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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, Chile Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chile ´lica de Chile, Av. Vicun ˜a Mackenna 4860, Santiago, Chile Centro de Minerı´a, Pontificia Universidad Cato d Division of Mining Engineering, Faculty of Engineering, Architecture and Information Technology, The University of Queensland, St. Lucia, Brisbane, 4072, Australia b c

a r t i c l e in fo

abstract

Article history: Received 12 November 2008 Received in revised form 15 January 2009 Accepted 29 January 2009

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.

Keywords: Prioritization Physical asset management Maintenance decision-making Resource assignment Criticality Subset selection Multicriteria analysis

1. Introduction To meet the increasing challenges of current industrial reality, organizations require to continuously enhance their capability to add value and improve the cost-effectiveness of their decision processes. The decision process includes the selection of those systems and actions that may render the highest overall savings, and then, their associated policy resolutions. Decision making in physical asset management (PAM) is generally focused on two levels: strategic and tactic. Strategic level 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 level performance evaluation; (iv) forecast of future market and operational conditions. The tactical level, on the other hand, concerns more specific technical management decisions for the individual projects. It includes: (i) assessing the causes of deterioration and determining/selecting candidate solutions; (ii) assessing benefits of the alternatives by life-cycle costing; (iii) selecting and designing the desired solutions. The prioritization technique introduced in this work deals with both strategic and

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E-mail address: [email protected] (R. Pascual).

tactical decision making, as selection of critical systems is present at both management horizons. The paper is organized as follows: first, we present a general review of priority setting in engineering problems and then to PAM problems. From there, we consider Pareto and Jack knife diagrams (JKD), which justify the introduction of the so-called cost scatter diagrams (CSD). An extended case study from a previous reference is used to illustrate the advantages of the new technique. 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 evaluation or design problems. When facing an evaluation problem, the decision maker analyzes a set of discretely predefined alternatives. The evaluation step can be done using aggregate value function approaches and/or outranking approaches. In the first group we may mention general techniques such as multi-attribute utility theory methods [1], simple multi-attribute rating techniques [2], inverse preference methods [3], and analytic hierarchy process (AHP) [4]. In the group of outranking techniques we include: ELimination Et Choix Traduisant la REalite´ (ELECTRE) [5] and Preference Ranking Organisation METHod for Enrichment Evaluations (PROMETHEE) [6]. Detailed comparison of these kinds of methodologies can be found in Zopounidis and Doumpos [7].

0951-8320/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ress.2009.01.013

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For instance, drawbacks of outranking methods arise from the many rather non-intuitive inputs that are required, i.e., the preference functions of PROMETHEE. If the number of alternatives is sizeable, a rank reversal problem may arise in the AHP method. Previously mentioned generic evaluation techniques have been used previously in PAM. Bevilacqua [4] describes an application of the AHP for selecting the best maintenance strategy for an oil refinery. Carnero [8,9], also uses AHP but combines it with factor analysis. As a drawback, the pairwise comparison required by AHP may become fairly time consuming if a large number of alternatives need to be evaluated. Karydas and Gifun [1] use it to prioritize maintenance in the context of facility management. Deshpande [10] studies the role of multicriteria priority codes in the military service parts system and the impact of these codes on systems performance. Dekker and Scarf [11] describe a ranking methodology that indicates the expected money loss by deferring execution of maintenance tasks. They also describe the decision support system where they implemented such technique and show a case study from the process industry. In the more general fields of risk assessment and vulnerability analysis, Hokstad and Steiro [12] and Einarsson and Rausand [13] provide frameworks for priority setting. In the first case, they use a broad definition of risk that accounts for up to 11 criteria simultaneously. Cooke et al. [14] develop a ranking tool which uses failure data and structured judgment to rank and upgrade the basis for decisions regarding inspection and replacement of underground pipelines. Chareonsuk et al. [15] propose a multicriteria approach to the rank and select preventive maintenance intervals using the PROMETHEE [6], one of the outranking methods for multiple criteria problems. In an engineering design problem, the decision maker also faces the identification of the preferred alternative from a infinite set defined by a set of constraints. The latter case is usually solved by using mathematical programming techniques. Examples of design problems in the context of PAM are the multicriteria project selection [16], the assignment of overhaul funding for fleet of diverse equipment under budget constraint [17] and the design of maintenance intervention protocols [18]. Mathematical programming is resource-intensive and relatively complex to implement.

1.2. Priority setting in PAM

value of a KPI only from the most critical elements, i.e., Al-Hajj and Horner [22] propose a predictive total cost model built only from the costs of the most critical sub-systems. A problem with Pareto is that it requires selecting a single classification criterion. To overcome this, other classification schemes have been proposed, i.e., risk priority numbers [23,24] and criticality numbers [25]. Another example of this type of method is the multicriteria classification of critical equipments proposed by Gomez and Ruiz [26]. These schemes build polynomials that assign a single classification number to each subsystem/failure mode. Beehler [27] proposes a decision matrix which includes a set of parameters to rank and select the most critical systems. Labib [28] and Burhanuddin et al. [29] present a decision making grid and a case study considering both frequency and downtime as classification criteria. Knights [30] enhances the concept by adding total downtime isoquantas to the diagram (also known as JKD and further described below). As a result, we find a 2D scatter diagram that concerns three criteria simultaneously: frequency, downtime, and unavailability. As it only contains time based information, it is insensitive to economic effects on the business cycle, something that is known to affect decision-making priorities. In order to overcome that, we propose the CSD methodology in the next section. To be able to assess savings, a cost estimation process is needed. Consequently, a cost structure is required. In this article the global cost is used, as defined in Jourden et al. [25]. It is composed of four terms: intervention costs, holding costs, reliability related investments, and consequential costs. Intervention costs include the value of spares and labour. Holding costs represent the financial cost of having spares available on-site. The reliability related investments term considers all acquisitions made to attenuate the effect of maintenance (i.e., redundant equipment, stock piles, and insurances). The final term refers to downtime costs and other costs associated with move from/to a standard production method for maintenance reasons (Fig. 1). 1.3. Jack knife diagrams The total downtime MDT j of a system during a given period of time T, due to an intervention code (or code), is the product of the number of times nj that this code occurred and the mean time out of service MTOSj the system: MDT j ðTÞ ¼ nj ðTÞ  MTOSj ðTÞ

Although previously mentioned methods have been used in the context of PAM, there are more intuitive techniques that use the particular properties that relate common use key performance indicators (KPIs) and facilitate decision making (further described below). In order to perform the systems selection, a holistic, life-cycle centered approach can be used. By doing so, the analysis is 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 (including maintenance), and retirement. It must set, control and balance a set of KPIs such as availability, reliability, productivity, overall equipment effectivity (OEE), intervention costs, and global cost. This set of KPIs must be balanced by setting maintenance policies that may range from corrective (run to failure) to proactive (system redesign [21]). Of course, setting such policies requires the availability of resources. As they are usually scarce, a prioritization process must be established. It must be at system or subsystem level, or, if they have been selected, at prioritizing failure modes. Traditionally, Pareto analysis has been used to set decision priorities. Pareto analysis is highly useful to focus decision making on a small set of systems/failure modes. Complementarily, they can also be used to estimate the global

(1)

If all codes are displayed in an n vs. MTOS diagram, it is possible to discriminate those codes that cause the major downtime, but it is also possible to assess if it is due to high frequency of to high time out of service. A disadvantage of using Eq. (1) directly is that iso-downtime curves are drawn as hyperbolaes. This can be easily overcome by using the identity: log MDT j ðTÞ ¼ log nj ðTÞ þ log MTOSj ðTÞ

(2)

Intervention costs Holding costs Reliability related investments Penalty costs Fig. 1. Components of the global cost.

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A con on using Eqs. (1) and (2) is that they depend on T. If it is desired to compare the system performance at two different intervals of time (or two different systems), they would have to be of the same length to make a logical comparison. One way to overcome that is by using the unavailability, as it is explained below. Unavailability (D) is the product of two factors; the frequency of interventions (f ) that occurred in a particular time frame and the average associated time-out-of-service (MTOS), which, in the case 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 those interventions that consume more availability and be able to discriminate if it is due to high frequency or to high time-out-ofservice. Again log Dj ¼ log f j þ log MTOSj

(4)

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

0.2

the line of D ¼ 1%. Any code above that line ‘eats’ more than 1% of the system availability. We observe that, in general, codes related to preventive maintenance affect the position of corrective codes. If this is not occurring, the preventive action is not being technically effective. Let us take for example the inspection of a hose of a shovel. If is not done well or with enough frequency, the failure rate of this component 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 of defects in a setting of evaluating construction contractors performance.

2. Cost scatter diagrams As mentioned before, JKD consider only times and frequencies, and correspondingly, no economic effect is explicitly taken into account. In what follows, we propose the CSD. The intention is to enhance the graphical analysis by adding the cost dimension. 2.1. Model formulation The expected maintenance global cost per unit time cg of a given system can be obtained by summing the gains from all interventions (i.e., failures, preventive replacements, inspections, and other shutdown actions):

0.18 0.16 0.14 Unavailability

3

cg ¼

0.12

n X ðci;j þ cf ;j þ csi;j þ ca;j Þf j  MTOSj

(5)

j¼1

0.1 cg ¼

0.08

n X

cgj Dj

(6)

j¼1

0.06 0.04 0.02 0 1 2 11 3 10 7 12 8 5 15 6 9 4 17 14 16 13 Code Fig. 2. Pareto analysis for unavailability, taken from the case study. Individual and aggregate contributions are shown.

where MTOSj is the mean downtime associated to each intervention j, f j corresponds to the frequency of intervention j, ci;j is the direct cost per unit time of intervention j (spares, labour, mobilization, planning, and administration), cf ;j corresponds to the downtime cost per unit time, ca;j is the holding cost due to spares and its amortizations per unit time, csi;j stands for the cost for 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

Table 1 Model parameters. ID

Description

Qty.

Duration (min)

Int. cost (USD/int.)

a

Capital spares (104 USD)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Electrical inspections Damaged feeder cable Change of substation Coupling repairs or checks Power cuts to substations Rope limit protection Auxiliary motors Main motors Lighting system Overload relay Motor over temperature Earth faults Miscellaneous Control system Air compressor Operator controls Over current faults

30 15 27 15 21 10 13 12 26 23 36 7 9 7 8 5 6

1015 785 690 225 395 277 600 555 240 685 745 575 115 165 355 155 220

80 300 50 500 40 50 300 400 500 2000 800 50 100 600 700 200 400

0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1

5.5 300 15 7 1.8 1.5 35 80 4 70 1 5 12 23 1 8 3

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

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generic time unit, must be transformed in two senses: as an investment equally distributed over time and as a financial cost [25]. The cost rate cgj can be considered as a weight for each unavailability. As MTOSj considers the full logistic cycle for each intervention: cij MTOSj ¼ C ij

(7)

where C ij 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 planning level of the intervention, the existence of stock piles and equipment redundancy and alternative production methods [32]. a represents the attained level of opportunistic maintenance of the action. For example, an inspection is an intervention that is planned to minimize effects for production, so a ! 0. In other cases, the estimation of a requires sensitivity analysis as it will be described in the case study. An example: what is the effect of a haul truck failure on the production program when there is a haul truck redundancy of 11 out of 10?

10

104 12

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

11

8 2 7 15 14 6 17 16

9

5 13

103

4 13

102 100.1 (h

r-o

ut-

0.05

MT OS

ou

of-

rvi

r)

/hou

y (1

se

ce

)

10-0.8

nc que

Fre

0.007

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

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

acf bci such situation arises often in the mining industry as the opportunity costs per unit time are large and no alternative production method is available: high unavailability means high global cost.

3. Case study Table 1 is taken from Knights [30] and lists the unplanned downtime recorded for electrical failures in a fleet of cable shovels at an open pit copper mine located in northern Chile, over a onemonth period. The cost terms have been added and do not represent the actual case. The JKD is shown in Fig. 4(a). The five most critical interventions when using the availability criterion are the following codes: 1, 2, 3, 10, and 11. Fig. 3 shows the 3D version of 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 intervention codes most critical for the business are: 2, 7, 8, 10, 11, and 12 (highlighted in both figures). This information can be added to a standard JKD in order to study the effect of the global cost in the selection of the most critical components (Fig. 4(b)): it can be noticed that codes 1 and 3 are important for the availability of the system, but, they are not as critical for the business, so their analysis can be postponed in front of components 7 and 2 which are 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. Of course, this approach would leave in a second plane various components which are critical for the business and not so much for the maintenance budget. Anyway, this version of CSD can be very 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 the reference value. Points move to the left as the global cost has been reduced, depending on the a factor for each intervention. Fig. 7 shows a sensitivity analysis W.R.T. a. The a values have been evaluated in the range ½0; 1. Accordingly, it generates lines instead of points in the CSD. They show the impact of moving from fully opportunistic interventions to fully unplanned (and without contingency plan) interventions. This information provides new insight for prioritization. It can be taken as a version of a Tornado diagram [33].

12 Feeder Cable 2 Iso 8 7 -u na va ila bil ity 6

15

10-0.2

17 16

10-0.4

D

=2

.3% Inspections 1 10 3

14

11

5

10-0.6

4 13

10-0.8 0.007

9

0.05 Frequency (1/hour)

MTOS (hour-out-of-service)

MTOS (hour-out-of-service)

12

100

100

2 8 7

15

10-0.2

17

1

16

10

6

10-0.4

3

14

11

5

10-0.6

4 13

10-0.8 0.007

9

0.05 Frequency (1/hour)

Fig. 4. Jack knife diagrams. Cutting axes have been drawn in the mean value of each criterion. Notice that the enriched JKD corresponds to a special case of Fig. 3 when it is observed above. Points marked with a cross are the most critical for the global cost. (a) Standard JKD. (b) Enriched JKD.

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

5

10-1

3.1. Trend analysis

1 Unavailability

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

2 11 10 127 8

3 10-2

5 15 6 17 9 16 14

4

13

10-3 102

103 104 Specific global cost (USD/hour-out-of-service)

3.2. Handling parameter uncertainty

105

Fig. 7. Sensitivity analysis vs. a.

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

10-1

10-1

64

8'

(U SD

2

10

7 8

12

10-2

11

5

Unavailability

r)

Unavailability

/h

1 3

15

6

9

4

17

11'

2' 7' 10-2

10'

14

16 13

10-3 101

10-3 102 103 Intervention Cost (USD/hour-out-of-service)

104

102

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

Fig. 5. Intervention costs scatter diagram.

Fig. 8. Trend analysis using CSD.

10-1

10-1

15

3

10

3

(U

SD

24

/h

r)

(U

SD

1

/h

3

r)

10-2

2

11 12 7 8 5

10

15

6 4

(U

SD

/h

r)

(U

SD

17

9

Unavailability

49

Unavailability

104

/h

r)

1

2

3

12

10-2

5

11 8

10

15

6

9

17 4

16 14 13

10-3 102 103 104 Specific global cost (USD/hour-out-of-service)

7

14

16 13

10-3 2 10

103

104

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

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

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can be easily handled by using circles instead of dots or lines. Of course, that would require at least two extra parameters for the MTOS and the specific global cost (i.e., standard deviations). 3.3. Advantages of CSD A CSD shows several advantages over existing prioritization schemes:  It is business oriented, as it considers the global costs. This helps to align the maintenance function with the organizations’ strategic goals. Priority changes produced by changes in the 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 to select systems and failure modes from a business oriented point of view. CSD provide an opportunity to graphically explore improvement opportunities using business oriented KPIs such as global costs, intervention costs, availability, frequency, and time-out-ofservice. The technique overcomes the disadvantages of both Pareto and JKD as it includes them but also adds a global-cost centered perspective. CSD provide additional information concerning the economical, both direct and indirect, of maintenance interventions. Unlike more generic multicriteria decision aid techniques such as AHP and other outranking methods, it is easy to understand CSD in terms of standard KPIs. CSD are based on a cost and reliability model that is closely related to PAM and is based on equations that relate all KPIs. The application of the proposed technique can range from strategic to operational levels as it is fairly general and easy to implement and use.

Acknowledgements Thanks are due to the reviewers of the paper for their constructive criticism, which were useful to improve an earlier version of this manuscript. The authors wish to acknowledge the partial financial support of this study by the FOndo Nacional de DEsarrollo Cientifico Y Tecnologico (FONDECYT) of the Chilean government (project 1090079). References [1] Karydas DM, Gifun JF. A method for the efficient prioritization of infrastructure renewal projects. Reliability Engineering and System Safety 2006;91:84–99.

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Please cite this article as: Pascual R, et al. Business-oriented prioritization: A novel graphical technique. Reliab Eng Syst Safety (2009), doi:10.1016/j.ress.2009.01.013