Computer-aided maintenance management systems ...

Advances in Engineering Software 42 (2011) 821–829

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Computer-aided maintenance management systems selection based on a fuzzy AHP approach Orlando Durán Pontificia Universidad Católica de Valparaíso, Av. Los Carrera 01567, Quilpue, Chile

a r t i c l e

i n f o

Article history: Received 5 August 2008 Received in revised form 7 January 2010 Accepted 13 May 2011 Available online 12 June 2011 Keywords: Computerized maintenance management software Analytic hierarchy process Fuzzy-AHP Software selection Triangular fuzzy numbers Comparison of fuzzy numbers

a b s t r a c t Computerized maintenance management systems (CMMS) are common in today’s industries. CMMS can bring a large number of benefits, which include increased productivity, reduced costs, and effective utilization of the assets in any manufacturing and service producer. The list of CMMS that are available in the market has grown very rapidly during the last years. When purchasing a system, one that suits the specific needs and objectives of the company’s maintenance operations should be preferred. Several selection methods were proposed in literature. Up to now, no article has considered ambiguity and uncertainty factors when selecting effective CMMS. In addition, CMMS selection decisions involve the simultaneous consideration of multiple criteria, including tangible and intangible factors; prioritizing these factors can be a great challenge and a complex task. Therefore, no attempt has been made to incorporate fuzziness into multicriteria decision-making in the area of CMMS selection. This work proposes a fuzzy–based methodology for comparative evaluation of a number of CMMS alternatives. The proposal is based on the well-known multicriteria decision method called Analytical Hierarchy Process (AHP) with triangular numbers. An example is given to illustrate the proposed methodology. Finally, a software prototype for implementing this method was implemented. To illustrate and validate the proposed approach and the software prototype developed some details are presented and discussed. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The increase in automation and the reduction in inventories in industries have clearly put more pressure on the maintenance systems. Any disruption to production flows becomes costly and critical. This makes the maintenance function relevant to operations management to keep organizations productive and profitable along time. Therefore, computerized maintenance management systems (CMMS) are becoming increasingly important in the last few years. Using CMMS is a highly relevant issue in a production environment where the number of critical equipment is high or where the need for maintenance resources management is significant. A large variety of computer software is available on the market for maintenance management. It is not surprising that many companies have been disappointed with the results of their implemented CMMS. An extensive survey [1] reported that there is a paradox in CMMS selection and implementations. According to this survey, 62% of the respondents changed their maintenance work process to fit the CMMS characteristics and 66% customized the CMMS to fit the work process. These numbers reflect that the selection of the most suitable CMMS is a crucial task to eliminate all these problems and difficulties. E-mail address: [email protected] 0965-9978/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2011.05.023

Selection and evaluation of a CMMS is a very difficult and complex task. The following five factors can be identified as the main causes of this complexity: (1) The tremendous number of software products available in the market. (2) The continual advancements and improvements in information technology (IT). (3) The existence of incompatibilities between various hardware and software systems. (4) The functional dissimilarities are difficult to evaluate among software packages. (5) The users lack the technical knowledge and experience for software selection decision making. As it was previously commented, decision making in the field of maintenance management software selection has become more complex due to a large number of software products in the market, ongoing improvements in information technology, and multiple and sometimes conflicting objectives. Some methodologies and frameworks for CMMS selection and evaluation have been developed. Raouf et al. [2] presented an instrument to select suitable system using a comparative strategy and the concept of relative importance among a set of required functions in accordance to

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O. Durán / Advances in Engineering Software 42 (2011) 821–829

the intended use of the CMMS. More recently, Carnero and Noves [3] presented an evaluation system for the selection of computerized maintenance management software in industrial plants using multicriteria methods. Braglia et al. [4] proposed a methodology to perform a selection of the best suited CMMS within process industries. To improve the effectiveness of the methodology proposed by Braglia et al. [4], they combined AHP with a sensitivity analysis. Those evaluation systems use the AHP method in its basic version (crisp numbers). Up to now, no article has considered ambiguity and uncertainty factors when selecting effective CMMS. In addition, software selection decisions involve the simultaneous consideration of multiple criteria, including tangible and intangible factors; prioritizing these factors can be a great challenge and a complex task. Labib [5] published an investigation of the characteristics of CMMS, identified their deficiencies. In addition, Labib proposed a model to aid the decision analysis capability in CMMS under selection [5]. These factors arise as the main motivation of this research work, which is aimed at how to select an appropriate CMMS facing the strategic and operational requirements of the organization using a multicriteria decision method incorporating concepts of uncertainty and uncompleted information. In other words, this study proposes a comprehensive CMMS selection framework in which the objective hierarchy is constructed and the appropriate attributes are specified using fuzzy numbers to provide guidance for CMSS evaluation. The analytic hierarchy process (AHP) method [6] and fuzzy numbers are applied for dealing with the ambiguities involved in the assessment of CMMS alternatives and relative importance weightings of attributes.

2. Multicriteria decision model The analytic hierarchy process (AHP) developed by Saaty [6] is a decision-making tool that can handle unstructured or semi structured decisions with multiperson and multicriteria inputs. It is a decision-rule model that relaxes the measurement of related factors to subjective managerial inputs on multiple criteria. AHP has several advantages, including its acceptance of inconsistencies in managerial judgments/perceptions and its user friendliness because users may directly input judgment data directly without the requirement of mathematical knowledge. It also allows users to structure complex problems in the form of a hierarchy or a set of integrated levels. One of the main advantages of this method is the relative ease with which it handles multiple criteria. In addition to this, AHP is easier to understand and it can effectively handle both qualitative and quantitative data. The use of AHP does not involve cumbersome mathematics. AHP involves the principles of decomposition, pair wise comparisons, and priority vector generation and synthesis. The power of AHP has been validated by empirical application in diverse areas such as healthcare [7], planning [8], mining [9], project management [10], missile systems [11], new product development [12] and manufacturing [13]. In addition AHP has been used in making decisions that involve ranking, selection, evaluation, and selection of machines and IT based systems [14–16]. To construct the hierarchy of objectives and attributes of a generic CMMS an extended review of the related literature was conducted. This review focused on CMMS selection and, on general-purpose software selection problem. Two works arise as the most significant ones to the goal pursuit by our approach. Cato and Mobley [17] listed some activities which constitute subsystems or modules of a generic CMMS: equipment/asset records creation and maintenance, asset bills of materials creation and maintenance, asset and work order history, inventory control,

work order creation and control, preventive maintenance planning and scheduling, human resources, purchasing and receiving, invoices matching, and, reporting. Considering Carnero and Novés’ [3] opinion the key functions for any CMMS are:

Easy work management. Planning function. Scheduling function. Budget/cost function. Spares management. Key performance indicators.

More recently, Bradshaw [18] listed the basic capabilities of a CMMS. They are: assets database, maintenance activities records, corrective maintenance, preventive maintenance and maintenance work scheduling and control. Besides, the same author incorporates what he called improved CMMS capabilities; they are integration and interfacing capabilities and, communication, data collection and transfer. Wei et al. [19] distinguish two categories of attributes to select an enterprise resource planning system, including system factors and vendor factors. Among the subcriteria related to the system factor they suggest the total cost, implementation time, functionality, user friendliness, flexibility and reliability. On the other hand, the subcriteria related to the vendor factor they used vendor reputation, technical capability and supplying ongoing service. These characteristics lead the authors to propose the hierarchy used in the evaluation approach. Table 1 presents the detailed description of the used attributes in the fuzzy AHP model. Since all organizations are different, it is very important to perform a previous identification of maintenance management (MM) IT requirements. Kans [20] presents a formal method for the identification of MM IT requirements. Accordingly Kans’ work, the choice of technical features of MMIT is dependent upon the needs and characteristics of the specific organization. Once the IT requirements identification is completed, a series of candidate software systems will arise as a result of the requirements identification phase. Those candidates software systems will have to be classified or ranked using a MCDM with the participation of domain (maintenance management) experts. For that objective, a fuzzy AHP approach was developed and applied to the problem of CMMS selection. The next section discusses the fuzzy-AHP methodology.

3. Fuzzy AHP methodology The fuzzy AHP methodology extends Saaty’s AHP by combining with fuzzy set theory. In the fuzzy AHP, fuzzy ratio scales are used to indicate the relative strength of the factors in the corresponding criteria. Therefore, a fuzzy judgment matrix can be constructed. The final scores of alternatives are also represented by fuzzy numbers. The optimum alternative is obtained by ranking the fuzzy numbers using special algebra operators. The next three steps can summarize the procedure of applying fuzzy AHP: i. Construction of a hierarchical structure for the problem to be solved. ii. Establish the fuzzy judgment matrix and a fuzzy weight vector. iii. Rank all alternatives and select the optimal one. Three levels compose the hierarchy of the evaluation system. The suggested hierarchy is depicted in Fig. 1. The first level is the

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O. Durán / Advances in Engineering Software 42 (2011) 821–829 Table 1 Attribute details. Factor

Attributes

Sub attributes

Functionality

System

Flexibility

Friendliness

Implementation Difficulties Reputation and Stability

Vendor

Good technical capability

Service

Module completion Function fitness Maintenability Upgrade ability Ease of integration Ease in-house customization Ease operation Ease learning Low customization Implementation time Implementation costs Scale of vendor Financial condition Market share (and internationalization) R&D capability On line support Experience in the industry Warranties Consultant services Training service Proximity

goal of the problem, that is, select the most suitable computer based maintenance management system. The two main decision criteria are placed in the second level. They are system and vendors factors. In the third level are the most relevant sub-criteria for each one of the criteria listed in level 2. In this methodology, triangular fuzzy numbers represents all elements in the judgment matrix and weight vectors. Using fuzzy

numbers to indicate the relative contribution or impact of each alternative on a criterion, a fuzzy judgment vector is then obtained for each criterion. The fuzzy judgment matrix A is built with all the fuzzy judgment vectors. The weight vector W is used to represent the decision maker’s opinion of the relative importance of each criterion during the decision process. Though the purpose of AHP is to capture the expert’s knowledge, the conventional AHP still cannot reflect the human thinking style. In spite of its popularity, this method is often criticized because of a series of pitfalls associated with the AHP technique. They can be summarized as follows: Its inability to adequately handle the inherent uncertainty and imprecision associated with the mapping of the decisionmaker’s perception to exact numbers [8]. In the traditional formulation of the AHP, human’s judgments are represented as exact (or crisp, according to the fuzzy logic terminology) numbers. However, in many practical cases the human preference model is uncertain and decision-makers might be reluctant or unable to assign exact numerical values to the comparison judgments. Although the use of the discrete scale of 1–9 has the advantage of simplicity, the AHP does not take into account the uncertainty associated with the mapping of one’s judgment to a number. In order to overcome the aforementioned shortcomings, a fuzzy extension of AHP, was developed to solve the hierarchical fuzzy problems. In the next sections a fuzzy AHP technique is proposed, and an example for the evaluation and justification of advanced manufacturing system is presented.

Functionality

Flexibility

System Factors

Friendliness

CMMS 1 CMMS 2

Selection of the most suitable CMMS

Implementation CMMS 3 Reputation

Technic. Cap.

Vendor Factors

Service Fig. 1. Hierarchy of the CMMS selection problem.

CMMS n

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A fuzzy number ~ x expresses the meaning ‘about x0 . Each membership function is defined by three parameters of the symmetric triangular fuzzy number, (l, m, r), the left point, middle point and right point of the range over which the function is defined. Fuzzy membership function and the definition of a fuzzy number are shown in Fig. 2.

lðxÞ ¼

8 1 > > > < xl

ml

x¼m l6x6m

nx > m6x6n > > : nm 0 otherwise

ð1Þ Vi ¼

e ¼ ða1; a2; a3Þ A e ¼ ðb1; b2; b3Þ B Then, fuzzy numbers multiplication is defined by:

ð2Þ

At the other hand, fuzzy numbers division is defined as follows:

e B e ¼ ða1=b3; a2=b2; a3=b1Þ A=

ð3Þ

whilst the reciprocal value of a triangular fuzzy number (a, b, c) is given by (1/a, 1/b, 1/c). The power of a triangular fuzzy number is given by

e n ¼ ða1; a2; a3Þn ¼ ða1n ; b2n ; c3n Þ A

ð4Þ

As can be seen in Fig. 3, the relative importance of a number over other fuzzy number is gradual and not abrupt. ~ i be a set of decision maker’s opinion of the relative imporLet w tance of the one alternative over other one. The meaning of each fuzzy number is defined in Table 2. e where aij eleUsing this scale we have the comparison matrix A, ments represent the estimative of the wi/wj relation.

~ w1 ~ w2= ~ w1 ~ . . . wn= ~ ~ w1 w1= e ¼ w1= ~ w2 ~ w2= ~ w2 ~ . . . wn= ~ A ~ w2 ~ ~ ~ w2=wn ~ . . . wn= ~ wn ~ w1=wn

ð5Þ

Experts’ judgments or preferences among the options using Saaty´s scale is represented now by triangular numbers to express

Fig. 2. Membership function of a triangular number.

n Y

!1=n ~ij a

ð6Þ

j¼1

When the decision-maker faces a complex and uncertain problem and expresses his/her comparison judgments as uncertain ratios, such as ‘about two times more important’, ‘between two and four times less important’, etc. the standard AHP steps, and specially, eigenvalue prioritization approach, cannot be considered as straightforward procedures. Indeed, the assessment of local priorities, based on pair wise comparisons needs some prioritization method to be applied. Next a brief description about addition, multiplication and division of triangular numbers is given. The fuzzy operators were adapted from [21] and are based on the extent analysis with the use of triangular fuzzy numbers for pairwise comparison scale [22]. Let A and B be two triangular fuzzy numbers, with their parameters as follows:

eB e ¼ ða1 b1; a2 b2; a3 b3Þ A

subjective pairwise comparisons or capture certain degree of vagueness (Table 2). We know that matrix A is a real and positive matrix. As well as, since aij = 1/aji, if i is not equal to j, A is a reciprocal matrix. Next, the eigenvector, eigenvalue and the IC index are calculated, now taking these parameters as fuzzy numbers. To estimate the fuzzy eigenvector from A matrix the next equation is used:

Therefore, we have

~11 a ~12 a13 a ~1n Þ1=n V 1 ¼ ða

ð7Þ

~n1 a ~n2 a ~n3 a ~nn Þ1=n V n ¼ ða

ð8Þ

Eigenvector V is compound by the n triangular numbers defined as:

V ¼ ðV1; V2; . . . VnÞ where Vi is a triangular number defined as (Vl, Vm, Vu) As the traditional AHP methodology, eigenvector is to be normalized according the next relation:

T ¼ ðw1=Rwi w2=Rwi w3=Rwi

...

wn=RwiÞ

ð9Þ

That is, by dividing each element of the preference matrix with the sum of its respective column each element of the normalized eigenvector can be obtained. Where T is the normalized eigenvector. From this normalized eigenvector the priorities or importance of the attributes under analysis is extracted. In order to control the result of the method, the consistency ratio need to be calculated. The deviations from consistency are expressed by the following equation:

CI ¼

kmax n n1

ð10Þ

The consistency ratio (CR) is used to estimate directly the consistency of pairwise comparisons. The CR is computed by dividing the CI by a value obtained from the table of Random Consistency Index (RI) created by Saaty

CR ¼ CI=RI

ð11Þ

If the CR is less than 10%, the comparisons are acceptable, otherwise not. RI represents the average index for randomly generated weights. Since kmax is a triangular number, it has to be defuzzified into a crisp number to compute the CI. We suggest here using the central value of kmax, because of the symmetry of the triangular number, the central value corresponds to the centroid of the triangular area. As an alternative, Leung and Cao [23] propose a fuzzy consistency definition with consideration of a tolerance deviation. Essentially, the fuzzy ratios of relative importance, allowing certain tolerance deviation, are formulated as constraints on the membership values

~

~

~

~

~

1

3

5

7

9

Fig. 3. Saaty´s scale expressed as fuzzy sets.

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Considering this method and Eq. (9), the second element of the eigenvector is the highest value and corresponds to the third attribute (AT3) operation easiness. The normalization process yields a new form of the eigenvector in which each entry is a triangular number, as follows:

Table 2 Saaty’s scale expressed in fuzzy numbers. Relative importance

Definition

~ 1 ~ 3

Weak importance

Equal importance Strong importance

~ 5 ~ 7 ~ 9

Demonstrated importance over the other Absolute importance

T ¼ ðð0:02 0:11 1:09Þð0:02 0:16 1:39Þð0:04 0:37 2:82Þ ð0:03 0:29 2:20Þð0:01 0:05 0:36Þð0:004 0:02 0:17ÞÞ For testing the consistency of the resulting eigenvector, Saaty proposed the following relation:

of the local priorities. The fuzzy local and global weights are determined via the extension principle.

kmax ¼ T w

4. Case study

W ¼ ðð5:3 11:3 19:5Þð4:5 8:7 15:6Þð1:8 2:4 5:9Þð2:6 3:9 8:9Þ

In this section, in order to prove the applicability and validity the proposed methodology is applied to a case study. An investment decision in CMSS technology of a given manufacturer was taken into consideration. Suppose that a set of three experts provide the following fuzzy preference relations on a set of three alternatives CMMS (CMMS1, CMMS2, CMMS3). This case study supposes that functional aspects are covered by the three alternatives of CMMS. They are in equal conditions regarding aspects as module completion, function fitness, maintainability and other functional aspects. This is corroborated in [24] that reports that main functionality elements all belong to the core of a CMMS and are almost always available regardless if the user asks for them or not. Therefore, other intangible aspects are the factors that were considered by the methodology. As it is known, it may be impractical to make paired comparisons among CMMSs with respect to every detailed dimension or sub attribute of the hierarchy. The difficulty arises because too many attributes lead to numerous paired comparisons in AHP and may cause an inefficient process. Therefore, a simplified model was formulated. After a set of interviews, a series of six qualitative attributes was selected to perform the analysis. The six attributes are: flexibility, operation easiness, reliability, quality, implementation easiness and maintainability (Fig. 4). This six attributes are represented by the six following symbols: AT1, AT2, AT3, AT4, AT5 and AT6 respectively. Once the decisions makers performed the pair wise comparisons for the set of attributes A matrix is obtained (Table 3). This comparison matrix is constructed by using Saaty’s scale but now with triangular numbers. To find the relative importance or priorities of the six attributes eigenvector, eigenvalue and the RC index are to be computed. Thus, the eigenvector (with triangular values) is as follows:

ð0:27 0:77 2:18Þð0:05 0:12 0:35Þð0:03 0:06 0:17ÞÞ Before to proceed to perform the normalizations is necessary an additional fuzzy ranking procedure in order to compare fuzzy scores and to obtain a linear order among them. There is a number of procedures to perform the ranking process [23] and more recently [25], among them we propose, because of its simplicity, the utilization of the representative method, which is given by the following relation:

b ¼ a1 þ 2a2 þ a3 A 4

where w is computed by the sum of the columns of the preferences matrix .

ð16:1 24:2 34:3Þð25:0 35:0 45:0ÞÞ Next kmax is calculated by

kmax ¼ ð0:55 6:55 98:94Þ Then, to calculate the CI (crisp) we used the central value of the triangular number kmax.

CI ¼ ð6:55 6Þ=5 ¼ 0:11 In addition, CR is computed

CR ¼ 0:11=1:24 ¼ 0:089 < 0:10 This proves total consistency of the evaluations expressed by the comparisons matrix. Based on the weight vector (eigenvector) the priorities or relative importance of the attributes were obtained by ranking the eigenvector values. The ranked order of the six attributes is as follows: AT3, AT4, AT2, AT1, AT5 and AT6. Next, the three possible CMMS were compared with respect each of the six attributes. The corresponding fuzzy pairwise comparison matrices are shown in Table 4. Next, we can find the scores of the alternative CMMS with respect to the six attributes, which are shown in Table 5. The local weights of all CMMS for each attribute are obtained by multiplying their relative weights by the weights of the attributes. Table 6 shows these local weights. The overall classification can be obtained by multiplying (triangular product) the weights matrix (Table 6) by the transposed eigenvector of the attributes (Table 5). Table 7 shows the overall classification vector. Thus the priority scores for the CMMS alternatives are obtained, and they are ranked based on their magnitude (using Eq. (12)). CMMS1 CMMS2 CMMS3

V ¼ ðð0:12 0:3 1:08Þð0:15 0:42 1:38Þð0:35 1:00 2:80Þ

ð12Þ

where A = (a1, a2, a3) is a triangular number and b a represents the representative ordinal of a triangular number.

ð13Þ

1.43 1.73 2.60

Thus, CMMS 3 must be selected by the users or recommended by the AHP fuzzy methodology. 5. Proposed software As can be easily proved, AHP with fuzzy numbers requires many time-consuming calculations. Depending upon the number of attributes and alternatives taken into consideration a lot of time is necessary to make all calculations in order to reach the final solution. As the number of attributes increases, the dimension of the problem expands. This could lead to a great number of mathematical

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Service

CMMS 1

Technic. Cap.

Flexibility Selection of the most suitable CMMS

CMMS 2 Reputation

Friendliness

CMMS 3

Implementation Fig. 4. Abbreviated hierarchy.

Table 3 Comparisons matrix of the attributes considered for selection of CMMS.

AT1 AT2 AT3 AT4 AT5 AT6

AT1

AT2

AT3

AT4

AT5

AT6

(1, 1, 3) (1, 3, 5) (2, 4, 6) (1, 3, 5) (1/5, 1/3, 1) (1/9, 1/7, 1/5)

(1/5, 1/3, 1) (1, 1, 3) (1, 3, 5) (2, 4, 6) (1/5, 1/3, 1) (1/9, 1/9, 1/7)

(1/6, 1/4, 1/2) (1/5, 1/3, 1) (1, 1, 3) (3, 5, 7) (3, 5, 7) (1/5, 1/3, 1)

(1/5, 1/3, 1) (1/6, 1/4, 1/2) (1/7, 1/5, 1/3) (1, 1, 3) (1, 3, 5) (1/7, 1/5, 1/3)

(1, 3, 5) (1, 3, 5) (1/7, 1/5, 1/3) (1/5, 1/3, 1) (1, 1, 3) (1/7, 1/5, 1/3)

(5, 7, 9) (7, 9, 9) (1, 3, 5) (3, 5, 7) (3, 5, 7) (1, 1, 3)

Table 4 Fuzzy pairwise comparisons for the alternative CMMSs. AT1

CMMS1 CMMS2 CMMS3

AT2

CMMS1

CMMS2

CMMS3

(1.0 1.0 3.0) (1.0 3.0 5.0) (1.0 3.0 5.0)

(0.2 0.33 1.0) (1.0 1.0 3.0) (0.2 0.33 1.0)

(0.2 0.33 1.0) (1.0 3.0 5.0) (1.0 1.0 3.0)

CMMS1 CMMS2 CMMS3

AT3 CMMS1 CMMS2 CMMS3

CMMS2

CMMS3

(1.0 1.0 3.0) (1.0 1.0 3.0) (1.0 1.0 3.0)

(0.33 1.0 1.0) (1.0 1.0 3.0) (1.0 1.0 3.0)

(0.33 1.0 1.0) (0.33 1.0 1.0) (1.0 1.0 3.0)

(7.0 9.0 9.0) (1.0 1.0 3.0) (3.0 5.0 7.0)

(0.11 0.11 0.14) (0.14 0.2 0.33) (1.0 1.0 3.0)

(4.0 6.0 8.0) (1.0 1.0 3.0) (1.0 1.0 3.0)

(0.33 1.0 1.0) (0.33 1.0 1.0) (1.0 1.0 3.0)

AT4

(1.0 1.0 3.0) (1.0 3.0 5.0) (7.0 9.0 9.0)

(0.2 0.33 1.0) (1.0 1.0 3.0) (5.0 7.0 9.0)

(0.11 0.11 0.14) (0.11 0.14 0.2) (1.0 1.0 3.0)

CMMS1 CMMS2 CMMS3

(0.2 0.33 1.0) (1.0 1.0 3.0) (0.2 0.33 1.0)

(0.33 1.0 1.0) (1.0 3.0 5.0) (1.0 1.0 3.0)

CMMS1 CMMS2 CMMS3

(1.0 1.0 3.0) (0.11 0.11 0.14) (7.0 9.0 9.0)

AT5 CMMS1 CMMS2 CMMS3

CMMS1

AT6

(1.0 1.0 3.0) (1.0 3.0 5.0) (1.0 1.0 3.0)

(1.0 1.0 3.0) (1.0 3.0 5.0) (1.0 1.0 3.0)

Table 5 Eigenvectors of the CMMS alternatives with respect to the six attributes. VAT1 VAT2 VAT3 VAT4 VAT5 VAT6

((0.06 ((0.09 ((0.08 ((0.15 ((0.07 ((0.13

0.22 0.33 0.17 0.29 0.27 0.38

1.05) 0.82) 0.40) 0.58) 1.03) 0.95)

(0.10 (0.11 (0.11 (0.08 (0.10 (0.10

0.46 0.33 0.25 0.16 0.46 0.34

1.79) 0.99) 0.55) 0.33) 1.76) 0.88)

(0.08 (0.13 (0.29 (0.26 (0.08 (0.12

0.32 0.33 0.58 0.55 0.27 0.28

1.37)) 1.19)) 1.14)) 1.11)) 1.23)) 0.97))

Table 7 Overall classification vector (with triangular numbers). CMMS1 CMMS2 CMMS3

(0.01 0.25 5.20) (0.01 0.27 6.38) (0.03 0.48 9.39)

Table 6 Local weights for the CMMS alternatives with respect to the six attributes.

CMMS1 CMMS2 CMMS3

AT1

AT2

AT3

AT4

AT5

AT6

(0.06 0.22 1.05) (0.10 0.46 1.79) 0.08 0.32 1.37

(0.09 0.33 0.82) (0.11 0.33 0.99) (0.13 0.33 1.19)

(0.08 0.17 0.40) (0.11 0.25 0.55) (0.29 0.58 1.14)

(0.15 0.29 0.58) (0.08 0.16 0.33) (0.26 0.55 1.11)

(0.07 0.27 1.03) (0.10 0.46 1.76) (0.08 0.27 1.23)

(0.13 0.38 0.95) (0.10 0.34 0.88) (0.12 0.28 0.97)


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Fig. 5. Screenshot of preference matrix.

Fig. 6. First phase analysis results.

and fuzzy operations. Therefore, software aid may be very useful to automatically carry out the fuzzy AHP process. A software prototype for fuzzy AHP application was developed. The software was programmed by using MATLAB 7.0 on a PC platform. The operation sequence will be demonstrated in the following paragraphs, through the use of several screenshots. Initially, user must select and input the criteria chosen for evaluation the CMSS alternatives. The software prototype keeps in a database a series of attributes that the user can select to perform the comparison analysis. Additionally, the attribute database contains a set of generic attributes labeled as ‘‘attribute i’’ where ‘‘i’’ stands for the number of a given attribute. Next, the user(s) must fill the pairwise comparisons matrix for the attributes. Fig. 5 shows the dialog box where the analyst can input the pairwise comparisons among software’s attributes. To find the relative importance or priorities of the six attributes eigenvector, eigenvalue and the RC index are to be computed. Once

the comparison matrix is entirely filled with importance values (using fuzzy scale and slide bars) and total consistency is proved, the system provides the ranking of the attributes according to the information input by the user. The system provides the eigenvector and the eigenvalue, plus the consistency value (Fig. 6). The system presents the eigenvector using crisp numbers. Conversions of fuzzy numbers into crisp numbers are carried out by the software. In the second part of the software, the user must input the pairwise comparisons between two specific CMMS. This task is made accordingly to each one of the considered attributes (Fig. 7). Next, the software finds the scores of the alternative CMMSs with respect to the six attributes. The software displays the results using crisp representation. Therefore, defuzzification of the values is performed and the priority scores for the CMMS alternatives are obtained. The ranked list indicates that in this case the CMMS with the higher value has to be selected by the users. In the final screen of the system, the results of analysis are shown (Fig. 8).

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Fig. 7. Comparison matrix among CMMSs with respect to the attribute Vendor’s market share.

Fig. 8. Final results.

6. Conclusions In this paper a fuzzy-AHP-based methodology for selecting Computerized Maintenance Management Software was proposed. In order to take into account the uncertainty and in order to improve imprecision in ranking attributes and/or software alternatives, the presented approach introduces triangular numbers into traditional AHP method. Adoption of fuzzy numbers allows decisions-makers to have more freedom of estimation regarding the overall importance of attributes and real alternatives. The proposed methodology was tested on a real-world example and was found that it functions satisfactorily. We believe that this methodology is a feasible alternative to both the conventional AHP method, as well as, other fuzzy-based approaches for CMMS selection, mainly because of its simplicity and the possibility of incorporating subjective parameters and linguistic terms in expressing main software characteristics. Additionally, a fuzzy AHP based Software for selecting computerized maintenance management was proposed. The program was written in MATLAB and run on a desktop PC powered by Microsoft Windows XP. It was tested on several tests and

was found to function satisfactorily. We believe that this methodology and the developed software tool is an alternative to both the conventional AHP method as well as other fuzzy-based approaches for software selection, mainly because of its simplicity and the possibility of incorporating subjective parameters.

References [1] O’Hanlon T. CMMS best practices. Mainten J 2004;17(3):19–22. [2] Raouf A, Zulfigar A, Duffuaa SO. Evaluating a computerised maintenance management system. Int J Operat Prod Manage 1993;13(3):38–48. [3] Carnero MC, Novés JL. Selection of computerised maintenance management system by means of multicriteria methods. Prod Plann Control 2006;17(4):335–54. [4] Braglia M, Carmignani G, Frosolini M, Grassi A. AHP-based evaluation of CMMS software. J Manuf Technol Manage 2006;17(5):585–602. [5] Labib A. A decision analysis model for maintenance policy selection using a CMMS. J Qual Mainten Eng (JQME) 2004;10/3:191–202. [6] Saaty TL. Analytic hierarchy process. New York: McGraw Hill; 1980. [7] Liberatore MJ, Nydick RL. The analytic hierarchy process in medical and health care decision making: a literature review. Eur J Operat Res 2003;189(1):194–207.

O. Durán / Advances in Engineering Software 42 (2011) 821–829 [8] Vahadilla OS, Kumar S. Analytic hierarchy process: an overview of applications. Eur J Operat Res 2006;169(1):1–29. [9] Kazakidis VN, Mayer Z, Scoble MJ. Decision making using the analytic hierarchy process in mining engineering. Trans Inst Min Metall Sect A – Min Technol 2004;113(1):A30–42. [10] Mustafa MA, Albahar JF. Project risk assessment using the analytic hierarchy process. IEEE Trans Eng Manage 1991;38(1):46–52. [11] Cheng Ching-Hsue. Evaluating naval tactical missile systems by fuzzy AHP based on the grade value of membership function. Eur J Operat Res 1997;96(2):343–50. [12] Ayag Z. A fuzzy AHP-based simulation approach to concept evaluation in a NPD environment. IIE Transactions; September 2005. p. 827–42(16). [13] Karsak EE, Tolga E. Fuzzy multicriteria decision making procedure for evaluating advanced manufacturing system in investments. Int J Prod Econ 2001;69:49–64. [14] Bozdag CE, Kahraman C, Ruan D. Fuzzy group decision making for selection among computer integrated manufacturing systems. Comput Ind 2003;51:13–29. [15] Shamsuzzaman M, Sharif Ullah AMM, Bohez ELJ. Applying linguistic criteria in FMS selection: fuzzy set AHP approach. Integrated Manuf 2003;14/3:247–54. [16] Ordoobadi Sharon M, Mulvaney NJ. Development of a justification tool for advanced manufacturing technologies: system-wide benefits value analysis. J Eng Technol Manage 2001;18(2):157–84.

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[17] Cato R, Mobley K. Computer-managed maintenance systems in process plants: a step-by-step guide to effective management of maintenance, labor, and inventory, 1st ed. Butterworth-Heinemann College; 1998. [18] Bradshaw L. Improved CMMS and asset management systems – but do they lead to success? Mainten Asset Manage 2005;20(2):21–8. [19] Wei Chun-Chin, Chien Chen-Fu, Wang Mao-Jiun. An AHP-based approach to ERP system selection. Int J Prod Econ 2005;96:47–62. [20] Kans M. An Approach for determining the requirements of computerized maintenance management systems. Comput Ind 2008;59:32–40. [21] Chiu C-Y, Park CS. Capital budgeting decisions with fuzzy projects. Eng Economist 1998;43(2):125–50. [22] Chang DY. Applications of the extent analysis method on fuzzy AHP. Eur J Operat Res 1996;95:649–55. [23] Leung LC, Cao D. On consistency and ranking of alternatives in fuzzy AHP. Eur J Operat Res 2000;124:102–13. [24] Ingwald A, Kans M. The use of IT within maintenance management for continuous improvement. In: Proceedings of MIMAR 2007 – 6th IMA international conference on modeling in industrial maintenance and reliability. p. 51–6. [25] Ciptomulyono U. Fuzzy goal programming approach for deriving priority weights in the analytical hierarchy process (AHP) method. J Appl Sci Res 2008;4(2):171–7.