ARTICLE IN PRESS

Reliability Engineering and System Safety 94 (2009) 1308–1313

Contents lists available at ScienceDirect

Reliability Engineering and System Safety

0951-83

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/ress

Business-oriented prioritization: A novel graphical technique

R. Pascual c,�, G. Del Castillo a, D. Louit b,c, P. Knights d

a Department of Mechanical Engineering, Universidad de Chile, Casilla 2777, Santiago, Chileb Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chilec Centro de Minerıa, Pontificia Universidad Catolica de Chile, Av. Vicuna Mackenna 4860, Santiago, Chiled Division of Mining Engineering, Faculty of Engineering, Architecture and Information Technology, The University of Queensland, St. Lucia, Brisbane, 4072, Australia

a r t i c l e i n f o

Article history:

Received 12 November 2008

Received in revised form

15 January 2009

Accepted 29 January 2009Available online 14 February 2009

Keywords:

Prioritization

Physical asset management

Maintenance decision-making

Resource assignment

Criticality

Subset selection

Multicriteria analysis

20/$ - see front matter & 2009 Elsevier Ltd. A

016/j.ress.2009.01.013

esponding author. Tel.: +56 2 9784906.

ail address: rpascual@ing.puc.cl (R. Pascual).

a b s t r a c t

Traditionally, Pareto analysis has been used to select the most critical components and failure modes of

a system. A clear disadvantage of this technique is that it requires preselecting a single criterion to

establish priorities. More recently, a graphical log-scatter diagram technique has been proposed. It

considers three key performance indicators simultaneously: reliability (MTBF), maintainability (MTTR),

and unavailability (D). This technique considers only times and does not include economical effects

explicitly. This article extends both techniques to explicitly consider both direct and indirect costs to

prioritize from the point of view of an asset manager or from a maintenance decision-maker, as

required. Due to the economic-based approach of this article, cost discounting is also considered inside

financial costs such as—but not limited to—reliability-related investments. Also, the results are

displayed on simple and accessible graphs which make them particularly useful for conveying results to

non-technical managers. The methodology is illustrated by analyzing a shovel from the copper mine

industry, and it clearly shows how the proposed technique facilitates business oriented decisions and

how they should change under different market conditions.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

To meet the increasing challenges of current industrial reality,organizations require to continuously enhance their capability toadd value and improve the cost-effectiveness of their decisionprocesses. The decision process includes the selection of thosesystems and actions that may render the highest overall savings,and then, their associated policy resolutions.

Decision making in physical asset management (PAM) isgenerally focused on two levels: strategic and tactic. Strategiclevel analysis is of greater interest because it involves: (i)identifying and ranking of candidate systems for improvements;(ii) system level budgeting and budget forecasts; (iii) system levelperformance evaluation; (iv) forecast of future market andoperational conditions. The tactical level, on the other hand,concerns more specific technical management decisions for theindividual projects. It includes: (i) assessing the causes ofdeterioration and determining/selecting candidate solutions; (ii)assessing benefits of the alternatives by life-cycle costing; (iii)selecting and designing the desired solutions. The prioritizationtechnique introduced in this work deals with both strategic and

ll rights reserved.

tactical decision making, as selection of critical systems is presentat both management horizons.

The paper is organized as follows: first, we present a generalreview of priority setting in engineering problems and then toPAM problems. From there, we consider Pareto and Jack knifediagrams (JKD), which justify the introduction of the so-calledcost scatter diagrams (CSD). An extended case study from aprevious reference is used to illustrate the advantages of the newtechnique. Discussion and future work is presented in Section 4.

1.1. Priority setting in the context of engineering

Decision problems in engineering can be classified as evalua-tion or design problems. When facing an evaluation problem, thedecision maker analyzes a set of discretely predefined alterna-tives. The evaluation step can be done using aggregate valuefunction approaches and/or outranking approaches. In the firstgroup we may mention general techniques such as multi-attributeutility theory methods [1], simple multi-attribute rating techni-ques [2], inverse preference methods [3], and analytic hierarchyprocess (AHP) [4]. In the group of outranking techniques weinclude: ELimination Et Choix Traduisant la REalite (ELECTRE) [5]and Preference Ranking Organisation METHod for EnrichmentEvaluations (PROMETHEE) [6]. Detailed comparison of these kindsof methodologies can be found in Zopounidis and Doumpos [7].

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R. Pascual et al. / Reliability Engineering and System Safety 94 (2009) 1308–1313 1309

For instance, drawbacks of outranking methods arise from themany rather non-intuitive inputs that are required, i.e., thepreference functions of PROMETHEE. If the number of alternativesis sizeable, a rank reversal problem may arise in the AHP method.

Previously mentioned generic evaluation techniques have beenused previously in PAM. Bevilacqua [4] describes an application ofthe AHP for selecting the best maintenance strategy for an oilrefinery. Carnero [8,9], also uses AHP but combines it with factoranalysis. As a drawback, the pairwise comparison required byAHP may become fairly time consuming if a large number ofalternatives need to be evaluated. Karydas and Gifun [1] use it toprioritize maintenance in the context of facility management.Deshpande [10] studies the role of multicriteria priority codes inthe military service parts system and the impact of these codes onsystems performance. Dekker and Scarf [11] describe a rankingmethodology that indicates the expected money loss by deferringexecution of maintenance tasks. They also describe the decisionsupport system where they implemented such technique andshow a case study from the process industry. In the more generalfields of risk assessment and vulnerability analysis, Hokstad andSteiro [12] and Einarsson and Rausand [13] provide frameworksfor priority setting. In the first case, they use a broad definition ofrisk that accounts for up to 11 criteria simultaneously.

Cooke et al. [14] develop a ranking tool which uses failure dataand structured judgment to rank and upgrade the basis fordecisions regarding inspection and replacement of undergroundpipelines. Chareonsuk et al. [15] propose a multicriteria approachto the rank and select preventive maintenance intervals using thePROMETHEE [6], one of the outranking methods for multiplecriteria problems.

In an engineering design problem, the decision maker alsofaces the identification of the preferred alternative from a infiniteset defined by a set of constraints. The latter case is usually solvedby using mathematical programming techniques. Examples ofdesign problems in the context of PAM are the multicriteriaproject selection [16], the assignment of overhaul funding forfleet of diverse equipment under budget constraint [17] and thedesign of maintenance intervention protocols [18]. Mathematicalprogramming is resource-intensive and relatively complex toimplement.

Interventioncosts

Holdingcosts

Reliability relatedinvestments

Penaltycosts

Fig. 1. Components of the global cost.

1.2. Priority setting in PAM

Although previously mentioned methods have been used inthe context of PAM, there are more intuitive techniques that usethe particular properties that relate common use key performanceindicators (KPIs) and facilitate decision making (further describedbelow). In order to perform the systems selection, a holistic,life-cycle centered approach can be used. By doing so, the analysisis not limited to points of view of the maintenance function.PAM considers five sequential steps of the life cycle [19,20]:conceptualization, design, implementation, operation (includingmaintenance), and retirement. It must set, control and balance aset of KPIs such as availability, reliability, productivity, overallequipment effectivity (OEE), intervention costs, and global cost.This set of KPIs must be balanced by setting maintenance policiesthat may range from corrective (run to failure) to proactive(system redesign [21]). Of course, setting such policies requiresthe availability of resources. As they are usually scarce, aprioritization process must be established. It must be at systemor subsystem level, or, if they have been selected, at prioritizingfailure modes. Traditionally, Pareto analysis has been used to setdecision priorities. Pareto analysis is highly useful to focusdecision making on a small set of systems/failure modes.Complementarily, they can also be used to estimate the global

value of a KPI only from the most critical elements, i.e., Al-Hajj andHorner [22] propose a predictive total cost model built only fromthe costs of the most critical sub-systems. A problem with Paretois that it requires selecting a single classification criterion.

To overcome this, other classification schemes have beenproposed, i.e., risk priority numbers [23,24] and criticalitynumbers [25]. Another example of this type of method is themulticriteria classification of critical equipments proposed byGomez and Ruiz [26]. These schemes build polynomials thatassign a single classification number to each subsystem/failuremode. Beehler [27] proposes a decision matrix which includes aset of parameters to rank and select the most critical systems.Labib [28] and Burhanuddin et al. [29] present a decision makinggrid and a case study considering both frequency and downtimeas classification criteria. Knights [30] enhances the concept byadding total downtime isoquantas to the diagram (also known asJKD and further described below). As a result, we find a 2D scatterdiagram that concerns three criteria simultaneously: frequency,downtime, and unavailability. As it only contains time basedinformation, it is insensitive to economic effects on the businesscycle, something that is known to affect decision-makingpriorities. In order to overcome that, we propose the CSDmethodology in the next section.

To be able to assess savings, a cost estimation process isneeded. Consequently, a cost structure is required. In this articlethe global cost is used, as defined in Jourden et al. [25]. It iscomposed of four terms: intervention costs, holding costs,reliability related investments, and consequential costs. Interven-tion costs include the value of spares and labour. Holding costsrepresent the financial cost of having spares available on-site. Thereliability related investments term considers all acquisitionsmade to attenuate the effect of maintenance (i.e., redundantequipment, stock piles, and insurances). The final term refers todowntime costs and other costs associated with move from/to astandard production method for maintenance reasons (Fig. 1).

1.3. Jack knife diagrams

The total downtime MDTj of a system during a given period oftime T , due to an intervention code (or code), is the product of thenumber of times nj that this code occurred and the mean time outof service MTOSj the system:

MDTjðTÞ ¼ njðTÞ �MTOSjðTÞ (1)

If all codes are displayed in an n vs. MTOS diagram, it is possibleto discriminate those codes that cause the major downtime, but itis also possible to assess if it is due to high frequency of to hightime out of service. A disadvantage of using Eq. (1) directly is thatiso-downtime curves are drawn as hyperbolaes. This can be easilyovercome by using the identity:

log MDTjðTÞ ¼ log njðTÞ þ log MTOSjðTÞ (2)

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A con on using Eqs. (1) and (2) is that they depend on T . If it isdesired to compare the system performance at two differentintervals of time (or two different systems), they would have to beof the same length to make a logical comparison. One way toovercome that is by using the unavailability, as it is explainedbelow.

Unavailability (D) is the product of two factors; the frequencyof interventions (f ) that occurred in a particular time frame andthe average associated time-out-of-service (MTOS), which, in thecase of a failure corresponds to the mean time to repair (MTTR):

Dj ¼ f j �MTOSj (3)

Eq. (3) offers the possibility to produce a diagram to show thoseinterventions that consume more availability and be able todiscriminate if it is due to high frequency or to high time-out-of-service. Again

log Dj ¼ log f j þ log MTOSj (4)

produces a straight line on a log–log diagram. This enhanced wayof producing the diagram shown in Fig. 2, permits drawing iso-unavailability lines which are easy to interpret; i.e., one can draw

1 2 11 3 10 7 12 8 5 15 6 9 4 17 14 16 130

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Code

Una

vaila

bilit

y

Fig. 2. Pareto analysis for unavailability, taken from the case study. Individual and

aggregate contributions are shown.

Table 1Model parameters.

ID Description Qty. Duration (min)

1 Electrical inspections 30 1015

2 Damaged feeder cable 15 785

3 Change of substation 27 690

4 Coupling repairs or checks 15 225

5 Power cuts to substations 21 395

6 Rope limit protection 10 277

7 Auxiliary motors 13 600

8 Main motors 12 555

9 Lighting system 26 240

10 Overload relay 23 685

11 Motor over temperature 36 745

12 Earth faults 7 575

13 Miscellaneous 9 115

14 Control system 7 165

15 Air compressor 8 355

16 Operator controls 5 155

17 Over current faults 6 220

Quantity recorded in a one-month period. Costs have been estimated arbitrarily.

the line of D ¼ 1%. Any code above that line ‘eats’ more than 1% ofthe system availability.

We observe that, in general, codes related to preventivemaintenance affect the position of corrective codes. If this is notoccurring, the preventive action is not being technically effective.Let us take for example the inspection of a hose of a shovel. If isnot done well or with enough frequency, the failure rate of thiscomponent will probably increase.

A modified version of the JKD is proposed in Karim et al. [31].In their case, the axes variables are number of defects and cost ofdefects in a setting of evaluating construction contractorsperformance.

2. Cost scatter diagrams

As mentioned before, JKD consider only times and frequencies,and correspondingly, no economic effect is explicitly taken intoaccount. In what follows, we propose the CSD. The intention is toenhance the graphical analysis by adding the cost dimension.

2.1. Model formulation

The expected maintenance global cost per unit time cg of agiven system can be obtained by summing the gains from allinterventions (i.e., failures, preventive replacements, inspections,and other shutdown actions):

cg ¼Xn

j¼1

ðci;j þ cf ;j þ csi;j þ ca;jÞf j �MTOSj (5)

cg ¼Xn

j¼1

cgjDj (6)

where MTOSj is the mean downtime associated to each interven-tion j, f j corresponds to the frequency of intervention j, ci;j is thedirect cost per unit time of intervention j (spares, labour,mobilization, planning, and administration), cf ;j corresponds tothe downtime cost per unit time, ca;j is the holding cost due tospares and its amortizations per unit time, csi;j stands for the costfor having redundancies and other reliability-related investments,per unit time.

Notice that there are two terms that acknowledge investments,ca;j and csi;j. Each of these terms, in order to be considered in one

Int. cost (USD/int.) a Capital spares (�104 USD)

80 0 5.5

300 0 300

50 1 15

500 0 7

40 1 1.8

50 1 1.5

300 1 35

400 1 80

500 1 4

2000 1 70

800 1 1

50 1 5

100 1 12

600 1 23

700 1 1

200 1 8

400 1 3

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generic time unit, must be transformed in two senses: as aninvestment equally distributed over time and as a financial cost[25]. The cost rate cgj can be considered as a weight for eachunavailability. As MTOSj considers the full logistic cycle for eachintervention:

cijMTOSj ¼ Cij (7)

where Cij is the mean cost charged for the work order or invoice.The consequential cost per unit time out of service is expressed as

cfj ¼ acf (8)

where a is a factor between 0 and 1 according to the planninglevel of the intervention, the existence of stock piles andequipment redundancy and alternative production methods[32]. a represents the attained level of opportunistic maintenanceof the action. For example, an inspection is an intervention that isplanned to minimize effects for production, so a! 0. In othercases, the estimation of a requires sensitivity analysis as it will bedescribed in the case study. An example: what is the effect of ahaul truck failure on the production program when there is a haultruck redundancy of 11 out of 10?

0.007

0.05

10-0.8

100.1102

103

104

9

11

Frequency (1/hour)

3

5

1

4

10

13

6

27

8

1415

1716

MTOS(hour-out-of-service)

12

Spe

cific

glo

bal c

ost

(US

D/h

our-

out-o

f-ser

vice

)

Fig. 3. Cost scatter diagram. 3D version. Points marked with a cross are the most

critical for the global cost.

0.007 0.0510-0.8

10-0.6

10-0.4

10-0.2

100

1

2

3

4

5

6

78

9

10

11

12

13

14

15

1617

Frequency (1/hour)

MTO

S (h

our-

out-o

f-ser

vice

)

Iso-unavailability

D = 2.3%

FeederCable

Inspections

Fig. 4. Jack knife diagrams. Cutting axes have been drawn in the mean value of each crit

observed above. Points marked with a cross are the most critical for the global cost. (a

Let us observe in Eqs. (7) and (8) that JKD and CSD produce thesame results when

acfbci

such situation arises often in the mining industry as theopportunity costs per unit time are large and no alternativeproduction method is available: high unavailability means highglobal cost.

3. Case study

Table 1 is taken from Knights [30] and lists the unplanneddowntime recorded for electrical failures in a fleet of cable shovelsat an open pit copper mine located in northern Chile, over a one-month period. The cost terms have been added and do notrepresent the actual case.

The JKD is shown in Fig. 4(a). The five most criticalinterventions when using the availability criterion are thefollowing codes: 1, 2, 3, 10, and 11. Fig. 3 shows the 3D versionof the CSD (Eq. (5)). It has been simplified to its 2D version(Eq. (6)) in Fig. 6(a). There, it can be observed that the interventioncodes most critical for the business are: 2, 7, 8, 10, 11, and 12(highlighted in both figures). This information can be added to astandard JKD in order to study the effect of the global cost in theselection of the most critical components (Fig. 4(b)): it can benoticed that codes 1 and 3 are important for the availability of thesystem, but, they are not as critical for the business, so theiranalysis can be postponed in front of components 7 and 2 whichare more critical for the global cost.

The analysis can also be made using only intervention costs(Fig. 5). In this case the most critical codes are: 4, 9, 10, and 11. Ofcourse, this approach would leave in a second plane variouscomponents which are critical for the business and not so muchfor the maintenance budget. Anyway, this version of CSD can bevery helpful for service-oriented organizations.

Fig. 6(b) shows the influence of changes in the business cycle.The product has reduced its price by 75% with respect to thereference value. Points move to the left as the global cost has beenreduced, depending on the a factor for each intervention.

Fig. 7 shows a sensitivity analysis W.R.T. a. The a valueshave been evaluated in the range ½0;1�. Accordingly, it generateslines instead of points in the CSD. They show the impact ofmoving from fully opportunistic interventions to fully unplanned(and without contingency plan) interventions. This informationprovides new insight for prioritization. It can be taken as a versionof a Tornado diagram [33].

0.007 0.0510-0.8

10-0.6

10-0.4

10-0.2

100

1

2

3

4

5

6

78

9

10

11

12

13

14

15

1617

Frequency (1/hour)

MTO

S (h

our-

out-o

f-ser

vice

)

erion. Notice that the enriched JKD corresponds to a special case of Fig. 3 when it is

) Standard JKD. (b) Enriched JKD.

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102 103 104 10510-3

10-2

10-1

Specific global cost (USD/hour-out-of-service)

Una

vaila

bilit

y

123

4

56

7 8

9

101112

1314

15

1617

Fig. 7. Sensitivity analysis vs. a.

R. Pascual et al. / Reliability Engineering and System Safety 94 (2009) 1308–13131312

The methodology has been implemented in a open-accessWeb-based decision support system called PAMþþ [34].

3.1. Trend analysis

Another benefit from CSD is that they permit visualizing trendsin physical asset performance. Fig. 8 shows the evolution of thefive critical case study during a period of time. This diagram canbe obtained by superposing CSDs from different periods of time. Itcan be observed that: codes 2, 7, and 10 have reduced its globalcost per unit time from the first period of analysis to the second.Only code 10 has reduced its unavailability significantly. Code 11remains essentially at the same point, while code 8 has worsenedits situation both in unavailability as well as on its global cost.Changes in the position of points are the result of modified assetmanagement policies and strategies, but they can also be theresult of changes in the business cycle as the specific global cost isalso a function of it.

3.2. Handling parameter uncertainty

Uncertainty in the parameters for each code (i.e., theeconomical effect on production or the frequency of occurrence)

102 103 10410-3

10-2

10-1

Specific global cost (USD/hour-out-of-service)

Una

vaila

bilit

y 123

4

5

6

7 8

9

101112

13

14

15

16

17

49 (USD/hr)

153 (USD/hr)

102 103 10410-3

10-2

10-1

Specific global cost (USD/hour-out-of-service)

Una

vaila

bilit

y 123

4

5

6

7 8

9

101112

13

14

15

16

17

24 (USD/hr)

103 (USD/hr)

Fig. 6. 2D-CSD for different market conditions. (a) Reference consequential cost. (b) 25% of reference consequential cost.

101 102 103 10410-3

10-2

10-1

Intervention Cost (USD/hour-out-of-service)

Una

vaila

bilit

y

12

3

4

5

6

7 8

9

101112

13

14

15

16

17

64 (USD/hr)

Fig. 5. Intervention costs scatter diagram.

102 103 10410-3

10-2

10-1

Specific global cost (USD/hour-out-of-service)

Una

vaila

bilit

y 2'7'

8'

11'

10'

Fig. 8. Trend analysis using CSD.

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R. Pascual et al. / Reliability Engineering and System Safety 94 (2009) 1308–1313 1313

can be easily handled by using circles instead of dots or lines. Ofcourse, that would require at least two extra parameters for theMTOS and the specific global cost (i.e., standard deviations).

3.3. Advantages of CSD

A CSD shows several advantages over existing prioritizationschemes:

�

It is business oriented, as it considers the global costs. Thishelps to align the maintenance function with the organiza-tions’ strategic goals. Priority changes produced by changes inthe business cycle are clearly observed. � It is intuitive, all axes in the graphic represent physical,

commonly used KPIs in maintenance and PAM.

� It is easy to implement, input data can be found in standard

maintenance information systems and ERPs.

� It is graphical, and explicitly shows the relationships between

key variables in the asset decision-making processes.

� It is multicriteria, different points of view are taken into

account simply by changing the view angle of the CSD.

� It allows trend analysis, and by doing so, analyze the effect of

decisions made in time.

� It is a sensitivity analysis tool, as it can easily show the impact

of a given measure on the KPIs.

4. Final comments

This work has introduced a novel decision support tool toselect systems and failure modes from a business oriented point ofview. CSD provide an opportunity to graphically explore improve-ment opportunities using business oriented KPIs such as globalcosts, intervention costs, availability, frequency, and time-out-of-service. The technique overcomes the disadvantages of bothPareto and JKD as it includes them but also adds a global-costcentered perspective. CSD provide additional information con-cerning the economical, both direct and indirect, of maintenanceinterventions. Unlike more generic multicriteria decision aidtechniques such as AHP and other outranking methods, it is easyto understand CSD in terms of standard KPIs. CSD are based on acost and reliability model that is closely related to PAM and isbased on equations that relate all KPIs. The application of theproposed technique can range from strategic to operational levelsas it is fairly general and easy to implement and use.

Acknowledgements

Thanks are due to the reviewers of the paper for theirconstructive criticism, which were useful to improve an earlierversion of this manuscript. The authors wish to acknowledge thepartial financial support of this study by the FOndo Nacional deDEsarrollo Cientifico Y Tecnologico (FONDECYT) of the Chileangovernment (project 1090079).

References

[1] Karydas DM, Gifun JF. A method for the efficient prioritization ofinfrastructure renewal projects. Reliability Engineering and System Safety2006;91:84–99.

[2] Edwards W. How to use multi-attribute utility measurement for socialdecision making. IEEE Transactions on Systems, Management and Cybernetics1977;SMC-7(5).

[3] Lagreze EJ, Shakun MF. Decision support systems for semi-structured buyingdecisions. European Journal of Operational Research 1984;16:48–58.

[4] Bevilacqua M, Braglia M. The analytic hierarchy process applied tomaintenance strategy selection. Reliability Engineering and System Safety2000;70:71–83.

[5] Roy B. How outranking helps multiple criteria decision making. In: CochraneJL, Zeleny M, editors. Multiple criteria decision-making. University of SouthCarolina Press; 1973.

[6] Brans JP, Vincke PH, Mareschal B. How to select and how to rank project: thePROMETHEE method. European Journal of Operational Research 1986;24:228–38.

[7] Zopounidis C, Doumpos M. Multi-criteria decision aid in financial decisionmaking: methodologies and literature review. Journal of Multi-CriteriaDecision Analysis 2002;11(4–5):167–86.

[8] Carnero MC. Selection of diagnostic techniques and instrumentation in apredictive maintenance program: a case study. Decision Support Systems2005;38:539–55.

[9] Carnero MC. An evaluation system of the setting up of predictive maintenanceprogrammes. Reliability Engineering and System Safety 2006;91:945–63.

[10] Deshpande V, Cohen MA, Donohue K. An empirical study of servicedifferentiation for weapon system service parts. Operations Research 2003;51(4):518–30.

[11] Dekker R, Scarf Ph. On the impact of optimisation models in maintenancedecision making: the state of the art. Reliability Engineering and SystemSafety 1998;60:111–9.

[12] Hokstad P, Steiro T. Overall strategy for risk evaluation and priority setting ofrisk regulations. Reliability Engineering and System Safety 2006;91:100–11.

[13] Einarsson S, Rausand M. An approach to vulnerability analysis of complexindustrial systems. Risk Analysis 1998;18(5):535–46.

[14] Cooke RM, Jager E, Lewandowski D. Reliability model for underground gaspipelines. Case Studies in Reliability and Maintenance; 2003.

[15] Chareonsuk Ch, Nagarur N, Tabucanon MT. A multicriteria approach to theselection of preventive maintenance intervals. International Journal ofProduction Economics 1997;49:55–64.

[16] Shohet IM, Perelstein E. Decision support model for the allocation ofresources in rehabilitation projects. Journal of Construction Engineering andManagement-ASCE 2004;130(2):249–57.

[17] Goodhart CA. Depot-level maintenance planning for marine corps groundequipment. Military Operations Research 1999;4(3):77–89.

[18] Grierson DE. Pareto multi-criteria decision making. Advanced EngineeringInformatics 2008;22(3):371–84.

[19] PAS-55, Asset Management, British Standards Institute; 2004.[20] AFNOR, Recueil des normes franc-aise X 06, X 50, X 60, AFNOR; 1994.[21] Kaplan RS, Norton DP. The balanced scorecard—measures that drive

performance. Harvard Business Review 1992;70(1):71–9.[22] Al-hajj A, Horner M. Modelling the running costs of buildings. Construction

Management & Economics 1998;16:459–70.[23] Moubray J. Reliability-centered maintenance. 2nd ed. London: Butterworth-

Heinemann; 1997.[24] Tam ASB, Price JWH. A maintenance prioritisation approach to maximise

return on investment subject to time and budget constraints. Journal ofQuality in Maintenance Engineering 2008;14(3):272–89.

[25] Jourden, et al. Pratique de la maintenance industrielle. Dunod Ed; 1998.[26] Gomez FC, Ruiz JJ. Maintenance strategy based on a multicriterion classifica-

tion of equipments. Reliability Engineering and System Safety 2006;91:444–51.

[27] Beehler ME. Reliability centered maintenance for transmission systems. IEEETransactions on Power Delivery 1997;12(2):1023–8.

[28] Labib AW. World-class maintenance using a computerised maintenancemanagement system. Journal of Quality in Maintenance Engineering 1998;4(1):66–75.

[29] Burhanuddin MA, Ahmad AR, Desa MI. An application of decision making gridto improve maintenance strategies in small and medium industries. IEEEconference on industrial electronics and applications 2007;23(25):455–60.

[30] Knights PF. Downtime priorities, Jack-knife diagrams, and the business cycle.Maintenance Journal 2004;17(2):14–21 Melbourne, Australia.

[31] Karim K, Marosszeky M, Davis S. Managing subcontractor supply chain forquality in construction engineering. Construction and Architectural Manage-ment 2006;13(1):27–42.

[32] Pascual R, Meruane V, Rey PA. On the effect of downtime costs and budgetconstraint on preventive and replacement policies. Reliability Engineeringand System Safety 2008;93:144–51.

[33] Howard RA. Decision analysis: practice and promise. Management Science1988;34(6):679–95.

[34] hhttp://opam.ing.uchile.cli (accesed on July 2008).