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2013 published online 26 JulyProceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit

Stephen Mayowa Famurewa, Tao Xin, Matti Rantatalo and Uday KumarOptimisation of maintenance track possession time: A tamping case study

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Original Article

Optimisation of maintenance trackpossession time: A tamping case study

Stephen M Famurewa1, Tao Xin1,3, Matti Rantatalo1,2

and Uday Kumar1,2

Abstract

Optimum allocation and efficient utilisation of track possession time are becoming important topics in railway infra-

structure management due to increasing capacity demands. This development and other requirements of modern

infrastructure management necessitate the improvement of planning and scheduling of large-scale maintenance activities

such as tamping. It is therefore necessary to develop short-, medium- and long-term plans for performing tamping on a

network or track section within a definite time horizon. To this end, two key aspects of infrastructure maintenance

planning are considered in this paper, deterioration modelling and scheduling optimisation. An exponential deterioration

function is applied to model the geometry quality of a series of 200 m segments of a 130 km line section, and an empirical

model for recovery after tamping intervention is developed. These two models are subsequently used to generate a

methodology to optimise a schedule for tamping intervention by minimising the total cost of intervention including the

cost of track possession while geometry quality is ascertained to be within a desirable limit. The modelling considers two

types of tamping interventions, preventive and corrective, with different intervention limits and tamping machines. The

result of this paper suggests a tamping plan which will lead to optimum allocation of track possession time while

maintaining the track geometry quality within specified limits.

Keywords

Tamping, track possession time, degradation, longitudinal level, optimization

Date received: 27 January 2013; accepted: 3 June 2013

Introduction

The improvement of the technical performance oftrack structures is essential to support the designcapacity and at the same time improve the servicequality of railway transport. Moreover, increasinglystringent safety requirements and demand for cap-acity for both freight and passenger traffic requiresadequately supported intervention measures withoptimum allocation and utilisation of track posses-sion time. These intervention measures are cate-gorised into track maintenance and track renewaltasks.1 Among the most important maintenance con-cerns for track structures are how to predict andcontrol degradation of track structure and how tomaintain the geometrical quality of the track.2

These factors influence ride quality and passengercomfort during operation, and also make a majorcontribution to the dynamics of the entire train/track system. Tamping is considered to be amaintenance task that has a large impact on the cap-acity of a railway network due to its particularrequirements such as track possession time, qualitydemand, heavy machinery involved and schedulingchallenges.

Effect of tamping operations on capacity

The time required to restore the geometry character-istics of a track is significant when the capacity of anexisting network is considered. Depending on themaintenance philosophies and track managementstrategies, the track possession demand for tampingcan vary for similar track sections. If an effectivetamping strategy is not deployed, the track designcapacity might not be achieved. Similar to other main-tenance activities on railway infrastructures, the par-ameters that affect the total track possession time arethe duration of the white period for each possession,travelling speed of the machine, working speed, prep-aration time and time for logistics considerations.3

Even though the duration of each possession

1Division of Operation & Maintenance Engineering, Luleå University of

Technology, Sweden2Luleå Railway Research Centre, Luleå, Sweden3Beijing Jiaotong University, Beijing, People’s Republic of China

Corresponding author:

Stephen M. Famurewa, Division of Operation & Maintenance

Engineering, Luleå University of Technology, Luleå 971 87, Sweden.

Email: [email protected]

Proc IMechE Part F:

J Rail and Rapid Transit

0(0) 1–11

! IMechE 2013

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window and working speed are important, schedulingprocedure is of particular interest in this studybecause redesign and innovation aspects are notwithin the scope of this work.

In the past, different principles have guided theplanning, scheduling and implementation of mainten-ance actions: these include manufacturers’ recommen-dations, experience within the railway organisation,assumed deterioration, availability of maintenanceequipment and other basic factors. However, thesefactors are not able to support the growing demandfor capacity, safety, cost-effectiveness and other ser-vice quality requirements for railway transport. Tothis end, several techniques and methods have beendeveloped for optimum planning and scheduling ofrailway infrastructure maintenance.

Track possession scheduling and optimisation

Developments in railway management have led toincreasing need for optimum planning and schedulingof maintenance activities. The parameters of interestin several maintenance optimisation tools and tech-niques include maintenance costs, labour cost, lifecycle cost, asset performance, track possession time,punctuality and other service quality parameters.4,5

Basically, maintenance optimisation of railway infra-structure gives short-, medium- or long-term plans forhow preventive maintenance will be performed, onwhich segments and within which time horizon. Tothis end, an overview of railway infrastructure main-tenance planning has highlighted two vital aspects ofinfrastructure maintenance planning: deteriorationmodelling and maintenance scheduling.6 On theaspect of track deterioration, important parametersto be taken into consideration for prognostics are ini-tial quality, initial settlement and rate of deterior-ation.3,7–10 The significance of the initial quality ofthe track at the time of installation was investigatedby Veit7, where the life cycle management perspectiveof track structures was also studied. The rate ofdeterioration is governed by an integrated process ofmaterial degradation, traffic-induced degradation andmaintenance. These phenomena are due to the designand layout of the track, rail profile, condition of theballast, bearing capability of the subgrade, drainageproblems, axle loads and traffic volume.3,11 On thescheduling aspect, maintenance activities are allocatedto available time intervals, or optimum track posses-sion windows are created for maintenance during thetimetable schedule. Higgins4 proposed a model todetermine the best allocation of maintenance activitiesand crews to minimise traffic disruption and comple-tion time. Miwa9 developed a mathematical program-ming model for an optimal tamping schedule; itindicated the track division for which tamping mustbe implemented within a specified horizon. Cheunget al.12 developed a track possession assignment

program to assign railway tracks to a given set ofscheduled maintenance tasks according to definedconstraints. The objective of the program is tocreate an assignment plan that maximises the assign-ment of job requests based on priorities while satisfy-ing all imposed constraints. A preventive maintenancescheduling program was presented by Budai et al.5 tocluster routine activities and projects for a link over acertain period such that the sum of possession costsand maintenance costs is minimised. They developedsome heuristics such as ‘most frequent work first’ and‘most costly work first’ to solve the formulated pre-ventive maintenance schedule problem. Andrade andTeixeira10 created a preventive maintenance schedul-ing program connected to track geometry qualityusing a bi-objective integer formulation that balancedrenewal and maintenance costs with train delays. Valeet al.8 developed a binary linear program to scheduletamping taking into consideration track degradationover time, track layout, quality recovery of track andtrack quality limits based on standards.

Several mathematical programs for preventivemaintenance scheduling problems have been formu-lated, and solutions have been proposed using multi-objective algorithms, artificial intelligenceapproaches, heuristic algorithms and other tech-niques. There is need to further address the optimumallocation and utilisation of track possession time formaintenance to enhance operational capacity. Thecontribution of this paper is an investigation of differ-ential deterioration along a length of a track andquantification of tamping intervention on a specificlength of track over a finite horizon. Also, a method-ology for optimum scheduling of tamping is proposedto minimise the direct cost of intervention and cost oftrack possession while maintaining geometrical qual-ity within the desired level.

Theory and model formulation

The lifetime of track structure, as well as the qualityof the track at any point in time, can be describedin terms of deterioration and recovery phenom-ena.7,9 There are some basic principles and theoriesthat are essential to the modelling of thesephenomena.

Track degradation

The passage of a train over a track generates enor-mous forces. This leads to deformation and wear oftrack components such as rails, sleepers, fasteners,ballast and subgrade, and consequently, long-termdeterioration of the track geometry.13 This phenom-enon is one of the most important aspects of railwayinfrastructure maintenance. Thus, it is a vital require-ment to adequately understand the pattern of deteri-oration of track geometry quality due to the

2 Proc IMechE Part F: J Rail and Rapid Transit 0(0)




accumulation of plastic and elastic deformation as aresult of traffic loading.

The geometry quality and irregularity of ballastedtracks are monitored by some key parameters includ-ing longitudinal level, alignment, gauge, cross leveland twist.3,14,15 To manage track geometry problems,infrastructure managers (IMs) and academic research-ers have monitored the evolution of principal param-eters such as longitudinal level and alignment2,8,15,16

while others have used derived indices such as vari-ation of acceleration (due to irregularity)7 and com-binations of quality parameters to monitor the growthof track quality defects. Moreover, the standard devi-ation of the irregularity in the vertical direction of thetrack coordinate system has been proven to be suffi-cient to model the track geometry quality and also tosupport maintenance decisions and actions. 3,15,17

The life cycle behaviour of track has beenexplained using different empirical models based onmeasurement records and load or time. These modelsinclude the grey model, linear model, exponentialmodel and other empirical models.2,7,8,11,15,16 Theexponential model in equation (1) is preferred in thisstudy considering the established behaviour of track;high-quality track or new track deteriorates slowlywhile low-quality track or ageing track deterioratesrapidly. The standard deviation of a vertical irregu-larity for a segment s at time t is given as

�ðs, tÞ ¼ �ðs, 0Þeb sð Þt ð1Þ

where � s, 0ð Þ is the initial standard deviation for seg-ment s estimated from vertical irregularity valuesfrom the recording car over a length of 200m andb(s) is the exponential constant or degradation ratefor segment s estimated from a series of measurementsover time.

Tamping and recovery

The quality of the track geometry eventually deterior-ates beyond the allowable threshold for maintenanceand safety giving rise to the need for intervention torestore it to the design specifications. The interventionlevel depends on the tamping strategy deployed.Common strategies in use by IMs include correctionof isolated defects and restoration of lines whenspecified thresholds are reached. The details of rec-ommended intervention limits can be found inEN-13848-5.17 Ideally, from a life cycle perspectivethese thresholds should be dynamic, thereby becom-ing dependent on the age of the track structure or thenumber of interventions carried out. This practice willenhance the durability of track quality and alsoextend the lifespan of the track. Other factors con-sidered in tamping are the availability of tampingmachines and the maintenance philosophy of theowner of the asset. When a prognostic tamping

strategy is to be deployed, the recovery or amountof improvement to be achieved by the tamping mustbe known in advance.

In reality, the recovery or efficiency of tampingdepends on several factors such as track quality attamping, age of track components, tamping tech-nique, number of previous tamping operations, bal-last condition and human factors. In the presentstudy, an empirical regression model based on datacollected in previous research on the investigatedroute has been developed.18 The model describes therelation between the standard deviation of the longi-tudinal level before tamping and the improvement fol-lowing tamping after passage of some traffic forstabilisation of the track. The model is used to predictchanges in the geometry parameter at any point intime when tamping is carried out. Figure 1 shows aplot of the observed recovery and quality at interven-tion. The regression model is given in equation (2),and it has an R2 value close to 0.7. In order toimprove the prediction accuracy of the simple regres-sion model, a 90% prediction limit was estimated forthe model to account for other parameters that couldaffect the recovery value

Recovery R ¼ 0:5445�ðs, tÞ � 0:8893 ð2Þ

The linear model shown in Figure 1 suggests thatrecovery depends on the quality at the point of inter-vention. Only the observation data that fall within theregion considered most likely for good substructureand ballast condition in the best-practice guide foroptimum track geometry durability15 are shown inthe figure.

Assumptions

The following assumptions underpin the model devel-oped in this paper.

1. Deterioration follows an exponential model basedon the explanation given earlier that high-qualitytrack deteriorates slowly, whereas low-qualitytrack deteriorates rapidly and irreversibly (seeequation (1)).

2. The degradation rate of each 200m track section isconsidered to be constant within the time horizonconsidered for the scheduling in this study.

3. The track section is considered to have good bal-last conditions because the track structure is rela-tively new. Thus, tamping recovery is assumed tolie within the region considered likely for efficienttamping in a good ballast condition and to followthe model described in the previous section. Thesame recovery model is used for all the segments.

4. Segments with switches and crossings and othercritical units will be maintained using spot tamp-ing considering them as isolated defects. The

Famurewa et al. 3




reason for this is because so many engineeringworks are carried out on these segments; thus tomodel their deterioration, additional measurementis required.

5. There are two tamping machines, one has limitedavailability, high tamping efficiency, and it isused for early or preventive intervention. Thesecond one is more available but has a relativelylow tamping efficiency and is suitable for lateintervention or corrective tamping. Optimumallocation seeks a balanced mix of the two pos-sibilities in terms of cost, quality and time onthe track.

6. There are four different stations that can providetemporary parking for the machines before andafter tamping.

Optimisation procedure

The activity breakdown structure shown in Figure 2is a simplified intervention process for both prevent-ive and corrective policies. The travelling timedepends on the speed and location of the tamperbefore the shift, while the set-up and dismantlingtimes are fixed.

A simplified representation of the optimization pro-cedure is given by the flow chart shown in Figure 3. Analgorithm was developed in FORTRAN to obtain asolution for the model formulated in equations (3) to(8). The notation is defined in Appendix 1.

The objective function for intervention decisions is

tw N tð Þð Þ ¼ max t1 þ t2 þ t3f g ð3Þ

Figure 1. Recovery of track geometry quality after tamping interventions. (1*- preventive intervention threshold and 2*- corrective

intervention threshold.).

t1= t

11+ t

12

t2= t

21+ t

22=2t

p

t12

t22t3t21t11

Tra

vell

ing

Tra

vell

ing

Tamping

Act

ivit

ybr

eak

dow

n

Track possession time

Set

up

Tak

edo

wn

Figure 2. Track possession time for interventions.





s:t:

tw N tð Þð Þ5 t�wtw N

0 tþ 1ð Þð Þ4 t�w

N0 tð Þ ¼PSs¼1

f � s, tð Þ � ��

f x½ � ¼1, x50

0, else

�

N tð Þ4N0 tð Þ

8>>>>>>>>>><>>>>>>>>>>:

The decision function is

g tw½ � ¼1, tw N tð Þð Þ ¼ max t1 þ t2 þ t3f g0, else

�ð4Þ

where

t1 ¼ min s 1ð Þ � pðiÞ�� þ s Nð Þ � pð j Þ�� þ s Nð Þ�

�s 1ð Þ � N� 1ð Þ� � dv0

i, j 2 1, . . . , npark� �

ð5Þ

t2 ¼ 2tp N� nað Þ ð6Þ

t3 ¼Nd

vð7Þ

The number of corrective intervention shifts requiredto maintain the line section, given a specific number ofpreventive maintenance shifts is

Nc:shift Tð Þ ¼XTt¼1

g tw Nc tð Þð Þ½ �

g tw½ � ¼1, tw ¼ max t1 þ t2 þ t3f g0, else

� ð8Þ

Case study

Description of case study

A line section in the network of the SwedishTransport Administration (Trafikverket) is con-sidered in the case study. The line section is 130 kmof single track from Kiruna to Riksgränsen. It isbasically a freight line because the majority of thetraffic is iron ore freight, although passenger trainsand other freight trains also use the line. Thus, the

I D DTTC C C TT−= +

( ) ( )( )1

T

I D p p c ct

C c N t c N t−=

= +∑ ( ) ( )( ) *. .p shift c shift wTT N T N T t= +

[ ] 1wg t =( ), 1 2s t Eqn Eqnσ = −

( ),0sσ ( )b s

( ),s Tσ

Track simplification and characterization

Track simplification and characterization

Yes

Track degradation Eq 1

Track degradation Eq 1

Degradation rateDegradation rate

Intervention decisionIntervention decision

Recovery Eq 2

Recovery Eq 2

Initial track qualityInitial track quality

Direct Intervention CostDirect Intervention Cost Track possession timeTrack possession time

Total Intervention Cost Total Intervention Cost Track quality after TTrack quality after T

No

Figure 3. Flow chart for the optimisation of track possession and cost of tamping.

Famurewa et al. 5




line has a high socio-economic importance and highmaintenance requirements. The train speed on the lineis between 80 and 120 km/h. The maximum allowableaxle load on the line section is 30 t and the annualaccumulated tonnage is over 22 MGT. The line hascontinuous welded rail, head hardened 60E1 rail type,with concrete sleepers and Pandrol fasteners. It ishighlighted that the track structure on this line sectionwas renewed between 2006 and 2009; this major workalso included ballast renewal. It should also be notedthat this line section operates in extreme climatic con-ditions which can influence the reliability, availability,maintainability and safety characteristics of the infra-structure. The winter season sees snowfall andextreme temperatures. The annual temperatures varybetween �40 �C and þ25 �C.

Inspection data

Inspection is an important element of any effectivepreventive maintenance programme. Track geometryinspection is needed for planning a tamping strategythat is optimum in the allocation and utilisation oftrack possession time. It also gives useful informa-tion to avoid tamping too early or too frequently,which degrades the ballast condition, and at thesame time to warn against intervening too late,which can result in a temporary speed restrictionor failure. Track inspection is done by the IMbased on two factors, speed and annual accumulatedtonnage on the section. For the case study, trackquality inspection was done three to six times ayear, generally between April and October. Theavailable inspection data extend from 2007 to 2012,and for each 200m segment, only data after the com-pletion of renewal were considered. Several geometryparameters were recorded by the train measurementvehicle, but only the standard deviation of the lon-gitudinal level over each 200m track length was used

for the geometry quality prognosis and maintenanceoptimisation. The standard deviations of the longi-tudinal level (3–25m wavelength) for a 200m tracksegment from four measurements on the 130 kmline section investigated in this study are shown inFigure 4.

Results and discussion

The results and findings of the modelling and predic-tions of deterioration and recovery phenomena in thisstudy are presented in this section.

Non-homogeneity of track sections

The degradation rate of the longitudinal level for each200m segment was estimated using the exponentialmodel explained in the previous section and the2007–2012 inspection data. The degradation rate isan indication of the evolution of the track geometryquality for each segment. The distribution of the deg-radation rates for all 592 segments is shown inFigure 5. It is heavily skewed to the right, indicatingthe existence of critical spots with rapid degradationin their geometric quality. More than 50% of thetrack section has an exponential degradation ratebetween 0.00024 and 0.00060. The differential degrad-ation rate along the track sections reflects non-homogeneity and variation of track componentsalong the track length. In fact the 200m track seg-ments can be regarded as non-identical units interms of quality deterioration.

An inference that can be drawn from this plot isthat continuous tamping of the whole length of thetrack section might not be the best strategy in terms oflife cycle management of the track. An essential main-tenance requirement revealed by the figure is the bal-ance of preventive and corrective tamping, since ahigher exponential rate will require more

Oct 2009

Sept 2010

Sept 2011

June 2012

0

2040

6080

100

120

0

1

2

3

Inspection dateLocation (km)

Std

dev.

Lon

g le

vel

Figure 4. Standard deviation of longitudinal level over the 130 km line section.





interventions than a lower exponential rate, this isalso noted by Arasteh Khouy et al.18

Tamping strategy

Based on the observation of a differential degradationrate along the track length, there is a need to optimisethe preventive and corrective tamping interventionson the track section. Using the model proceduredescribed in the flow chart (Figure 3) and equation(8), the number of corrective interventions that will berequired in 2 years for different numbers of allocatedpreventive tamping shifts was estimated, and the

result is shown in Figure 6. The sensitivity of theresult is also shown using the 90% prediction limitof the recovery model fit. Increasing the number ofallocated shifts for preventive tamping decreases theconsequent number of corrective tamping shifts up toa point where there is no need for corrective tampingafter the initial one which was necessary at the begin-ning when few sections were above both interventionthresholds.

Direct cost of intervention

Using the proposed optimisation procedure shown inFigure 3 with different cost ratios for the two tampingpolicies, the total cost for tamping interventions overa short period of 2 years is given in Figure 7. A highvalue of the ratio cp/cc results in a higher cost of inter-vention when the number of preventive maintenanceshifts increases.

For all cost ratios, the direct cost of intervention isconstant after 16 shifts because no more segments willexceed the preventive maintenance threshold withinthe 2 year period of planning. For low correctivemaintenance costs, the economic optimum plan in ashort period will always be to carry out correctivemaintenance. However, this is not always the bestpolicy, particularly during the early life of the track,because it will reduce the service life. From Figure 8the economic optimum policy considering a cost ratioof cp/cc¼ 1 is to have only a few preventive interven-tion shifts. However, track possession time and qual-ity of the track are other parameters that need to beconsidered.

0,00

192

0,00

168

0,00

144

0,00

120

0,00

096

0,00

072

0,00

060

0,00

048

0,00

036

0,00

024

0,00

012

0,00

000

120

100

80

60

40

20

0

Exponential constant

Num

ber

of s

egm

ents

Figure 5. Distribution of exponential constant or degradation rate.

Figure 6. Corrective interventions and scheduled preventive

interventions.

Famurewa et al. 7




Cost of intervention and track possession

The present demand on railway infrastructurerequires augmented allocation and utilisation oftrack possession time, and thus there is a need toimplement optimum maintenance practice. In view

of this, the global cost model proposed in Galaret al.19 was adapted to estimate the total cost of inter-vention by adding the direct and indirect costs ofintervention. Following the model procedure outlinedin Figure 3 and using stochastic simulation for therecovery model (equal chance of obtaining recovery

Figure 8. Maintenance costs for a finite horizon using a cost ratio cp/cc¼ 1. (P.I.¼ preventive intervention; C.I.¼ correctiveintervention).

Figure 7. Total maintenance costs at different cost ratios.





within the prediction limits, see Figure 1), robust esti-mation of track possession time was obtained andalso the indirect cost of intervention (usingCDT � 2cc). Figure 9 shows the total track possessiontime over a short period of 2 years for different num-bers of preventive intervention shifts. Strategies withan Np.shift value of between five and eight are efficientbecause they are in the range of the values of theminimum track possession time. Furthermore,Figure 10 shows the total cost of intervention withdifferent numbers of shifts allocated for preventiveintervention. According to the results shown inFigure 10, selecting strategies with more than eightpreventive maintenance shifts will result in additionalcost due to overly frequent track possession. An opti-mum strategy should have a high economic perform-ance, process efficiency and satisfy the requiredeffectiveness in terms of track quality. In view ofthis, strategies with Np.shift values up to eight arecost-efficient because they are in the neighbourhoodof the minimum total intervention costs. However, it

is necessary to confirm the optimality of any of thesestrategies by assessing the resulting quality character-istics to see if they meet the quality requirement of theinfrastructure manager. In this study Np.shift¼ 8 issuggested because it is cost-efficient and producesbetter quality than other strategies with lower pre-ventive maintenance shifts.

Track quality characterisation

The tamping strategies were evaluated by characteris-ing the predicted geometry quality using the proced-ure in the current state-of-the-art description for trackgeometry quality.20 Figure 11 presents the cumulativefrequency distribution of the predicted longitudinallevel defects over the length of the entire track section.The figure characterises the initial quality and alsotrack quality after 2 years for three different scenarios:no tamping, Np.shift¼ 8 and Np.shift¼ 16. If it isrequired by the IM that at least 90% of the total seg-ments on the track section should not exceed trackquality class C (�LL< 1.8mm) for safety, comfort,ride quality and life cycle management reasons, thenfrom Figure 11 having Np.shift¼ 8 is adequate.

Table 1 gives the detailed description and extendedclassification of the track section into track qualityclasses for the 2 years under consideration using theprocedure mentioned previously. If the requirement ofthe IM puts a limit on the proportion of the tracksegments expected to be in each quality class withina certain time horizon, then this can be checked.

Conclusions

The demand on the allocation and utilisation of trackpossession time is increasing, and there is a need todevelop a model to support maintenance decisions,particularly for maintenance tasks with high posses-sion requirements. This paper has presented an

Figure 11. Cumulative frequency distribution of track quality

indicator.

Figure 9. Track possession time.

Figure 10. Total cost of intervention.

Famurewa et al. 9




optimisation tool to support the allocation of trackpossession time in a short-term plan for tamping.It considered the exponential function to model thedeterioration of each 200m segment in the case study.

The study found a varying degradation rate of thelongitudinal level over the studied 130 km track sec-tion with about half of the segments having an expo-nential degradation rate of between 0.00024 and0.0006. The objective of the optimisation model is tominimise the direct costs of intervention and trackpossession while geometry quality is maintained at adesirable level. In the case study, the optimum tamp-ing strategy for a 2 year planning horizon will be toallocate eight shifts for preventive tamping while add-itional quality failures will be restored using a correct-ive intervention policy. This will support adequateplanning and resource allocation including orderingof tamping machines. This approach provides: know-ledge of track behaviour; quantification of tampingrequirements; and a suggested tamping strategy thatreduces track possession time and associated costs.

Finally, in future work a long-term plan will bedeveloped that considers dynamic intervention thresh-old levels for the two policies: low threshold levels atthe early stage of the track life and high thresholds atthe later part.

Funding

The authors wish to thank Trafikverket and Luleå RailwayResearch Centre for financial support.

Acknowledgement

The technical support provided by Professor Diego Galar,

Dr Arne Nissen and Jens Jönsson was greatly appreciatedby the authors.

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geometry durability. UIC Railway TechnicalPublications, 2008.

16. Quiroga LM and Schnieder N. Monte Carlo simula-

tion of railway track geometry deterioration andrestoration. Proc IMechE, Part O: J Risk Reliab 2012;226(3): 274–282.

17. EN-13848-5: 2010. Railway applications – track – trackgeometry quality – Part 5: geometric quality levels –plain line.

18. Arasteh Khouy I, Juntti U, Nissen A and Schunnesson

H. Evaluation of track geometry maintenance (tamping)in Swedish heavy haul railroad – a case study.Proceedings of the Institution of Mechanical Engineers,

Part F. Journal of Rail and Rapid Transit. Epub aheadof print 25 March 2013. DOI: 0954409713482239.

19. Galar D, Parida A, Kumar U, et al. The measurement

of maintenance function efficiency through financialKPIs. J Phys: Conf Ser 2012; 364(1): 012112.

20. EN-13848-6: 2012. Railway applications – track – track

geometry quality – part 6: characterisation of trackgeometry quality.

Table 1. Percentage of the track falling into each quality class (A is the best, and E is the worst).

Scenario A< 0.75 mm B 0.75–1.1 mm C 1.1–1.8 mm D 1.8–2.5 mm E> 2.5 mm

Initial 24.12 41.48 30.02 4.21 0.17

Np.shift¼ 8 5.40 26.98 58.68 8.94 0.00Np.shift¼ 16 5.40 37.27 57.16 0.17 0.00No tamping 5.39 23.94 49.07 14.68 6.92





Appendix 1

Notation

cp,cc cost of preventive and corrective inter-vention per segment

CDT cost of downtime per hour (depends online class)

CI�D direct cost of intervention in T daysCI�I indirect cost of intervention in T daysd length of segment¼ 200mna number of adjacent segments among

tamped segmentsnpark total number times tamping machine is

parked (in this study npark¼ 4)N number of segments tamped in preven-

tive intervention shift Np� �

or correctiveshift Ncð Þ

Nc:shift number of corrective intervention shiftsrequired for a specified number of pre-ventive intervention shifts Np:shift

N0 tð Þ number of segments above preventivethreshold ðN0pÞ or corrective thresholdN0c� �

on day t

p location of start parking lot p ið Þ and endparking lot p jð Þ i, j 2 1, . . . , npark

� �s ið Þ location of tamped segments

8s ið Þ 2 S and i ¼ 1, . . . ,Ntp, t1 time for each set-up and disassemble¼

10min, total travelling time during ashift

t2,tw total set-up and disassemble time for ashift, duration of shift. (minimum dura-tion t�w ¼ 6 hÞ

TC total cost of intervention in T daysTT total track possession timev tamping speed for preventive tamper

vp ¼ 1:4 km=h and corrective tampervc ¼ 0:8 km=h

v0 travelling speed for preventive tamperv0p ¼ 90 km=h and corrective tamperv0c ¼ 80 km=h

�� threshold for preventive interventions��p ¼ 1.8mm and corrective interven-tions ��c ¼ 2:1mm from EN-13848-5.

Famurewa et al. 11


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