operation........ 80
Table 6-4 : A comparison of the subsystems for the expected and observed number of failures . 83
Table 11-1 : Results from trend test for the Langa-Belhar corridor....................................................... 111
Table 11-2 : Parameter estimation results for the Langa-Belhar corridor .......................................... 112
Table 11-3 : Results from the trend test for the Nyanga-Phillipi corridor ........................................... 114
Table 11-4 : Parameter estimation results for the Nyanga-Phillipi corridor ...................................... 115
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List of Abbreviations
AWS Automatic Warning System
PM Performance measurement
RP Renewal Process
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1 Introduction
1.1 Background
A reliable and sustainable public transport infrastructure sustains the socioeconomic activities of
a country and is the backbone of an effective and efficient public transportation system. Rail
transport is a significant player in providing public transport in South Africa. The national
household transport survey conducted by the Department of Transport of South Africa (DoT SA)
reveals that metro workers were more likely to use trains than buses as their main mode of
transport [1]. However, railway transport is competing with new modes of urban transit
characterised by on-demand transit services and bus rapid transit systems. This is attributed to
various factors related to rapid urbanisation, an ageing infrastructure, and increasingly high
demands from customers for infrastructure service quality and reliability. To respond to these
challenges requires strategies that place railway transport at a competitive edge over other modes
of transport. As a result it puts pressure on railway organisations to be innovative in developing
well-informed maintenance management strategies for their railway infrastructure assets to
guarantee high quality of service. In addition, railway infrastructure assets have high asset value
which makes maintenance efforts highly valuable. Therefore, it is important to determine
intervention policies in railway infrastructure environments that would achieve the required
performance targets at minimum costs [2].
The first of two factors considered to maintain infrastructure quality is the ability to measure the
quality of infrastructure on a continuous basis. Secondly there must be criteria to establish the
appropriate maintenance and management strategies to restore the infrastructure quality when
it falls below acceptable levels. Railway infrastructure assets, however, cover large geographical
areas which presents challenges in the maintenance and management of these infrastructure
assets. Traditionally, the maintenance and management of railway infrastructure assets consisted
of 'blind' periodic inspections on critical maintenance issues based on the knowledge and
experience of maintenance staff [3]. This approach is not consistent and cannot continuously
capture the performance of infrastructure quality over time. In order to operate a system of high
complexity with minimal interruptions, informed decision-making becomes a strategic element in
improving the maintenance and management strategies.
Following the success of a reliability centred approach in various industries, developments in the
railway industry show that railway organisations are adopting this methodology in their
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1.4.1 Scope
The scope of the study focused on the maintenance and management of railway infrastructure
assets in the South African passenger railway industry. The study will develop a reliability
assessment model to evaluate the reliability performance of railway infrastructure assets to assist
in predictions for effective and efficient maintenance planning.
1.4.2 Limitations
The research is limited to the reliability performance assessment of railway infrastructure
systems. The analysis methods and models only considered the reliability performance of
infrastructure assets to reduce the operational expenditure related to maintenance planning and
not profit making. The assessment will only focus on identifying critical infrastructure subsystems
to assist in railway infrastructure asset management. Application of the model to a case study to
verify the applicability of the reliability model in evaluating the performance of railway
infrastructure assets is limited to railway lines with sufficient asset failure data.
The research design shown in Figure 1-2 guided the development of a model for reliability-
informed decision-making by following an inductive and deductive approach. Generally the
inductive and deductive approaches are associated with qualitative and quantitative research
respectively. To build a holistic reliability model requires a thorough definition of the system
boundaries, a rigorous elicitation of the system data and the integration of that data to create a
model. To achieve this a deductive approach was used to generate relationships between system
entities and their attributes according to functional and operational requirements derived from
logical conclusions based on the existing modelling theories. In addition, the deductive approach
was used to build the theoretical frame of reference required for the research through an
extensive literature survey and consultations with maintenance experts from PRASA.
The inductive approach focused on the problem solution by applying the developed reliability
model to a case study using the developed knowledge base and empirical data. The empirical data
consisted of historical asset failure data collected from PRASA Metrorail Information Management
System (IMS) and from a series of interviews and consultations with maintenance experts from
PRASA Metrorail division. By developing coherent ideas governed by the assumptions which align
with the modelling methodology, the inductive and deductive approaches outlined the anticipated
outcomes of the reliability model and provided conclusions on the behaviour of the system. In
addition, the relationship between the theoretical (model) results and the observed values
validated the model for improvements from a reliability-informed perspective.
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Specify
relationships
among variables
Empirical Inductive
Data reasoning
Theory Deductive
Experience reasoning
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INTRODUCTION
Research methodology
Background Research problem Research objectives
and design
TRANSPORTATION SYSTEMS
MODELLING INFRASTRUCTURE
RELIABILITY
CASE STUDY
METRORAIL WESTERN CAPE
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2 Transportation systems
2.1 Transport infrastructure
A transportation system must guarantee the movement of material objects in time and space. The
main function of any transportation process is to move people and goods from one point to
another on time, safely and with minimum negative impact on the environment. The different
modes of transportation processes have distinct functional, service and operational
characteristics which create the core of a mobility system [28]. A mobility system is a collection of
civil transport systems that satisfy the needs of a transportation process. The function of a
transportation system in meeting the demands of a mobility system depends on several socio-
economic factors which are external to the transportation system and its supporting
infrastructure.
There is a substantial difference between the different types of civil transport systems. Surface
transport systems such as rail and road require infrastructure that spans large geographical areas.
Transport infrastructure refers to all the routes and fixed installations that allow for the safe and
timeous circulation of traffic. It follows that an unhealthy transport infrastructure is an obstacle
to achieving the fundamental goals of a transportation process. There are several challenges to
managing transport infrastructure, primarily because once the design and installation is complete
it becomes difficult to modify the initial design of the infrastructure assets. Providing a transport
infrastructure that is resilient enough to keep up with the increasing mobility needs and resource
constraints, depends on maintenance and renewal decisions. Under these circumstances,
infrastructure maintenance and management processes should be efficient and effective to
guarantee functional and reliable civil transportation systems.
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mentioned three distinct subsystems when presenting a maintenance decision support model for
railway infrastructure; the track system, power system and the signalling system. Apart from the
station buildings, marshalling yards and warehouses, the fundamental infrastructure subsystems
that primarily enable the movement of a train between two points are signals, electricals, and the
permanent way shown in Figure 2-1. A brief discussion of the subsystems and their functions
follows.
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2.1.1.2 Signalling
The signalling subsystem is a complex multi-component system comprising hardware and
software systems with a primary purpose of traffic control and maintaining traffic regularity. Due
to the development of high-speed rail, signalling has become an important technological
component in ensuring safety by preventing the occurrence of accidents hence minimising the risk
to passengers [17], [31]. The performance of railway signalling systems is determined by the
correct functioning of a number of subsystems. The major components of a signalling system
include the control centre, track circuit, interlocking system, signals, and point machines. The
signal devices which include the signal lamps, track circuits and point machines are controlled by
the interlocking system [30]. Figure 2-3 shows the structure of point to point machine. Other
important elements of the signalling subsystem include the protection system which contains the
Train Protection Warning System (TPWS) and the Automatic Warning System (AWS). The track
circuit used to establish the occupation of a railway block by a train can detect broken rails. The
control centre manages train scheduling, timetables and assigns speed restrictions (including
both temporary and permanent speed restrictions) for the trains. The interlocking system sends
the commands to the signals, point machines and the protection system.
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Power Transformer
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a fundamental asset on its own as it supports good asset management practices. This is highlighted
by Grigg [34] who defines asset management as 'an information-based process' used for life cycle
asset management. The gathering of information relating to the performance and the condition of
infrastructure assets is an important part of an asset management process. Flintsch & Bryant [35]
highlighted that data collection, data management and data integration are essential parts of an
asset management framework. Collecting asset information provides an understanding of lifetime
characteristics of infrastructure assets. This can assist in quantifying the impact of how planned
interventions on an asset group influence other parts of the infrastructure system. An effective
asset management system must deliver infrastructure outputs with cost savings without the risk
of compromising safety.
The International Union of Railways (UIC) [36] suggested an asset management framework which
identifies the key elements of an asset management system. These key elements of the asset
management system focus on the core decisions and activities that link strategy to the delivery of
the work. To achieve this, there must be mechanisms such as accurate data collection on asset
information. This information is used to develop reviewing mechanisms that can monitor and
improve the effectiveness of the asset management regime in meeting its objectives. Network Rail
[26] emphasised that asset management enables evidence-based decision-making by utilising the
knowledge of how assets degrade and fail to maximise the outputs of maintenance and renewal
interventions. Federal Highway Administration (FHWA)[35] presented an asset management
system with the major elements highlighted in Figure 2-5. These elements which are constrained
by the available budget and resource allocations look at the goals and policies of an organisation.
An inventory of data enables the continuous monitoring of the asset performance. The evaluation
exercise on asset performance informs the short- to long-term plans and project selection criteria
that align with the goals and policy of an organisation.
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Asset Inventory
Budget
Condition Assessment/ Allocations
Performance Prediction
Alternative Evaluation/
Program Optimisation
Short-&Long-Term Plans
(Project Selection)
Programme Implementation
Performance monitoring
(Feedback)
2.2.1.1 Maintenance
Maintenance is defined as a combination of all technical, administrative, and managerial actions
during the life cycle of an asset intended to retain it, or restore it to a state in which it can perform
the required function. Maintenance is primarily needed because of the lack of reliability and loss
of quality over time. This means minimal maintenance will result in excessive failure rates and
poor performing infrastructure assets. The different impacts of maintenance on the reliability
performance of assets is shown in Figure 2-6 .
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Reliability
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 5 10 15 20 25 30 0 10 20 30 40 50
Time (days) Time (days)
1
0.6
Reliability
0.8
0.4 0.6
0.4
0.2
0.2
0 0
0 10 20 30 40 0 20 40 60 80
Time (days) Time (days)
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Maintenance
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An effective maintenance management strategy ensures the successful management of costs and
quality and their relationship to asset performance. Figure 2-9 shows the relationship between
maintenance management, asset performance, and asset maintenance. To manage performance it
needs to be measured, hence performance indicators are utilised to reflect the performance of
complex systems. Quality indicators for asset performance are interpreted through cost and
system effectiveness; these indicators act as decision tools for the different interventions specific
to asset maintenance [42]. To assess if the maintenance management process supports the overall
objectives of the organisation, performance measurement systems are adopted to generate useful
information on the condition of infrastructure assets [41]. Infrastructure performance
measurement systems will be discussed in section 2.3.2.
Asset management
Effectiveness
System
Asset performance
RAMS management
Maintenance
management
Effectiveness
Cost
LCC management
Asset maintenance
Applying the RCM methodology to railway infrastructure systems as part of the RAIL project,
Carretero et al [3] developed an RCM framework that could be applied to railway infrastructure
maintenance. This framework was later adopted by the Spanish railway company (RENFE) and
the German railway company (DB A.G.). Jidayi [24] highlighted the benefits of applying an RCM
approach to railway infrastructure maintenance management which included improvement in
system reliability, availability and, most importantly, a reduction in the life cycle costs of railway
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infrastructure related to safety. Gonzalez et al [9] explicitly modelled the uncertainty that
characterises the deterioration rate of railway infrastructure and developed an optimal
maintenance and repair policy for a railway network using an RCM methodology.
Infrastructure that reliably meets or exceeds the quality of service expectations at low cost is
performing well. From the perspective of an organisation, the reliability of infrastructure is the
likelihood that infrastructure effectiveness will be guaranteed over an extended period. On the
other hand, from the perspective of the customer, reliability is the probability that a service will
be available at least at the specific times during the design life of the infrastructure system.
Infrastructure performance captures the ability to move goods, people, and a variety of other
services that support economic and social activities. In this regard, infrastructure is a means to an
end. The effectiveness, efficiency, and reliability of its contribution to these other ends must
essentially be the measures of infrastructure performance.
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The performance of an asset is a result of an execution of various programs that have an ultimate
goal of improving its performance. These programs include asset management interventions,
maintenance and performance measurement models that can be used to evaluate the impact of
the intervention processes. Infrastructure asset management is an information-based process. As
such, the most common approach in developing these programs utilises empirical evidence
(quantitative data) collected during the investigation of failures. The performance of an asset can
be outlined by four distinct elements which are:
From these distinct elements, it can be observed that capability and efficiency are measures that
are determined and influenced by the design and construction of the infrastructure asset.
Essentially, capability and efficiency reflect the levels to which an infrastructure asset is designed
and built. Reliability, on the other hand, is related to the operation of a component and is
influenced by its ability to remain operational. In some cases, an asset can achieve high reliability
levels but fail to achieve high performance. This occurs usually when the asset fails to meet design
objectives. On the other hand, reliability and availability are the building blocks that ensure high
asset performance. A conceptual hierarchy for an integrated approach to improving performance
by way of focusing on reliability and availability is presented as in Figure 2-11. From the hierarchy,
the role of reliability and availability analysis is put into context. Evidently, it can be seen that the
performance of an asset can be improved through a continuous reliability improvement
programme and can further increase the design life cycle of the infrastructure assets.
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Asset performance
Developing sustainable strategic plans for large complex geographically spread-out technical
systems involves the collection of information, setting goals, changing the goals to specific
objectives and setting up activities that enable the achievement of these objectives. The impact of
the interventions on railway infrastructure assets needs to be quantified to establish their
performance against the operational objectives. To achieve this, the infrastructure assets'
performance is monitored and steered according to the objective of the organisational asset
management strategy. Stenstrom [46] conducted a study to review railway infrastructure
performance indicators that are used by researchers and professionals in the field of railway
infrastructure asset management. The indicators are classified as managerial and infrastructure
condition indicators as shown in Figure 2-12. Managerial indicators provide insight into the
overall system-level performance while condition monitoring indicators are at the component or
subsystem level. Managerial indicators are obtained from computer systems like computerised
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Technical
Perway
Organisational
Signalling
Economic
Electricals
HSE
continuous improvement program in railway operations [48]. A discussion of RAMS and its
influence on infrastructure reliability will be given in the following section.
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“Safety related”
Safety
failure modes
Failure modes
Reliability
Maintainability
Achieved
reliability
Maintenance
support
Operational
reliability
Availability
In order to achieve a dependable system, the external factors that influence RAMS parameters
need to be identified. In railway systems, RAMS is influenced by three conditions: 1) the system;
2) maintenance conditions, and 3) operating conditions. The system conditions are sources of
failures that are introduced internally in the system throughout its life cycle, whereas operating
and maintenance conditions are sources of failures that are introduced during the operations and
maintenance interventions on the system. These three sources of failure can interact with each
other through the internal and external factors of the system and their causes need to be assessed
and managed throughout the life cycle of the system. Figure 2-14 shows a simplified approach to
performing a RAMS analysis which incorporates life cycle costs (LCC) according to the EN50126.
A RAMS analysis is a measurement framework that utilises failure information to develop
probability distributions representing a system’s ability to perform the intended functions. RAMS
techniques can be employed to predict failures in railway infrastructure systems and have been
applied extensively to develop measurement systems for railway infrastructure maintenance
management [12], [42], [50], [51].
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Operation and
environment Reliability analysis Fault Tree Analysis
(FTA)
Analysis of
maintainability Results
• MTTF
LCC analysis
• MTBF
Analysis of • MTTR
availability • MTTM
• MUT
• Failure frequency;
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The main objective of known modelling work in infrastructure reliability evaluations is to assist
management by predicting the consequences of alternative decisions. A challenge to transport
infrastructure managers is how to effectively measure reliability. Reliability of transportation
systems is perceived in terms of travel time reliability from a passenger point of view and system
availability from that of the operator [28]. Restel [54] investigated the impact of infrastructure
type on the reliability of railway transportation systems; the correlation between infrastructure
type and the frequency of failures and failure consequences was highlighted. Reliability theory
utilises failure data in modelling and quantifying system reliability, hence with Restel's [54]
findings and Stenstrom's [11] influencing factors for infrastructure availability, it is possible to
map the occurrence of failures and their consequences to measure system reliability.
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Multicriteria criticality
Routes and lines
analysis
Multicriteria criticality
Line section
analysis
System FTA,FMEA,RCA
FTA,FMEA,RCA,
Subsystem/Assembly
adapted analysis methods
Reliability and
Maintainable item
Maintainability analysis
Figure 3-2 : Indenture levels for maintenance analysis for continuous improvement[53]
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Modelling
Paradigm
Time-driven Event-driven
The methods of fault identification and criticality ranking require decomposing a complex system
into subsystems, noting the relationships between the different subsystems and finally
determining the internal and external factors that impact a system's performance. These physical
interactions between the different subsystems need to be identified, described, and summarised
in a dependency matrix. In a study of critical infrastructure interdependency modelling, Pederson
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et al [58] utilised a dependency matrix to show the dependencies between critical infrastructure
networks and their relative impact. In railway systems, many different fault states can occur
during operation. To assist infrastructure managers and railway undertakings with their safety
management systems, Andreas et al [59] developed a cause-consequence fault state matrix to
describe the complex dependencies between different fault states in railway systems.
The design structure matrix (DSM) is an analysis tool for modelling and can be used for purposes
of decomposition and integration of subsystems. A DSM shown in Figure 3-4 presents the
relationships between the different system components in a compact, visual, and analytical
format. System components are represented by the shaded elements along the diagonal and off-
diagonal marks signify the dependency of one component on another. When the matrix is read
across a row it reveals what other elements in the row it provides to. On the other hand, reading
down a column reveals what other elements in the column an element depends on. In other words,
reading down a column reveals the input source and reading across the row indicates output sinks
[60].
Interpretative Structural Modelling (ISM) is a method for analysing and identifying complex
relationships by breaking down a complicated system between the various systems elements into
a clear hierarchical structure. Singh and Gupta [61] identified critical infrastructure sectors and
their dependencies using the ISM and structural self-interacting matrix (SSIM) to develop
hierarchical relationships among the system elements. The SSIM defines the nature of
relationships between components in a system by establishing whether a relationship exists
between two infrastructures i and j and further determines the direction of association given that
a relationship exists. Figure 3-5 shows an example of an SSIM with 8 elements, the symbols V, A,
X and O show the type of relation that exists between the elements.
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From the SSIM a reachability matrix is developed which is then partitioned into different levels
upon which ISM is used to build a structural model. ISM has been used to evaluate the service
quality of railway passenger trains to guide the improvement process of railway service quality
for passenger trains [62]. These different approaches can be used to identify the dependencies in
modelling the reliability of railway infrastructure systems. The DSM approach presents a
straightforward methodology in comparison to the SSIM. An increase in the number of variables
to a problem or issue increases the complexity of the ISM methodology [63]. The DSM will be used
in the study to highlight the infrastructure dependencies in railway infrastructure environments.
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presentation of failures and faults (along with their combinations) of the components of the
system which are detrimental to one of the dependability attributes (reliability).
Validation
Functional Qualitative Quantitative
criteria and
analysis analysis analysis
conclusions
• Data colection. • Objectives of the • Dependability • Identifying critical
• Functional and dependabilty study. measure components
technical • Qualitative analysis • Sensitivity studies • validate results
characteristics. methods. • Validation
• Resolution levels
• Modelling of system
dependability.
Quantitative analysis is concerned with characterising the system dependability with measures
such as probability. The probabilities can be obtained from mathematical statistical modelling
which utilises probability failure distributions derived from information collected during
elementary events within the system. A quantitative analysis identifies the strong and weak points
of the system, the critical components, and the level of dependability that the system carries.
Information of a quantitative nature apart from dependability data includes operating time,
characteristics of preventative and corrective maintenance, and the statistical data about severe
environmental conditions. There is some degree of uncertainty that comes with collecting failure
data of a system. Validating the developed model integrates the outcomes of the quantitative and
qualitative analysis. This process will draw conclusions and establish the failures and the
combinations that influence the dependability of the system as well as identifying the most critical
components and the most important functions of a system.
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4 Reliability theory
To develop a substantive reliability model requires a study of reliability theory and the different
modelling methodologies that can be employed in modelling railway infrastructure systems. This
section presents the concepts involved in reliability modelling and the methodologies to study the
failure processes in railway infrastructure systems. Repairable systems theory applicable to
railway infrastructure systems is presented together with the appropriate statistical theory
required to develop reliability models for railway infrastructure systems.
The goal in a reliability analysis is to obtain an understanding of the system's likely behaviour by
calculating the different performance measures. The performance measures are often presented
as indices to aggregate information on the frequency of failure scenarios and their respective
consequences. Quantitative reliability assessments emphasise the importance of estimating
probabilities of failures. The probabilities can be used as a measure to estimate the effect of a
component's performance towards a system's unreliability. Reliability systems analysis follows a
stochastic approach where the objective is to obtain failure information for the entire system
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based on the failure information of the systems components as shown in Figure 4-1. The
quantitative assessments are then used to inform asset management decisions [68].
Component 1 Component 2
Weibull (λ,α) Lognormal(ν,τ)
SYSTEM A
F(t), MTTF,…...
Component 3 Component 4
Normal(μ,σ ) Exponential(λ or MTBF)
1. System configuration Determine the basic functional List of functional blocks, function ,
definition blocks for the infrastructure system input , output, etc.
and dependencies among
components
5. Results and analysis Simulation results calculation Results of parameters and reliability
functions of interests
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Figure 4-2 : Functional diagram (adapted from Risk Analysis in Engineering: 2006) [51]
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function. A structure function is used to map the state of the components to that of the system. A
basic characteristic of all functional systems is coherence. A system can be described to be
coherent if all components that constitute it are relevant and if its structure function is monotone
[57]. Two main classes exist that combine system components into a structure; a series structure
and a parallel structure. Complex configurations use a combination of both series and parallel
structures. A series structure only functions if and only if all n components in that configuration
are functioning, whereas for a parallel structure, the system can function if one out of the n
components is functioning [70]. The configuration of a series and a parallel system are shown in
Figure 4-3.
Series system
Parallel system
Figure 4-3 : Reliability block diagram showing the two main classes of configuring systems
The equations that are used to evaluate the system reliability of series and parallel configurations
are given in equation 4.1 and 4.2 respectively
n
Rs ( t ) = ∏ Ri ( t )
R1 ( t ) ⋅ R2 ( t ) .....RN ( t ) =
i =1
[4.1]
n
Rs ( t ) = 1 − ∏ Ri ( t )
R1 ( t ) ⋅ R2 ( t ) .....RN ( t ) = [4.2]
i =1
At the heart of any prediction, the problem is to select a suitable model structure. A model
structure is a parameterised family of candidate models of some sort, within which the search for
a model is conducted. A basic rule in estimation is not to estimate what you already know. In other
words, one should utilise prior knowledge and physical insight about the system when selecting
the model structure [71]. The decision as to whether to take the black-box or white-box approach
is determined by the correct use of reliability engineering theory. Valenzuela [57] highlighted a
white-box versus black-box dichotomy where the distinction is based on whether the failure
process of a system is modelled with or without the explicit recognition of individual components
that comprise the system. A component refers to the elementary building block of a white-box
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system model. These correspond to the lower level entities if the models are developed
hierarchically. Black-box models are constructed by correlating input measurables with output
observables where parameters of various models are estimated. In reliability modelling, the
primary goal is the most accurate replication of data, which makes a black-box modelling
approach useful.
A model structure was presented by Rama and Andrews [2] in developing a holistic approach to
infrastructure asset management. The model structure utilised a modelling approach that
supported a multi-asset system by developing a framework to support informed decision-making
in railway infrastructure asset management. Figure 4-4 shows a generic framework for modelling
infrastructure life cycle costs (LCCs) railway infrastructure assets with two elements, the
infrastructure state model, and the cost model. Using the infrastructure state model and the cost
model, performance parameters can be estimated by studying the effects of changes in individual
assets and how those changes are cascaded to the rest of the infrastructure system.
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• Hub stations
RAILWAY LINE • Series logic
• Tracks and stations along the line
MODELLING • MSS logic
• Alternative transport routes
RAILWAY ITEM
MODELLING • Families of real railway items (placed within the track • Series logic
The reliability modelling approaches that have been presented prove that several analytical
methods can be applied to evaluate the reliability of the railway infrastructure systems. Holistic
models that have been presented accounted for the functional and operational characteristics of
the infrastructure assets. These models, however, do not consider the common role of humans
who execute the different processes required for effective asset management. Felice and Petrillo
[72] proposed a methodological approach to improving railway transportation systems' reliability
based on FMECA and human reliability analysis (HRA). This integrated approach seeks to consider
the inherent complexity of human influence in improving system reliability. HRA provides a
comprehensive logical analysis of factors influencing human performance, which enables
recommendations for system improvement and prioritises attention on critical tasks that may
jeopardise system reliability.
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Significant Cancellations
Major Delays
Failures in a railway network occur in different parts of the network and may only be studied
together within comparable parameters. In that case when failures are recorded the criteria on
the infrastructure and impact on traffic must be provided [12]. Esveld [73] suggested that failure
data should be grouped into comparable sets by presenting guidelines on the process of recording
failures. Furthermore, when collecting failure data it is important to highlight each failure mode
separately. A failure mode is an effect by which a failure is observed. There is a difference between
failure causes and failure modes. Failure causes of a component are failures of that part whereas
failure modes are the tangible effects that these failures produce on the functions of the asset.
More significantly it must be noted that failure modes have a direct impact on system reliability
in terms of the probability of occurrence of the failure modes. Additionally, failure modes depend
on the response time to restore a system into safe mode and the maintenance support for effective
and safe maintenance procedures.
When analysing system reliability, particularly that of railway infrastructure which has a complex
configuration, it is required to critically ascertain the root cause of infrastructure failures and their
effects in order to understand the nature and occurrence of system failures. Studying railway
infrastructure failure modes assists in assessing the impact of infrastructure defects on the
performance of the network. McNaught [14], Jidayi [24] and Brinkman [47] identified and
categorised critical railway perway failure modes. The failure modes identified that have
secondary effects on the infrastructure system include rail breaks, faulty block joints, and
pantograph hook-ups. Hassankiade [74] performed a failure analysis of railway switches and
crosses and identified the critical failure modes in railway signalling infrastructure based on
historical data and failure frequency. Saba [50] presented a hazard log list showing the different
failure interfaces between the electrical, signalling and perway railway infrastructure subsystems.
Patra and Kumar[75] also performed an availability analysis on a railway track circuit and
highlighted rail breaks and rail joint failure as one of the most critical failure modes.
The study of failure processes of complex systems can be defined either as failure-based reliability
approach or as degradation-based approach. The random variable of interest in a reliability-based
approach is the failure time of components while degradation-based models are interested in the
remaining useful life of components [57]. A failure-based reliability approach will be the focus of
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this study. Figure 4-6 shows a typical process to be followed when performing a failure-based
reliability study. It can be seen that the first step to a successful reliability evaluation is
establishing the system characteristics and related failure modes.
Figure 4-6 : Reliability and failure rate forecasting procedure (adapted from Pereira [12])
Component Functions
FMEA can be extended to classify potential failure effects according to their severity and criticality
to become FMECA (Failure Modes, Effect, and Criticality Analysis). FMECA documents the
catastrophic and critical failures in a system. Identifying these critical and catastrophic failures
implies that the criticality of the consequence and severity of the failure in a system can be
established. The fundamental objective of a criticality assessment is to determine the failure
modes on the basis of their consequence and the probability of occurrence. Using the FMECA, the
successful assessment of asset criticality is achieved by utilising two common methods which are
the Risk Priority Number (RPN) technique and the Military standard technique (MIL-STD-1629).
The RPN technique calculates the risk priority number which is based on the probability of the
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failure occurrence (Or), the severity of its effects (Sr) and the detectability (Dr) of the failure [66].
Failures that score high RPN values are areas of greatest risk requiring their causes to be
minimised.
RPN = Or × Sr × Dr [4.3]
The military standard technique (MIL-STD-1629) categorises and prioritises failure modes
according to severity so that the appropriate interventions can be recommended and it looks at
two types of criticality analysis; qualitative and quantitative. Qualitative criticality analysis looks
at the severity of the potential effects of failure and the likelihood of occurrence for each potential
failure mode. A criticality matrix is developed to identify and compare each failure mode with all
other failure modes with respect to severity [76]. Quantitative criticality analysis considers the
reliability or unreliability of system components at a given operating time and identifies the
portion of the component's reliability that can be attributed to each potential failure mode.
Saba [50] utilised FMECA to develop a RAMS program for railway infrastructure identifying failure
modes and potential hazards within the infrastructure system. To identify the potential hazards,
two common methods were found in literature which are the preliminary hazard analysis (PHA)
and the Hazard and Operability analysis, which place priority on hazards and not on failure [41].
Preliminary hazard analysis (PHA) utilises pre-existing experience or knowledge of a hazard or
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failure to identify potential hazards and events that might cause harm. On the other hand, the
Hazard and Operability Study (HAZOP) is a rigorous analysis method that utilises guide words to
identify potential deviations from a system's normal operating conditions. The guide words
utilised describe functional losses at system and subsystem level. PHA and HAZOP are more useful
when applied to safety analysis than to reliability evaluations, but they can apply in the initial
stages of reliability studies to understand failure modes and unwanted events that led to those
failures.
Fault Tree Analysis has been extensively used to evaluate the reliability, assess the failure effects,
and investigate the impact of maintenance practices on railway electrical systems [19], [20], [79],
[80]. Fault Tree Analysis (FTA) is a diagnostic tool used to predict the most likely failure to cause
system breakdown. In a systematic way, the combination(s) of conditions required for an event to
occur are delineated by identifying how failure-related events at the higher level are caused by
events at the lower level, known as 'primary events'. The results from an FMEA analysis can be
used as an input for performing FTA methods. However, when Fault Tree Analysis is compared
with FMEA/FMECA, it can be seen that an FTA predicts the causes for usually known problems. In
contrast, FMEA/FMECA methods systematically predict new problems and their causes. In other
words, the FTA identifies part failure as a cause of functional failure whereas FMEA/FMECA
identify functional failure as a result of part failure. For all the above-mentioned techniques, it is
worth noting that the best performance of the methodologies is achieved when the techniques are
used properly for a particular requirement at a specific stage within the framework of modelling
and quantifying railway infrastructure reliability.
Generally, a failure rate function exhibits a bathtub shape often referred to as the bathtub curve
shown in Figure 4-8. A bathtub curve displays three distinct phases in a component's life cycle as
it is a superposition of three different failure distributions. The curve in the early failure region,
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also known as 'infant mortality region', exhibits a decreasing failure rate which can be attributed
to design defects or the period of adjustment for interacting components in a system. The constant
failure rate region referred to as the 'useful life' is a period in the life cycle characterised by
random failures of the component likely caused by random events resulting from external factors
and other unavoidable loads. The 'wear out' region in contrast to the early lifetime region exhibits
an increasing failure rate characterised mainly by complex ageing and degradation processes.
Not all components exhibit the bathtub-shaped failure rate curve. Mechanical components do not
show a constant failure rate region but rather exhibit a gradual transition between the early
failure rate and wear out stages [65]. Electrical devices exhibit a relatively constant failure rate
distribution. The distributions in the wear out curve are believed to be the dominant failure
distributions in most components. Failure rates grow with the load for railway infrastructure
components. Jorge et al [12] in the study of the failure of railway infrastructure, recommended the
use of a formula with non-constant failure rate. When working with variable failure rates it is of
little value to consider the actual failure rate since only reliability and MTBF are meaningful. The
non-constant failure rate is often used when working with reliability and MTBF directly because
it does not require knowledge of the actual failure rate of the components. Performing an
analytical calculation when dealing with non-constant failure rate will result in extremely
complicated functions. As a result, several expressions and statistical models can be written and
assigned to non-constant failure rate using empirical datasets.
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The Renewal Process (RP), Homogeneous Poisson Process (HPP), and Non-Homogeneous Poisson
Process (NHPP) are the general stochastic processes employed in analysing the reliability of
repairable systems. A stochastic point process is a mathematical model for a physical phenomenon
characterised by highly localised events distributed randomly in a continuum [81]. RP methods
analyse data on the assumption that the times between failures are independent and identically
distributed in the time domain. This assumption makes the RP appropriate for non-repairable
systems. In scenarios where the RP is applied to repairable systems the assumption that the repair
returns the system to 'as good as new' is taken [82]. When the HPP and NHPP are applied to
repairable systems the continuum is the time and the highly localised events are failures or repairs
which occur at instants within the time continuum. Figure 4-9 represents a portion of a sample
path of a stochastic point process representing successive failures of a single system. The failure
rate of the process is the instantaneous rate of change of the expected number of failures with
respect to time, which means it is a failure rate of the process that measures wear-out of the
system.
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When dealing with reliability evaluations for repairable systems Basile et al [81] posed two
assumptions: 1) the system will be operated wherever possible; and 2) repair times are negligible.
Reliability evaluations of repairable systems study the process of failures and repairs of a system.
Typically times between failures will be neither independent nor identically distributed. As a
result, in reliability analysis, the time is measured in terms of the operating time between failures
ignoring repair times [82]. O’ Connor [83] supports this when recommending the use of time-
based failure distributions stating that replacement or repair times are usually small as compared
with standby or operating times hence is it is feasible to assume that the failure of the component
is independent of its repair actions.
are two functional parametric NHPP models that have been highlighted in literature [25] [14][81];
the log-linear model and the power law model. When dealing with repairable systems the focus is
on predicting the probability of system failure, the expected number of failures, the probability
structure of time between failures and the probability structure of the time to failure as a function
of system age [82]. The equations related to the NHPP for the power law and log-linear law to
determine these parameters are given as follows.
Reliability
(
− λ T2 β −T1β )
R ( T1 , T2 ) = e [4.6]
T2 − T1
MTBF2 (T1 , T2 ) = [4.7]
λ (T2 β − T1β )
Reliability
(
− eα0 +α1T2 − eα0 +α1T1 )
R (T1 , T2 ) = e α1
[4.10]
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α1 (T2 − T1 )
MTBFlog (T1 , T2 ) = e α 0 +α1T2
[4.11]
e − eα 0 +α1T1
t −γ
−
F ( t,θ , γ )= 1 − e θ
[4.12]
t −γ
1 − θ
f ( t,θ , γ ) = e [4.13]
θ
1
h ( t , θ ,=
γ) ,t > γ [4.14]
θ
t −γ
−
R (t ) =
1 − F (t ) =
eθ
[4.15]
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log ( t ) − µ
F ( t , µ , σ ) = Φ nor [4.16]
σ
1 log ( t ) − µ
=f ( t, µ ,σ ) φnor , t > 0 [4.17]
σt σ
log ( t ) − µ
F ( t , µ , σ ) = Φ sev [4.18]
σ
β
β −1 − t
βt
η
f ( t, β ,η ) = e [4.19]
η η
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1 β −1
1 t σ −1 β t
h ( t, µ ,σ )
= = t>0 [4.20]
σ e µ e µ η η
β
t
−
R (t ) = e η
[4.21]
The equations presented for time to failure distributions need to fit the failure data. Ahmad et al
[87] presented a new approach to failure distribution fitting and established that the application
of incorrect failure distribution in maintenance optimisation studies will yield inaccurate results.
Maillart and Pollock [88] in their study of the effect of failure distribution specification errors
found that if the failure distribution is incorrectly specified, the cost per unit time will significantly
increase in the long run. Preventative maintenance strategies are more effective in cases where
the failure rate increases with time. If a preventative maintenance strategy is carried out at
decreasing or constant failure rate, the replacement and downtime costs will increase significantly
by time. As a result, it is important to employ the correct failure distributions. This is achieved by
utilising statistical methods that will be the subject of the next section.
When using observed failure data to select and estimate failure distribution models to perform a
reliability evaluation there are non-parametric and parametric methods that can be utilised for
this exercise. Empirical methods provide a non-parametric graphical estimate of the failure rate
versus the asset age or rate of asset utilisation. Furthermore, empirical methods do not assume
the form of the mean function or the process of generating system histories. Parametric methods,
on the contrary, use probability distributions like the Weibull or exponential distributions to
model the failure behaviour of the system components. Meeker [84] recommended that data
analysis should begin with empirical techniques which do not require assumptions in assigning
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models. Therefore empirical analysis can be interpreted as an intermediate step towards a more
complex model. Lewis [67] supported this by stating that empirical analysis can provide insight
toward selection of the most appropriate time to failure distribution. The use of parametric
methods can complement empirical methods precisely because parametric models provide
smooth estimates of failure time distributions and can be described accurately with just a few
parameters, unlike empirical methods which have to report an entire curve.
To determine which failure distribution to assign in the reliability evaluations, three stages are
usually employed when analysing statistical data. The stages which enable the development of a
probabilistic model of a system are trend testing, parameter estimation and selection of the best
fit for the appropriate point process model [14]. The data analysis for the reliability modelling of
repairable systems can follow a basic methodology as presented in Figure 4-10 . The flow chart
presents criteria for model identification and can be used as a basis for the analysing of failure
data.
Failure data
(Interarrival times)
in original chronological order
Trend ?
YES NO
Figure 4-10 : Framework for analysis of failure data for reliability evaluations
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S − n
1
∑
n −1 S
U = n −1 2
j =1 j
[4.22]
Sn
12 ( n − 1)
Where the system is observed until a time t0, the test statistic is given
∑ j =1 S j − t0 2
1 n
U = n [4.23]
t0
12n
In the both cases, the test statistic U is approximately standard normally distributed when the null
hypothesis H0 is true. The numerical value of U will indicate the direction of the trend with U <0
for a happy system and U >0 for a sad system. Table 4-3 shows the different interpretations of the
Laplace Trend Test values U. The rejection criteria is based on the assumption that U follows a
standard normal distribution. Conradie [25] and Lindqvist [90] advised that the use of the Laplace
Trend Test (LTT) should not be done without questioning the data and the results. For Laplace
Trend Test values within the grey area as highlighted in Table 4-3, further tests are required such
as the Lewis- Robinson test, Mann- Kendall Test and the Weibull test.
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n −1
Sn
Z = 2∑ In [4.24]
i =1 Si
Where the system is observed until time t0, the test statistic is given by:
n
t0
Z = 2∑ In [4.25]
i =1 Si
For the Military handbook test, the null hypothesis is 'HPP' which is rejected when the z values
are small or large. Low values correspond to deteriorating systems, while the large values of Z
correspond to improving systems. In strict terms, the rejection of the null hypothesis implies that
the process is not HPP but in principle, it could still be a renewal process and thus still have no
trend. These false rejections can be avoided by utilising the Mann test or the Lewis-Robinson test.
UL
U LR = [4.26]
CV
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probabilities governed by an unknown parameter Θ, the PDF for each of the n observations is
given as:
P ( X=i x=
i) f ( xi | θ ) =
, i 1,.....n [4.27]
These random observations are independent and as such the joint probability is the product of
the PDFs for all the n observations and is called the likelihood function given as:
L = f ( xi | θ ) ........... f ( xn | θ ) [4.28]
The concept behind the maximum likelihood function is maximising the natural logarithm L and
solving for Θ from which the maximum likelihood estimate Θ is obtained [94]. This is achieved by
taking the derivative of the natural logarithm of L (In L) with respect to Θ and equating it to zero
as shown.
∂In L (θ ; x )
= 0= for i 1, 2........m [4.29]
∂θi
The maximum likelihood method is applicable for both part components and systems and as such
the variable x can be replaced with time t [14].
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k
(oi − ei ) 2
= χ=
W 2
∑
i =1 ei
[4.30]
From the equation of the statistic χ2, if oi differs significantly from ei the value of W will be large
implying that the fit is poor [95]. The chi-squared test performs poorly for small data samples.
=d Max | F ( x ) − E ( x ) | [4.31]
where F(x) and E(x) are the theoretical and empirical distribution functions respectively. The
function F(x) is a continuous function and the distribution of d does not depend on the underlying
hypothesised distribution which makes the K-S test method computationally attractive.
Ahmad et al [87] developed a new approach to identify the best-fit time to failure distribution
methods which provide a different perspective to reliability modelling. In the traditional
approach, Least Square Estimator (LSE) and the Maximum Likelihood Estimator (MLE) are used.
The LSE is utilised to specify the best failure fit failure distribution by examining all the possible
time to failure distributions (lognormal, Weibull etc.). The MLE is then applied to calculate the
parameters of the selected time to failure distribution. With the new approach, the LSE method is
used to determine the β parameter of the Weibull distribution. The value of the β parameter can
then be used to determine the best-fit failure distribution using the MLE technique. A comparison
of the old method and the new approach is presented in Figure 4-12.
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Figure 4-12 : Comparison of the traditional and new approach adopted from Ahmad et al [87]
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The organisation of the PRASA maintenance department is split into engineering services and
maintenance operations. The engineering services department is responsible for planning,
policies, and procedures in facilitating the execution of maintenance-related tasks. The
engineering services department is divided according to the infrastructure subsystem. Each
department within engineering services has its own specific RAMS and RCM framework that are
followed in executing the infrastructure asset management strategy. The maintenance operations
department is responsible for executing the plans and procedures and provides maintenance
support to the engineering services department. The two divisions, therefore, mirror each other
and coordinate all infrastructure-related interventions on the railway network. It is, however, part
of a bigger framework which has parallel strategic and delivery components relating to the
operation of the network such as supply chain and human resource management as shown in
Figure 5-2.
Structure of
maintenance
division
Electrical
Electrical
Electrical
division
Perway
Perway
Perway
division
Signalling
Signalling
Signalling
division
Maintenance
support
Drawing office
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The Enterprise Maintenance Planning and Control (EMPAC) is the Integrated Management System
(IMS) used in PRASA's maintenance management operations. This system documents the
performance, planning and budgeting of all maintenance management-related activities by
generating statistics, reports, and summaries on the performance of the railway network. The
general indicators of infrastructure performance obtained from the system include the number of
delays and cancellations caused by each infrastructure system. The infrastructure access and
planning process of PRASA articulates a maintenance strategy which comprises of all activities
that require secure access to the railway passenger service by improving the availability and
reliability of rolling stock and infrastructure systems.
Maintenance dimensioning in PRASA addresses the issue of resource allocation across the
infrastructure network by considering traffic volumes, safety, reliability and the economic needs
that impact the decision-making process. The performance of the maintenance intervention
strategies developed by the engineering services is measured using the number of productive
hours spent on an asset during maintenance operations. The travel time to restore system failure
is categorised as unproductive hours; unavailable hours refer to the time where maintenance
resources are unavailable. This performance measure captures the scope of PRASA`s
infrastructure maintenance management which focuses on a preventative maintenance plan
strategy. A preventative maintenance plan is the first line of defence for ensuring minimal
infrastructure failures and consists of routine tasks, planned tasks, and feedback systems on the
tasks performed. Figure 5-3 summarises PRASA's asset management decisions and activities
arranged in a plan-do-review framework. The framework provides a simple representation of the
major building blocks of asset management and the key interfaces between them. In addition, it
provides a detailed process mapping the different responsibilities assigned in the asset
management systems strategy. PRASA recognises that maintenance is a technical process and as
such a maintenance programme needs to be managed in a manner that yields greater service
reliability, ultimately enhancing the commuter experience. To achieve this means spending more
productive time on the infrastructure assets to keep the condition of the assets at acceptable
operating levels.
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The framework for reliability evaluations is a continuous systematic analysis which must be
applied at the relevant levels of the railway network. To achieve this the researcher established
the format and structure in which the data is recorded within the IMS. From a maintenance
perspective, there is a difference between a point and linear assets depending on the criticality
and the length of the asset. For point assets maintenance is not assigned to a particular length of
the asset but rather to the entire asset or to some of its indenture levels. A linear asset, on the
other hand, is an asset whose length plays a central role in its maintenance, an example being the
track or catenary system. The inventory from the IMS accounts for these characteristics and
defines the location of a point or a section of the network to describe an infrastructure asset. When
a failure event occurs on the railway network the location of the failure is defined by a point or
section along the asset between the geographically closest stations. Using the network topology
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map the location of failures on a network section can be identified and traced in accordance with
the asset tags specified in the asset registry. A hierarchical representation of the infrastructure
indenture levels formulates the modelling methodology. This approach ensures that
infrastructure failures with critical consequences on the operation of the railway service are given
attention. The indenture levels followed to analyse the data in developing the reliability model for
the analysis are shown in Figure 5-4.
Multicriteria criticality
Operational route
analysis
Multicriteria criticality
Railway line
analysis
Figure 5-4 : Breakdown structure for reliability evaluation to support the modelling of the
infrastructure network [53]
Once an asset experiences a failure at a given time the asset starts to malfunction. After a reaction
time, the failure is registered and a work order is opened with the aim of restoring the normal
activity of the asset. The distinction between the time to the first failure and the time between
failures will be applied using repairable systems theory. The time to failure is understood as the
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time elapsing from when the item was put into operation until it fails for the first time and is
interpreted as a random variable T. To apply statistical analysis the variable is not always
interpreted in calendar time but can be a discreet or continuous variable which determines the
random distribution used to model the reliability. To simplify the process of data analysis,
suspension of the railway infrastructure system was assumed to occur between the start and end
of the data sets. This means that the period under study using the collected data assumes
uninterrupted operation. Thus any system downtime is assumed to be as a result of infrastructure
failure events as recorded in the database.
Asset mode
TTF TBF
Available
TTM or DT
UT
WT TTR
Unavailable
Time
T=0
Open WO
Close WO
Corrective action
Failure reported
Start corrective
Logistics
Failure identified
action
The researcher studied the weekly failure data recorded to identify the failures reported on the
network by looking at the different corridors and operational routes on the network. The weekly
report logs all the daily failure information according to infrastructure type and provides
information on the location, asset ID, failure date, and cause of failure for the different
infrastructure subsystems. Table 5-1 shows an example of a daily failure log for the signalling
system and the impact that such an incident has on train service reliability. To trace a failure to a
line corridor the train stations that fall on that corridor must be determined to establish the
failures collected at these stations on the network. The reality is that not all items under study
registered in the asset registry will contain a failure event. The modelling approach taken by the
researcher can only be certain that a number of items have not failed in a particular period, not
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knowing whether they would have failed after a longer period. Sections, where smaller errors are
present, were preferred for the analysis. Additionally, a study of the different corridors in the
network performance revealed duplicate data entries that had to be removed to avoid multiple
entries.
From the analysis of the different corridors, the cleaned failure data was utilised to model the set
of arrival times of each infrastructure subsystem for the application of repairable systems
reliability theory presented in section 4.2.3. The prediction intervals chosen account for the
statistical uncertainty in reliability predictions that occurs because of limited data samples and
variability in system failures. In cases where the failure times of the infrastructure subsystems
took values in a particular range, the data was truncated to remove the uncertainty and bias that
may occur in statistical approximation because of inconsistencies in the recording of failures. To
validate the model, resampling or cross-validation techniques will be used. With these techniques,
a complete data set is divided into two subsets. The first set becomes the training set that is used
for model selections and parameter estimations; the second set, which is known as the validation
set, is used for model validation and error estimation. Application of future forecasting will be
tested in this manner.
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The aim of this exercise is to assist in reliability modelling of the infrastructure system, in that the
analysis gives attention to the failures that disrupt the performance of the system more in
comparison to others. Infrastructure failure modes are classified according to the consequence
that they have on the system. The most significant failure consequence is a delay and in extreme
instances a service cancellation with other consequences related to a reduction in track capacity
and speed restrictions. The classification of failures used is shown in Table 5-2 according to the
consequences. The combination of the frequency of occurrence and severity of impact guides the
classification of the infrastructure failure modes. The probability of occurrence used by the
researcher to classify the failure modes is shown in Table 5-3. The correlation between the type
of infrastructure elements and the number of occurring failures and the methods provided in
section 4.2 were used to establish the criticality of failure modes. A matrix shown in
Table 5-4 is created using the Military Handbook technique to determine the criticality of the
infrastructure failure modes. The criticality index is shown in Table 5-5.
Catastrophic Cancellations
Critical Delays
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Severity
Insignificant Marginal Critical Catastrophic
Very high R3 R4 R4 R4
High R2 R3 R4 R4
Frequency
Moderate R2 R3 R3 R4
Low R1 R3 R3 R4
Remote R1 R2 R3 R4
Criticality
Evaluation Definition
index
R1 Negligible Acceptable
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Symptom
Triggering
event
Consequence
Vibrations
Root cause Occupied track • Cancellations
at train • Delays
Signal box dispatcher • Capacity lowered
Bad
loses
workmanship
contact
Alarm notifying
Failure
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identified causes of ballast failure are related to voiding and settlement. In addition, the condition
of the ballast influences the track circuit in the signalling subsystem. This is because the ballast
offers electrical resistance and the track circuit is only functional at specific ballast resistance
levels. If this resistance drops to values lower than that specified, the flow of current drops and
makes the track circuit non-functional. The occurrence of such failures is intermittent in nature
and more likely to occur during the wet winter season than in summer.
The most severe infrastructure failure related to the perway subsystem is a derailment. Falling
levels of infrastructure renewal and worsening track quality results in high dynamic forces during
operation which may lead to broken and or defective rails. Broken and defective rails are the
highest causes of derailments which can have fatal consequences. Furthermore, faulty rails trigger
track circuit failures which affect the performance of the signalling subsystem. The study observed
that there is a distinction between a broken rail and a defective rail as such – a defective rail is not
considered a broken rail. A broken rail is a rail with a complete break or a missing piece.
Exceptions are rails that break in possessions and in sidings. A defective rail, however, is a rail
identified as containing defects that are related to geometry and the characteristics of the track
such as alignment defects. Other failures related to the perway subsystem can be attributed to rail
clip and sleeper failures which are a result of high rates of vandalism on the network's
infrastructure.
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The researcher utilised a dependency matrix to map out the different infrastructure dependencies
that exist in the railway infrastructure system. This can be seen in Appendix A. Some
infrastructure assets exhibit both unidirectional and bidirectional interdependencies. Modelling
these characteristics is important to estimate the physical and functional propagation effects of
failures. Failure propagation decreases the quality of service due to the loss of physical
interactions and functional relationships between connected assets in the infrastructure system.
Figure 5-7 shows the interdependencies and functional flow diagram of the railway infrastructure
system. Single arrows indicate a unidirectional relationship while double arrows indicate a
bidirectional interdependence of the infrastructure assets. The track circuit, OHTE, and signalling
power depend on the uninterrupted availability of electric power from the substations and
transmission lines exhibiting a unidirectional dependence. On the other hand, the OHTE and
perway superstructure exhibit a bidirectional interdependence between the infrastructure
components.
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11kv
Interlocking
Substations
3/11kv
Perway
transmission Signalling
(Superstructure)
lines
Signalling
power supply
The railway network topology for the infrastructure system can be assumed to consist of
indenture levels as shown in Figure 5-8. Utilising a top-down approach, the whole rail
infrastructure network can be broken down into operational routes representing the different
parts of a railway network. The operational routes constitute a specified number of lines made up
of multiple segments representing a corridor between two locations (stations) or a section
between two signals called a signal block. Multiple segments characterise individual maintainable
items according to technical and functional properties to represent the distinct infrastructure
subsystems. Individual maintainable assets for which degradation mechanisms and intervention
processes can be determined are lowest on the indenture level.
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Railway Infrastructure
System
Overhead
Superstructu Transmissio Track Point to Signal
Substructure Track Substations Interlocking Signal
re n Lines circuit point Power
Equipment
Figure 5-9 shows an example of an operational route between two stations that constitute part of
a larger network with point and linear assets. This configuration examines the relationship
between the point and linear assets and formulates the basis of the holistic infrastructure
reliability model. The redundancies that exist in railway infrastructure systems, particularly the
electrical system, were accounted for in the functional mapping of the reliability model developed
for the network segment. This approach takes into account the most essential functional
properties of the system to be modelled in order to provide a comprehensible reliability model.
Network segment
Station Station
A B
Legend
Point asset
Line A
Line B
To identify critical components that constitute a network segment for railway infrastructure
system, systematic and exhaustive consequence investigations for the different component
failures were performed. The practical issue, however, was analysing combinations of failures by
assuming that they increase as the number of simultaneous failures increase. This assumption
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PERWAY
Superstructure Substructure
Forward, Stop, Speed
ELECTRIFICATION Restriction, warnings
and brake commands
SIGNALLING
Point-to-Point
Track circuit Interlocking Signals
machines
Signalling
Power
From the functional reliability model the asset state models for the different infrastructure
subsystems can be developed. The individual asset state model is built for a specific
infrastructure's subsystems, taking into consideration the integration of the degradation-failure
and intervention processes to simulate its state changes over time. The reliability block diagram
for each infrastructure subsystem has a series configuration that represents the infrastructure
state models as shown in Figure 5-11.
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Sleeper
system
Ballast and
Rail system Rail clip system
subgrade
Perway
Overhead
3Kv /11Kv Signalling
3Kv /11kv Track
Electricals transmission Power
Substations equipment
lines supply
(OHTE)
Figure 5-11 : Reliability block diagrams for the infrastructure asset state models
The infrastructure asset state models are used as building blocks for the infrastructure system
state model. From the functional reliability model presented the system state model is a series
configuration of the infrastructure subsystems as shown in Figure 5-12. A collection of
infrastructure system state models assembled together construct network segment models that
can be used to model higher network hierarchical and/or infrastructure indenture levels. The
abstraction level and network system details govern the configuration of the network segment
models. If the network segment models are combined at the relevant abstraction levels, railway
lines and operational routes can be modelled holistically for performing reliability evaluations of
railway infrastructure systems. The modelling approach shown in Figure 5-13 uses the system
and subsystem utilisation information and the possible strategic interventions that influence the
degradation process of the different infrastructure subsystems.
Figure 5-12 : Reliability block diagram for network segment railway infrastructure systems
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MODELS
Perway system
Electricals system
Signalling system
Figure 5-13 : Modelling approach showing asset state and system reliability model
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SIGNALLING PERWAY
Interarrival time N(t) Interarrival time N(t)
4 1 20 1
13 2 34 2
19 3 66 3
29 4 67 4
39 5 84 5
45 6 88 6
46 7 132 7
47 8 168 8
59 9 178 9
62 10
67 11
79 12 ELECTRICALS
84 13 Interarrival time N(t)
89 14 70 1
90 15 77 2
96 16 96 3
98 17 125 4
99 18 128 5
101 19 129 6
102 20 145 7
109 21 165 8
119 22
124 23
128 24
137 25
152 26
154 27
155 28
156 29
160 30
160 31
163 32
165 33
168 34
169 35
177 36
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Table 6-1: Summary of the test statistic and the recommended modelling distributions.
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subsystem whereas the power law is more representative of the data for the electrical and
signalling subsystems.
40
35
30
Number of failures
25
20 Observed-Signalling
15 NHPP Log-linear
10 NHPP Power-Law
5
0
0 50 100 150 200
Time (days)
Figure 6-2 : Graph of the power law and log-linear law for the signalling system
1.2
1
Cumulative failures
0.8
0.6
Perway - Weibull
0.4 Observed - perway
0.2
0
0.00 50.00 100.00 150.00 200.00
Time (days)
Figure 6-3 : Cumulative distribution function for the Weibull distribution and observed values
Perway Weibull HPP dmax < dcritical Good fit η = 107.54 β = 1.5127
0.1816 < 0.6082
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107.54
T
− n
R (t ) = e 1.5127
[6.2]
Similarly, the reliability equation for the power law shown in equation 6.3 applied to the signalling
and electrical subsystem using the estimated parameters yields equations 6.4 and 6.5 respectively.
For each of the infrastructure subsystems, the reliability predictions are determined from the time
of the last failure.
Power law
(
− λ T2 β −T1β )
R (t ) = e [6.3]
Signalling subsystem
( )
R (t ) = e
−0.0663 T21.2104 −T11.2104
[6.4]
Electrical subsystem
( )
R (t ) = e
−0.000345 T21.9770 −T11.9770
[6.5]
Using the reliabilities of the individual asset state models, the reliability of the railway
infrastructure system state model can be determined using the appropriate reliability modelling
equations. The reliability block diagram for the railway infrastructure system state model
developed in section 5 concluded that the railway infrastructure system state model assumes a
series configuration which follows the equation below.
n
R ( t ) system = ∏ R ( t )i [6.6]
i =1
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107.54
T
− n
( ) ( )
R ( t ) System =
−0.0663 T21.2104 −T11.2104 −0.000345 T21.9770 −T11.9770
e 1.5127
×e × e [6.8]
Equation 6.8 is used to calculate the reliability performance of the Southern line for the first 150
days of operation, Figure 6-4 shows a graphical representation of the reliability performance of
the Southern line with time. Table 6-3 shows the predicted reliability performance of 48.2 % for
the railway infrastructure system after 7 days. Reliability predictions were conducted from the
last recorded failure for all the infrastructure subsystems.
1.2
0.8
0.6 perway
Reliability
Electrical
0.4 Signalling
Infrastrcuture system
0.2
0
0 14 28 42 56 70 84 98
-0.2
Time (days)
Table 6-3 : Reliability of the railway infrastructure system in the first 14 days of operation
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Perway subsytem
1 January, 2015 - 28 June, 2015
Signalling subsystem
1 January, 2015 - 27 June, 2015
Electrical subsystem
1 January, 2015 - 15 June, 2015
Figure 6-5 : Timeline showing the location of the last failure for the infrastructure subsystems
Using the equations presented in section 4.2.3 for determining the time to first failure (MTBF) and
expected number of failures E (N) for the infrastructure subsystems, the validation of the results
from the reliability predictions for each of the infrastructure state models follows.
6.1.5.1 Perway
The parameter values for the two-parameter Weibull function modelling the perway subsystem
are η = 107.54 and β = 1.5127. To predict the time to first failure (MTBF) of the perway
infrastructure subsystem. Setting T2 = 186 days for the perway state model. The predicted time to
first failure and expected number of failures for the perway subsystem is given as follows:
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1
E ( T2 , T1 ) =ηΓ 1 + where Γ ( n ) is the gamma function
β
1
E ( T=
2 , T1 ) 107.54 × Γ 1 + [6.9]
1.5127
E ( T=
2 , T1 ) 107.54 × 0901828
= 97 days
The actual inter-arrival time from the failure data is 17 days which means that the perway
subsystem lasted 79 days shorter than predicted. The deviation in the results can be attributed to
various factors. Weibull models with values of β > 1 have a failure rate that increases with time.
This highlights that the reliability model assumes high failure rates with time. The reliability at
the observed MTBF is 94.1%. The number of failures from the observed data N (t) = 4 failures,
while the predicted number of failures in the same period is 3 failures.
6.1.5.2 Signalling
The power law parameters for the signalling subsystem are given as λ = 0.0599 and β = 1.2503.
Setting T2 = 187 days for the signalling subsystem. The predicted time to first failure and expected
number of failures for the signalling subsystem is given as follows:
T2 − T1
MTBF2 (T1 , T2 ) =
λ (T2 β − T1β )
187 − 0
MTBF2 ( 0,187 ) = [6.11]
0.0599 (1871.2503 )
= 4.5 days
E p ( N ( T2 ) − N ( T1 ) ) =λ (T2 β − T β 1 )
0.0599 (1871.2503 )
E p ( N (187 ) − N ( 0 ) ) = [6.12]
= 41.48 failures
The observed inter-arrival time after the last failure is 5 days, which means the signalling
subsystem lasted 0.75 days longer than the prediction. The observed number of failures E (N) =
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37 failures versus the predicted E (N) = 41 failures. The reliability of the signalling system when
the first failure is observed yields 63.9 %.
6.1.5.3 Electrical
The power law parameters for the electrical subsystem are given as λ = 0.0599 and β = 1.2503.
Setting T2 = 199 days for the electrical subsystem. The predicted time to first failure and expected
number of failures for the electrical subsystem is given as.
T2 − T1
MTBF2 (T1 , T2 ) =
λ (T2 β − T1β )
199 − 0
MTBF2 ( 0,199 ) = [6.13]
0.000345 (1991.9770 )
= 16.45 days
E p ( N ( T2 ) − N ( T1 ) ) =λ ( T2 β − T β 1 )
0.000345 (1991.9770 )
E p ( N (199 ) − N ( 0 ) ) = [6.14]
= 12.1 failures
The observed inter-arrival time for the electrical subsystem was 48 days from the day of the last
recorded failure, which means the electrical subsystem lasted 30.56 days longer than the
prediction. The observed number of failures E (N) = 11 versus the predicted E (N) =12.13. The
reliability of the subsystem at the observed time to failure is 48.2%. The researcher conducted the
predictions on shorter intervals for each of the subsystems for the expected number of failures.
The predictions were compared with the observed values in the same time frame. The results are
presented Table 6-4 below.
Table 6-4 : A comparison of the subsystems for the expected and observed number of failures
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7 Multi-criteria analysis
The aim of the study seeks to quantify the reliability of railway infrastructure systems to assist in
the maintenance and management of railway infrastructure assets. Reliability as a performance
measure can assist maintenance managers in prioritising infrastructure assets during
maintenance interventions on the railway network. In this section, the model will be applied to
multiple corridors and the application of the reliability model in maintenance management
prioritisation will be demonstrated.
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1.2
System
1
0.8
Reliability 0.6
0.4
0.2
0
0 7 14 21 28 35 42 49
-0.2
Time (days)
Nyanga-Phillipi Langa-Belhar
Figure 7-1 : Reliability performance for the Nyanga-Phillipi and Langa-Belhar corridors
Figure 7-2 and Figure 7-3 show the reliability performance of the subsystems for the Langa-Belhar
and Nyanga-Phillipi corridors respectively. For the Langa-Belhar corridor, it can be seen from
Figure 7-2 that the poor reliability performance of the perway subsystem has the governing
criticality that influences the performance of the infrastructure system on that corridor. For the
Nyanga-Phillipi corridor shown in Figure 7-3, the signalling subsystem has the governing
criticality on that corridor. These results show the subsystems that require prioritisation for each
individual corridor.
1.2
Langa-Belhar corridor
1
0.8
Reliability
0.6
0.4
0.2
0
0 14 28 42 56 70 84 98
Time (days)
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1.2
Nyanga - Phillipi corridor
1
0.8
0.6
Reliablity
0.4
0.2
0
0 14 28 42 56 70 84 98
-0.2
Time(days)
For maintenance planning on a large network, the reliability model can be applied to assist in
decision-making for prioritising and selecting the best intervention methods on the two corridors
that will improve the reliability performance of the railway network. Figure 7-4 and Figure 7-5
shows that the performance of the Langa-Belhar corridor presents better reliability performance
for the signalling and electrical subsystems. The outcome of this prediction means that the
Nyanga-Phillipi corridor must be prioritised for maintenance for both the signalling and electrical
subsystems to improve system performance. The observed time to first failure for the Nyanga-
Phillipi signalling subsystem was 4 days, this reflected the predicted value over the same period
of 4 days. The predicted time to first failure for the Nyanga-Phillipi electrical subsystem was 102.4
days against an observed value of 208 days, which means the first failure was observed 94.2 days
later than the predicted value. For longer maintenance windows however the Langa-Belhar
corridor must be prioritised for maintenance because after 84 days the rate of reliability
degradation for the electrical subsystem on the Langa-Belhar corridor increases in comparison to
that of the Nyanga-Phillipi corridor.
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1.2
Electrical
1
0.8
Reliability
0.6
0.4
0.2
0
0 14 28 42 56 70 84 98 112 126 140 154 168 182
Time (days)
Nyanga-Phillipi Langa-Belhar
1.2
Signalling
1
0.8
Reliability
0.6
0.4
0.2
0
0 7 14 21 28 35 42 49
-0.2
Time (days)
Figure 7-6 for the perway subsystem performance shows reliability performances that contrast
to that of the electrical and signalling. Instead, the reliability performance of the perway system
for the Nyanga-Phillipi corridor registers high-reliability performance over the same period. This
result shows that for the perway subsystem, priority should be given to the Langa-Belhar corridor
to maintain acceptable levels of reliability performance. The predicted time to the first failure for
the perway subsystem on the Langa-Belhar corridor was 10.61 days against an observed value of
4 days. This means for the Langa-Belhar corridor the time to first failure was recorded 6.61 days
earlier than the predicted value.
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1.2
Perway
1
0.8
Reliability 0.6
0.4
0.2
0
0 14 28 42 56 70 84 98 112 126 140 154 168 182
Time (days)
Nyanga-Phillipi Langa-Belhar
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8 Discussion of results
From the preceding section, it is evident that the reliability modelling approach given for railway
infrastructure systems can assist in maintenance prioritisation by highlighting sections/lines and
routes that require attention based on the reliability performance of the infrastructure assets. The
study identified that in railway infrastructure environments, two factors influence infrastructure
quality. The ability to continuously measure infrastructure quality over time and the ability to
employ the necessary measures to restore infrastructure quality suppose it falls below acceptable
levels. This section discusses the results of the reliability model which quantify infrastructure
quality along with their implication on the asset management strategy to restore infrastructure
quality to acceptable levels.
To support primary decisions in the maintenance and renewal of infrastructure systems spread
over wide geographic areas, the asset information and performance data must be synthesised into
information that can be useful to make informed decisions. Figure 8-1 shows a summary of the
results from the multi-criteria analysis for the two routes. From these results at operational route
level, the Nyanga-Phillipi line exhibits low reliability performance as compared with the Langa-
Belhar line. In addition, the results from the analysis show that the critical subsystems governing
the reliability performance of each line is the signalling and perway subsystems for the Nyanga-
Phillipi and Langa-Belhar lines respectively. Using the information produced by the proposed
modelling framework, all the potential asset management decisions are incorporated, allowing
policies and regulations to be formulated that deliver the required performance level of the
infrastructure assets on the railway network. From the summary of results in Figure 8-1 the
electrical and signalling subsystem of the Nyanga-Phillipi line should have maintenance resources
prioritised whereas for the Langa- Belhar line the priority asset group for maintenance is the
perway subsystem.
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Operational Route
Electrical Electrical
Perway Perway
Electrical Electrical
Perway Perway
The reliability-based approach quantified the variations that arise at the subsystem interfaces and
identified the effects of various intervention strategies related to improving the reliability
performance of the railway infrastructure assets. Results from the Pareto analysis seen in Figure
8-2 show the type of infrastructure component and its contribution to infrastructure system
downtime as recorded by the number of failures. From the figure, points-and-crossings failure
mode demonstrate a high frequency of occurrence highlighting the impact of the signalling
subsystem on the reliability performance of the infrastructure system. In addition, the block joint
and defective rail failure modes register high frequency of occurrence highlighting the impact of
the perway subsystem on the reliability performance of the infrastructure system. Overhead
Track Equipment (OHTE) and cable related failure modes of the electrical subsystem although
registering a relatively low frequency of occurrence significantly impact the reliability
performance of the infrastructure system.
The criticality ranking of the failure modes is summarised in the Appendix from the results of the
FMECA study. From the FMECA study, points and crossings and interlocking failure modes ranked
intolerable on the criticality scale. The effect of these failures is severe causing on-track machine
failures and loss in detection between interlocking components and point to point machines of the
signalling subsystem. The effect of failures in the perway subsystem is observed by faulty track
circuits, derailments and burnt out catenary. Failure modes related to the perway subsystem like
faulty block joints and defective rails caused most track circuit related failures in the signalling
subsystem. Studying the failure cause variation in the railway infrastructure system reveals that
low-frequency events that have high impact are inherently difficult to predict. This was observed
with the electrical and perway subsystem which registered low failure incidences as compared
with the signalling subsystem. On the other hand, high-frequency low-impact events are
constantly active in the system and can be predicted easily. This was observed on the signalling
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subsystem which showed relatively high rates of failure occurrence when compared with the
other subsystems.
180 120
160
100
140
Number of failures
120 80
100
60
80
60 40
40 Number of failures
20
20 cumulative %
0 0
Figure 8-2 : Pareto analysis for failure modes and frequency of failure.
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inefficiently. To improve the infrastructure system therefore based on these outcomes means
supporting maintenance policies that emphasise spending more productive hours on
infrastructure assets i.e. condition and reliability-based maintenance, than policies based on the
operating time of the components i.e. corrective and time-based maintenance. A holistic
reliability-based integrated maintenance planning approach based on system status compliments
preventative and condition-based maintenance to support overall system improvement. From a
reliability-based perspective the results recommend that focusing on high-frequency and low
consequence events (incidences) can yield as much benefit to infrastructure reliability
performance as focusing on low frequency and high-consequence events.
90
80
70
% of trains delayed
60
50
40
30
20
10
0
2 011 2 012 2 013 2 014 2 015
Year
Figure 8-3 : The impact of the different infrastructure subsystems failures to train delays
100
90
80
% of trains cancelled
70
60
50
40
30
20
10
0
2 011 2 012 2 013 2 014 2 015
Year
Figure 8-4 : The impact of the different infrastructure subsystems to train cancellations
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Although whole life and whole system thinking is difficult to initiate in the short term due to
various resource constraints, railway organisations need to actively promote the right values and
behaviours to support a holistic approach to asset management. Part of this requires organising
around a common asset management strategy and having the right organisational and governance
structure that cuts across functions. To deliver a reliable railway infrastructure system a multi-
disciplinary and function based thinking approach is required which promotes partnerships to
develop solutions that meet the internal needs by building new internal capabilities and
competencies.
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8.4 Limitations
Access to accurate information supports new processes and ways of thinking and is a requirement
for the successful application of a holistic reliability-based approach to infrastructure asset
management. In addition, infrastructure performance can be considerably improved if the
Information Management Systems are populated with accurate failure data that correctly
references failure causes for the different assets in the registry. During the failure analysis, the
root cause triggering certain events in some datasets could not be determined. Some failure
records studied by the researcher indicated causes that are likely not to be accurate. The root
cause in some cases was hard to tell from a single instance, which suggests that further checks
were required. The data, however, was detailed with regards to components and functionality but
did not concisely define and describe all the events that led to failure. During the failure analysis
for the reliability model the researcher concluded that causes given just to complete the data may
be misleading, hence the necessity of filling in all fields was not overemphasised. It becomes,
therefore, essential for railway organisations to have a technological infrastructure which
supports the collecting, organising and managing of the correct data.
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9 Conclusions and
recommendations
The aim of the research study was to develop a model to measure the reliability performance of
railway infrastructure systems to facilitate integrated maintenance planning in railway
infrastructure environments. A systematic analysis to develop a holistic reliability model for
railway infrastructure systems to improve railway infrastructure asset management processes
has been presented. The model presented in this research is an evidence-based decision-making
tool which uses asset failure information to account for the joint dependability attributes that
characterise railway infrastructure systems. The model developed in the study was applied to a
case study on PRASA`s railway network to support the development of appropriate maintenance
strategies to improve infrastructure reliability. The model identified critical infrastructure
subsystems that impact the reliability performance of the railway infrastructure systems which
enables the strategic alignment of asset management plans for the different subsystems to
maintain the railway network at acceptable operating levels. Aligning asset management plans
using a reliability-based maintenance and management approach moves away from the silo
approach which currently characterises railway infrastructure asset management in the South
African passenger railway industry. This enables railway organisations to exploit opportunities
that can increase capacity and improve the resilience and reliability of railway infrastructure
systems in the short to long term period. The reliability modelling approach presented in the study
has the capacity to improve asset performance to meet the increasing demands of service quality
and infrastructure reliability in railway environments. It can be concluded that reliability analysis
can be utilised to develop an integrated reliability-based approach in the maintenance and
management of railway infrastructure assets.
in multidisciplinary teams to integrate and interpret the different factors that influence decision-
making in such environments. Furthermore, it was observed that it is important to have tools that
capture high-quality asset data to support decision-making which enables efficient asset
management strategies in collaborative environments. This requires a diverse mix of practical and
thinking skills sustained by knowledge and understanding relevant to the planned intervention
processes. This must further be complemented by collaborative behaviour and enhanced
mechanisms for automated data capture, collation, and visualisation.
9.2 Recommendations
Asset management is no longer a matter of trading off one asset against the other, but rather a
matter of trading off how each asset impacts the performance of the whole system in achieving
the highest functional performance in terms of safety, availability, and reliability with least
possible costs. Railway infrastructure maintenance interventions need to minimise train
disruptions, this requires efficient and effective coordination of maintenance planning activities
of the railway infrastructure assets. The current structure around asset management in PRASA
has two divisions which are the engineering services and maintenance operations. Each
department has its own planning process. To facilitate the practical application of the reliability
model presented in this research it is recommended that PRASA Metrorail division adopts an
integrated planning process in maintaining and managing railway infrastructure assets. An
integrated approach will facilitate collaborative sharing of knowledge for decision-making by
considering all aspects of required outcomes, including skills required to evaluate cost and
reliability performance trade-offs. In addition, increasing the productive time on infrastructure
assets can significantly improve the reliability performance of the railway infrastructure system.
This means that an integrated approach to maintenance must have the capacity to consistently
evaluate and monitor the implementation of the asset management strategies for continuous
reliability improvements. However, support for developing integrated maintenance planning in
the South African passenger railway requires an increase in awareness within the leadership
structure and willingness across the different functional departments to seek, share, and adopt
others' learning.
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infrastructure network models that enable the railway system to be viewed both topographically
as a map and topologically as schematic logical views showing how individual assets are
connected. Network models provide a geospatial view of the railway network showing the
location of assets on the network and the underlying asset information for each infrastructure
asset. Rail infrastructure network models can bring together infrastructure data sets describing
system-level utilisation and performance, connecting asset management, operations, and
maintenance allowing infrastructure managers to understand relationships between assets.
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11 Appendices
11.1 Railway infrastructure failure modes
Failure Criticality
Subsystem Failure cause Failure effect
mode Frequency Severity Criticality
Perway Faulty block joints • Wear and tear • Faulty Track circuit High Critical Intolerable
Electrical Cable + wires • Vandalism • Overhead power failure Moderate Critical Undesirable
• Maintenance works • Signal power failures
• Cable faults •
Signalling Interlocking • Wear and tear • Faulty signalling Very High catastrophic Intolerable
(Crossings) • Broken blades
Signalling Point to point • Wear and tear • On-track machine failures Very High Catastrophic Intolerable
machines • Vandalism • Loss in detection
• Blown fuses
• Faulty micro switch
Signalling Track circuit • Faulty block joints • Track circuit failures Very High Marginal Intolerable
• Faulty transmitter
• Defective rail bond
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Signalling On track machines • Track circuit failures • False occupation alarm Moderate Critical Undesirable
(Signals) • Signal power failures • Loss of signal
• Faulty fuse holder • Faulty block signal
Electrical Substation Power • Feeder cable failures • Feeder cable failures Low Catastrophic Undesirable
• Blown fuses • Low overhead supply
Perway Broken rail and • Wear and tear • Loss in signal Moderate Catastrophic Intolerable
defective rails • Tonnage • Derailments
• Geometric • Short circuit on track
misalignments circuit.
• Rail to rail bond off • Burnt out catenary due to
short circuit
Perway Drainage (Track • Settlements • Faulty track circuit Moderate Critical Undesirable
substructure) • Voiding
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KEY
PERWAY
Superstructure S1
Substructure S2
ELECTRICALS
OHTE OHTE
11 kv Substation SUB11kv
3kv Substation SUB3kv
3lv/11kv Transmission lines TRANSL
SIGNALLING
Track Circuit TC
Point to Point Machines PPM
Interlocking INTLOCK
Signalling SIG
Signalling power SIGPOW
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Start
Database
Responsible
department
Analyse
Collect data
Extract failure events
causing delays and
cancellation
Reliability Test
NO
• Identify configuration
• Arrange data for system
• System level approach
Parametric
approach
Chronologically arranged
interarrival times YES
YES
NO
YES NO
NO Conventional Parameter
analysis techniques evaluation
Non parametric
approach
Failure rate
evaluation
Calculate
cumulative failure Inference about Verification and
number vs failure failure pattern validation
times
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Table 11-1 : Results from trend test for the Langa-Belhar corridor
Perway
18
16
14
Cumualtive failures
12
10
8 observed - perway
6 NHPP - Power Law
4
2
0
0 50 100 150 200
Time (days)
Figure 11-2 : Graphical representation of the NHPP power law vs observed values
Signalling
1.2
1
Cumulative failures
0.8
0.2
0
0 50 100 150 200
Time (days)
Figure 11-3 : Cumulative distribution function for the Weibull distribution and observed values
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Electricals
4.5
4
3.5
Cumulative failures
3
2.5
2 observed - electricals
1.5 NHPP - Power Law
1
0.5
0
0 50 100 150 200
Time (days)
Figure 11-4 : Cumulative distribution function for the Weibull distribution and observed values
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Table 11-3 : Results from the trend test for the Nyanga-Phillipi corridor
Perway
1.2
1
Cumulative failures
0.8
0.6
observed - perway
0.4 HPP-Weibull
0.2
0
0 50 100 150 200
Time (days)
Figure 11-6 : Cumulative failures for the observed and Weibull approximations
Signalling
50
45
40
Cumulative failures
35
30
25
observed - signalling
20
15 NHPP - Power Law
10
5
0
0 50 100 150 200
Time (days)
Electricals
1.2
Cumulative failures 1
0.8
0.6
observed electrical
0.4 HPP-Weibull
0.2
0
0 50 100 150
Time (days)
Perway Weibull HPP dmax < dcritical Good fit η = 114.28 β = 1.4047
0.200 < 0.6082
Electricals Weibull HPP dmax < dcritical Good fit η = 113.80 β = 0.8548
0.0502 < 0.430
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117