USING FUZZY LINGUISTICS TO SELECT OPTIMUM MAINTENANCE AND CONDITION MONITORING STRATEGIES

Mechanical Systems and Signal Processing (2003) 17(2), 305d316 doi:10.1006/mssp.2000.1395, available online at http://www.idealibrary.com on

USING FUZZY LINGUISTICS TO SELECT OPTIMUM MAINTENANCE AND CONDITION MONITORING STRATEGIES CHRIS K. MECHEFSKE Department of Mechanical Engineering, Kingston, ON, Canada, K7L 3N6. E-mail: [email protected] AND

ZHENG WANG Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ONT., Canada N6G 5B9. E-mail: [email protected] (Received 14 June 2000, accepted 13 June 2001) Continued pressure on companies to reduce costs and improve customer satisfaction has resulted in increasingly detailed examinations of maintenance practices and strategies. The justi"cation of any given maintenance strategy or practice within an organisation must consider multiple criteria. It should also be based on the overall objectives of the organisation, many of which are &intangible' or &non-monetary'. A fuzzy linguistic approach to achieve the inclusion of somewhat subjective assessments of maintenance strategies and practices in an objective manner is outlined in this paper. This approach is also demonstrated with two examples. Implementation of this approach will assist decision makers in the evaluation and selection of maintenance strategies and particular condition-monitoring techniques.  2003 Published by Elsevier Science Ltd.

1. INTRODUCTION

Recently, there has been tremendous pressure on manufacturing and service organisations to be competitive and provide timely delivery of quality products. This new environment has forced managers and engineers to optimise all systems involved in their organisations. Maintenance, as a system, plays a key role in achieving organisational goals and objectives. It contributes to reducing cost, minimising equipment downtime, improving quality, increasing productivity and providing reliable equipment that is safe and well con"gured to achieve timely delivery of orders to customers. Although the importance of maintenance is recognised, it is not as developed and integrated in engineering and management curricula as are project management and production systems. Production systems and project management have been studied extensively, and the application of optimisation and statistical techniques in these areas has matured to a greater degree than in the "eld of maintenance, possibly for the following reasons: (1) traditionally, maintenance has been regarded as a &necessary evil' and, at best, as a system driven by production; (2) maintenance in an organisation has complex relationships with other functions; and (3) the output of maintenance is hard to measure and quantify. All these items are related to the evaluation of maintenance strategy. Although the issue has been the subject of many archival journal articles, trade journal articles, books, 0888}3270/03/#$30.00/0

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chapters in books and handbooks for a long time, the employed justi"cation methodologies are those traditional &bottom-up' engineering economy approaches (present worth, annual worth, internal rate of return). These approaches ignore the &intangible' or &non-monetary' bene"ts resulting from maintenance [2}7]. The justi"cation methodology explored in this paper illustrates the use of fuzzy linguistic variables in a heuristic algorithm to assist decision makers in their evaluation and choice of maintenance strategies and condition-monitoring techniques.

2. BACKGROUND

The original plant maintenance technique is Breakdown Maintenance. In this case an item of the plant would be repaired each time that it breaks down. The problem, however, is that the process of failure often creates consequential damage, which calls for more extensive repairs. Also, there may be delays in the repair process because spare parts and specialised skilled labour may not be immediately available. The fact that there is a breakdown may also result in an interruption of a process that could then cause delays in downstream processes, lost revenue, and/or unsafe conditions. An improvement can be obtained by moving to regular Preventive Maintenance where the plant is stopped at intervals, often annually, and partly stripped and inspected for faults. It is also called Scheduled Maintenance. Machine components that have predictable and well-understood failure modes can have their time between failures vs number of failures plotted. If all failures in a given population of machines are to be avoided, the time between preventive maintenance actions needs to be shorter than the earliest failure that is likely to occur. This means that most, if not all, machines are maintained with a signi"cant amount of useful life remaining. An alternative is to use Condition-Based Maintenance (CBM) where the critical components are monitored for deterioration and the maintenance is carried out just before the failure occurs. The principle is to select an appropriate method of monitoring deterioration and apply it to the machine in order to obtain a lead time of warning in advance of a failure. This lead time allows for scheduling of maintenance just before complete failure [8]. In practice, the choice of the optimum maintenance strategy is not as simple as noted above. Not all failures can be detected by monitoring. The economics of the situation may limit the number of components that can be monitored. There will also be a number of components and/or machines for which condition monitoring is not particularly appropriate. In many cases these three strategies mentioned above are used simultaneously within an organisation. Thus, decision makers face such questions as: (a) Which strategy should be introduced for a speci"c type of machine? (b) How to justify their decision? Answering these questions is a di$cult task. This is due to the incapability of traditional economic analysis methods, such as net present value (NPV), internal rate of return (IRR), payback period and bene"t/cost (B/C) ratio, to handle the kind of projects which involve a high degree of intangible bene"ts. There are always a variety of objectives that a company wants to achieve through its maintenance strategy. But most traditional economic analysis methods are based upon a comparison of the initial investment to the estimated cost savings and often focus on easily quanti"able factors. The majority of the recognised bene"ts of condition monitoring are considered to be &intangible' or &non-monetary'. They are hard to quantify and therefore often ignored in traditional discounted cash #ow analysis methods [9]. To overcome the shortcomings of the traditional discounted cash #ow analysis methods, a fuzzy linguistic

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approach developed by Parsaei and Wilhelm [6, 7] is employed to assist in justifying condition monitoring. Fuzzy linguistic models permit the translation of verbal expression into numerical terms, thereby dealing quantitatively with the expression of the importance of various objectives. These quantities can then be used to assess the optimum degree of investment in various maintenance strategies and in various condition-monitoring techniques. 3. FUZZY LINGUISTICS

In using our everyday natural language to impart knowledge and information, there is a great deal of imprecision and vagueness or fuzziness. Our main concern is representing, manipulating, and drawing inferences from such imprecise statements. Establishing an exact limit will always result in undesired behaviour in the transition zone, since almost identical objects are treated as completely di!erent. In the theory of fuzzy sets one tries to avoid these di$culties by generalising the binary view to the notion of membership, where an object either is an element of a set or is not. A degree of membership is allowed which may assume all values between 0 and 1. Due to the intermediate degrees of membership (all values between 1 and 0) a smooth transition from the property of being a member to the property of not being a member can be achieved. In Fig. 1, a &generalised' characteristic function is shown. Height is associated with degrees of membership. In Fig. 1, the height of 150 cm corresponds to the predicate tall with a membership degree of 0.7 on a scale from 0 to 1. The closer the membership degree
(x) i is to 1 the more strongly x satis"es the predicate tall. The example mentioned above suggests the formalisation of linguistically described data with the help of generalised characteristic functions. Four di!erent levels in the de"nition of a linguistic variable may be distinguished. At the top level there is the name of the fuzzy variable (e.g. height). At the level below it there are the labels of fuzzy values (starting with an initial set of values called primary values). Further down there are membership functions and at the bottom, the universe of discourse. All four levels are indispensable in the de"nition of a variable. It is important to observe that linguistic variables have a dual nature; at higher levels we have a symbolic linguistic form, and at lower levels we have a well-de"ned quantitative analytical form. This double identity is a general feature of fuzzy linguistic descriptions rendering them convenient for performing both symbolic (qualitative) and numerical (quantitative) computations [10]. In applying a fuzzy linguistic variable

Figure 1. A characteristic function representing the vague predicate tall.

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Figure 2. Diagrammatic de"nitions of fuzzy linguistic variables X"IMPOR¹ANCE and >"CAPABI¸I¹>.

approach to the evaluation of maintenance strategies two fuzzy linguistic variables are de"ned speci"cally for this situation: X"&IMPOR¹ANCE' and >"&CAPABI¸I¹>'. The use of these two linguistic variables allows Importance to be associated with each of a set of goals common to all maintenance strategies and the Capability of each maintenance strategy to meet the goals of the organisation to be speci"ed. For example, consider the following sentence. Condition-Based Maintenance is Indeed Superior in its ability to improve product quality, which is an Indeed Critical goal in accomplishing the maintenance strategy of the organisation. In the above sentence, the term Indeed Superior is a value of the fuzzy linguistic variable CAPABI¸I¹>, and the term Indeed Critical is a value of the fuzzy linguistic variable IMPOR¹ANCE. The primary values of the two fuzzy linguistic variables, de"ned on the universe of discourse 0, 1, are shown in Fig. 2. The primary variable values are selected somewhat arbitrarily here, but could also be determined by using neural networks. In addition to primary values, compound values are generated by using the connectives AND and OR and a collection of linguistic modi"ers such as NO¹, , MORE OR

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TABLE 1 Transition of linguistic modixers into fuzzy set operations Modi"er

Membership Function Operation

Very A More or less A Indeed A

[f (u )] + V [f (u )] + V 2[ f u )] + V 1!2 [1!f (u )] + V [f (u )]  + V [f (u )]  + V 1!f (u ) + V 0 1!f (u ) + V 0 1!f (u ) + V

Plus A Minus A Over A (or above A) Under A (or below A) Not A

for for

0)f (u ))0.5 + V 0.5)f (u ))1.0 + V

for for for for

x*x

x)x

x*x

x*x

   

TABLE 2 Compound values of membership function for X"IMPORTANCE Universe of discourse Variable value, x

0.0

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.0

Indeed Critical More or ¸ess Critical
0 0

0 0

0 0

0 0

0 0

0 0

0 0

0.01 0.22

0.05 0.39

0.92 0.89

1.0 1.0

0 0

0.01 0.32

0.06 0.50

0.56 0.87

0.81 0.95

1.0 1.0

0.81 0.95

0.56 0.87

0.06 0.50

0.01 0.32

0 0

1.0

0.90

0.75

0.25

0.10

0

0.10

0.25

0.75

0.90

1.0

¸ESS. Suppose M(x) is de"ned as a semantic rule for associating a meaning with each variable name, and is itself a fuzzy subset on the universe of discourse (; ) for linguistic V variable X, written as M(x)"x, f (u ) u 3; , where f (u ),the membership func+V V V V +V V tion of u in M(x). When A represents a fuzzy value (e.g. Important), the operations that can V be used to modify A are shown in Table 1. These modi"ers allow for a more realistic set of values for each membership function by further subdividing the universe of discourse. In this way, we can utilise the primary values to generate the compound values which are shown in Tables 2 and 3. Four equations which will be used for our problem are introduced as follows: (a) Go( delian implication operator (
g) [11]. The GoK delian implication operator is de"ned as




[ f \ (u ), f (u )]" E +V V +W V f where f

if f \ (u ))f (u ) +V V +W W (u ) if f \ (u )'f (u ) +V W +V V +W W 1

(1)

(u ) is the membership function of u and f (u ) the membership function of u . +V V V +W W W

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TABLE 3 Compound values of membership function for >"CAPABILITY Universe of discourse Variable Value, y

0.0

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.0

Indeed Superior More or ¸ess Superior Above Average Below Average
0 0

0 0

0 0

0 0

0 0

0 0

0 0

0.02 0.32

0.18 0.55

0.98 0.95

1.0 1.0

0 1.0 1.0

0 0.95 0.64

0 0.90 0.16

0 0.65 0.04

0 0.20 0

0 0 0

0.20 0 0

0.65 0 0

0.90 0 0

0.95 0 0

1.0 0 0

Using the operator, we can obtain the membership function of the implication relation r between the two linguistic variables X and >. GH (b) Intersection of fuzzy relations () [12]. This intersection is de"ned as a fuzzy relation R " r having a membership function (or matrix) given by H G GH fR (u , u )"R f (u , u ) over i"1, 2,2, m H V W +P V W r GH

"Min [ f (u , u )] (2) +P V W SVSW where f (u , u ) is the membership function of (u , u ), r a linguistic assessment of the +P V W V W GH extent to which a maintenance goal i can be achieved if a maintenance strategy j is selected for implementation and R the Minimum. (c) Compositional operator () [13]. This operator is de"ned such that the membership function of [ f (u , u ) f (u )] is determined from +P V W +V V (u )]. (3) f \ (u )"R 
[ f (u , u ), f +W W E +P V W +V V Using the operator when the implication relation between the two linguistic variables X and >, and one of their membership functions are known, the other is inferable. (d) Hamming distance () [12]. The Hamming distance is de"ned as 1 (u )!f * (u )  for 1, 2,2,n (4) " f +W W +W  W H s SW where s is the number of elements in the universe of discourse u and y* the Indeed Superior. W 4. HYPOTHETICAL EXAMPLES

4.1. SELECTION OF MAINTENANCE STRATEGIES As indicated in Section 2, there are three main maintenance strategies used by industries: Breakdown Maintenance, Scheduled Maintenance and Condition-Based Maintenance. A heuristic algorithm is now presented that is based on the use of fuzzy linguistic variables to characterise the capability of available maintenance strategies to satisfy a common set of maintenance goals and to select the &best' strategy from those available. It is assumed that the implementation of the maintenance plan is for a speci"c type of machine and that the availability of any particular maintenance strategy will be constant. The algorithm consists of seven steps:

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4.1.1. Step 1 The organisation must set goals for its maintenance strategy "rst. These goals might include some or all of the following: (a) (b) (c) (d) (e) (f ) (g) (h) (i) ( j) (k)

enhanced competitiveness, high product quality, low maintenance cost, development of management and engineering expertise, improved reliability, improved safety, minimum inventories, #exibility, return on investment, acceptance by labour, perceived by others as a leader in the use of technology.

4.1.2. Step 2 By interviewing managers and employees, direct observation and reference to the organisation's mandate we can establish a linguistic description of the Importance of each of a common set of i maintenance goals as well as the Capability of each of j di!erent strategies to satisfy each goal. These descriptions become the values of the fuzzy linguistic variables x and y , respectively (see Tables 4 and 5). G H 4.1.3. Step 3 For each maintenance goal and strategy, solve equation (1) using the membership functions contained in Tables 2 and 3. For example, from Table 5 we see that ConditionBased Maintenance, or strategy j"3, is rated as Indeed Superior in its ability to impact the maintenance goal of high product quality, or maintenance goal i"2, which has been judged to be an Indeed Critical goal in the maintenance strategy of the organisation (see Table 4). This relationship between the maintenance strategy and the maintenance goal is expressed by the fuzzy relation r .  In a similar fashion, the fuzzy relations representing the 30 entries in Table 5 are computed to complete step 3. When this step is completed, Table 5 can be thought of as

TABLE 4 Linguistic assessment of the IMPORTANCE of each maintenance goal

Maintenance goal Enhanced competitiveness High product quality Low maintenance cost Development of expertise Improved reliability Improved safety Minimum inventories Return on investment Acceptance by labour Technological leadership

Linguistic assessment (variable value)
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C. K. MECHEFSKE AND Z. WANG

TABLE 5 Linguistic assessment of the CAPABILITY of each strategy to achieve each maintenance goal Strategy Maintenance goal Enhanced competitiveness High product quality Low maintenance cost Development of expertise Improved reliability Improved safety Minimum inventories Return on investment Acceptance by labour Technological leadership

Breakdown Maintenance

Scheduled Maintenance

Condition-Based Maintenance

! ! ! ! # # # ## # #

# # # ## # ## # ## # #

# ### ## ## # ## # ### # ##

Note: ###, Indeed Superior; ##, More or ¸ess Superior; #, Above Average; !, Below Average.

a 10;3 matrix of strategies and goals, with the meaning of each element represented by an 11;11 fuzzy relation. 4.1.4. Step 4 In this step, the intersections of the fuzzy relations computed in step 3 are formed across each of the 10 maintenance goals for each of the three strategies [see equation (2)]. For example, R represents the intersection of the fuzzy relations associated with j"3, Condi tion-Based Maintenance, across the 10 maintenance goals. 4.1.5. Step 5 Suppose the IMPOR¹ANCE of implementing the overall maintenance strategy to the company's future is assessed as x*"Indeed Critical. This value of the linguistic variable was selected because at any phase of the strategic planning process, decision makers are likely to want to achieve the maintenance goals that are indeed critical to the maintenance plan. Thus, the meaning of the &ideal' value of x*"Indeed Critical is found in Table 2 f * (u )"[0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.05 0.92 1.0]. +V  V 4.1.6. Step 6 Solve the fuzzy relational equation y\"R  x*\ for strategy j"1, 2,2, n, to deterH H mine the CAPABI¸I¹> of each to implement the maintenance strategy of the company [see equation (3)]. For example, the capability of Condition-Based Maintenance ( j"3) to implement the maintenance strategy is found as f \* (u )"[0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 1.00 1.00 1.00] +W  W for j"3. 4.1.7. Step 7 The relative Hamming distances of each of the compatibility functions computed in step 6 from the &ideal' compatibility function y*"Indeed Superior given in Table 3, are shown in

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TABLE 6 Relative Hamming distances Strategy

Relative Hamming distance

Breakdown Maintenance Scheduled Maintenance Condition-Based Maintenance

0.62090 0.25636 0.07909

TABLE 7 Some available condition-monitoring techniques Vibration Oil/debris Inspections Current Conductivity Performance Thermal Corrosion

Table 6 [also see equation (4)]. Thus, we select Condition-Based Maintenance as the best strategy to implement at this phase since it has the minimum relative Hamming distance from the &ideal' linguistic assessment of CAPABI¸I¹>. 4.2. SELECTION OF CONDITION-MONITORING TECHNIQUES Once Condition-Based Maintenance is adopted, the next step is to select an appropriate condition-monitoring technique. It is a critical step in the successful implementation of Condition-Based Maintenance. There are many condition-monitoring techniques widely used by industries and available in the market (Table 7) [14]. Which techniques can be used for a speci"c machine? Again the fuzzy linguistic approach can be employed to assist in selecting an appropriate technique from those available. This time we have to set up a set of selection criteria "rst and then assess the Importance of each of those criteria in terms of the linguistic variable X"IMPOR¹ANCE (Table 8). We identify the set of techniques presently available and suitable for the speci"c machine. Let us suppose that three techniques, thermal monitoring, oil/debris analysis and vibration analysis, are suitable for our problem. The next step is to assess the capability of each one to meet each of the common criteria above by the use of the values of the linguistic variable >"CAPABI¸I¹>. Such assessments are shown in Table 9. Following the same algorithm mentioned above, we can get the results shown in Table 10. Thus, we select vibration analysis as the best technique for our problem. It should be noted that certain restrictions may need to be placed on the use of this approach. When selecting the optimum maintenance strategy for instance, a particular focus on one section of the plant or division of the company may override the algorithm proposed. In the case of optimum Condition-Based Maintenance technique, again, particular plant locations or speci"c machines may require special treatment. The results presented in this section are based on the assessments presented in Tables 4, 5, 8 and 9. These assessments were made based on the authors' experience. In a true test of the

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TABLE 8 Linguistic assessment of the IMPORTANCE of each selection criterion Selection criteria

Linguistic assessment (variable value)
Costs Accuracy Ease of use Ruggedness Degree of technical expertise required Repeatability Diagnostic ability Trending ability Ease of maintenance Ease of mounting

TABLE 9 Linguistic assessment of the CAPABILITY of each technique to satisfy each selection criteria Techniques Selection criteria

Thermal monitoring Oil/debris analysis

Costs Accuracy Ease of use Ruggedness Degree of technical expertise required Repeatability Diagnostic ability Trending ability Ease of maintenance Ease of mounting

Vibration analysis

# # # ## #

## ## # ## #

## ### ## ## #

## # ## # #

## # ### ## ##

### ## ### # ##

Note: ###, Indeed Superior; ##, More or ¸ess Superior; #, Above Average; !, Below Average.

TABLE 10 Relative Hamming distances for examples

Strategy Thermal monitoring Oil/debris analysis Vibration analysis

Relative Hamming distance 0.25636 0.16545 0.07909

procedure these values would be selected by the users of the programme. Such users would be the maintenance and operations managers and the technologists, technicians and engineers directly involved in the maintenance and condition-monitoring work. The condition-monitoring techniques used in Table 9, as suitable for a speci"c problem, were selected as an example and do not represent a true case study. The next section presents the results of a case study conducted at a chemical-processing plant.

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FUZZY LINGUISTICS FOR OPTIMUM MAINTENANCE

TABLE 11 Relative Hamming distances for case studies Relative Hamming distance Strategy

Case 1

Case 2

Case 3

Case 4

Breakdown Scheduled Condition

0.52636 0.16636 0.24909

0.52636 0.24909 0.16545

0.56273 0.16545 0.16545

0.48364 0.16545 0.16545

5. CASES STUDIES

In order to apply this approach to real maintenance activities the Manager of Crude Units, the Manager of Oil Movement and Storage, the Manager of Improvement and the Leader of the Machinery Group at the Chemicals and Products Division of Imperial Oil Limited in Sarnia, Canada were interviewed. They assessed the importance of the maintenance goals within their company. They then assessed the di!erent capabilities of each maintenance strategy when used for maintaining di!erent types of machines: centrifugal pumps (critical)*Case 1, centrifugal pumps (non-critical)*Case 2, centrifugal compressors*Case 3, and reciprocating compressors*Case 4. The details of the data collected are not presented here because of space limitations. The same analysis procedures as outlined in the sections above were used in these case studies. The "nal results for these four cases are shown in Table 11. For each case, the maintenance strategy with the smallest Hamming distance is selected as the best strategy to implement at this phase. From the examples presented, it is shown that even the same maintenance strategy will have di!erent capabilities when used for di!erent applications. This di!erence in capabilities is re#ected in the linguistic assessments and determines whether the maintenance strategy is suitable for a particular application or not. It was noticed in case studies 3 and 4 that the Scheduled Maintenance and ConditionBased Maintenance have the same Hamming distance. This may be due to similar assessments in terms of capability of the di!erent maintenance strategies provided by the maintenance personnel. A sensitivity analysis of these parameters is currently being undertaken. 6. CONCLUSIONS

The justi"cation of condition monitoring should consider multiple criteria. It should also be based on the objectives of an organization, many of which are &intangible' or &non-monetary'. A fuzzy linguistic approach to achieve this has been outlined and demonstrated through examples and case studies. It was found to be useful in determining the optimum maintenance strategy or the Condition-Based Maintenance technique to be employed in a speci"c situation based on qualitative verbal assessment inputs. Further work is planned to make the analysis system more resistant to ties. Hopefully, this approach can assist decision makers in the evaluation and selection of maintenance strategies and condition-monitoring techniques. 7. ACKNOWLEDGEMENTS

The authors wish to thank the Imperial Oil Charitable Foundation for the funding needed to carry out this study and the personnel at Imperial Oil's Products and Chemicals Division, Sarnia, Ontario, Canada for their kind assistance.

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