Prioritizing equipments for preventive maintenance (PM) activities using fuzzy rules

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Computers & Industrial Engineering 54 (2008) 169–184 www.elsevier.com/locate/dsw

Prioritizing equipments for preventive maintenance (PM) activities using fuzzy rules Amir Khanlari, Kaveh Mohammadi, Babak Sohrabi

*

Department of Information Technology Management, School of Management, University of Tehran, P.O. Box 14155-6311, Tehran, Iran Received 3 August 2006; received in revised form 8 July 2007; accepted 12 July 2007 Available online 19 July 2007

Abstract Maintenance, as a support function in businesses, plays an important role in backing up any emerging business and operation strategies. It is required to maximize the reliability of equipment and systems. Among them, preventive maintenance (PM) involves the repair, replacement, and maintenance of equipment in order to avoid unexpected failure during use. The objective of any PM program is the minimization of the total cost of inspection and repair, and equipment downtime (measured in terms of lost production capacity or reduced product quality). Maintenance activities have been regarded as a necessary expense that belongs to the operating budget. But since, organizational resources are limited and scarce, prioritizing equipments for assigning resources is essential. In this paper, fuzzy rules used to interpret linguistic variables for determination of priorities. Using this approach, such verbal expressions, which cannot be explicitly analyzed or statistically expressed, are herein quantified and used in decision making.  2007 Elsevier Ltd. All rights reserved. Keywords: Preventive maintenance; Priority; Rule base; Fuzzy

1. Introduction Once a system or a piece of equipment has been purchased, it must be maintained. Tsang (2002) argues that experience, judgment and vendor recommendations are the common bases for determining the content and frequency of a maintenance task. Maintenance can be defined like the activities intended to preserve or promptly restore the safety, performance, reliability, and availability of plant structures, systems, and components to ensure superior performance of their intended function when required (Weinstein & Chung, 1999). Production and service systems are heavily affected by their respective maintenance systems. Maintenance systems operate in parallel to the production systems to keep them serviceable and safe to operate at minimum cost. One way to reduce the cost of operation and production is to optimize utilization of maintenance resources (Duffuaa & Al-Sultan, 1997). Historically, maintenance activities have been *

Corresponding author. Tel.: +98 2188008969. E-mail address: [email protected] (B. Sohrabi).

0360-8352/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.07.002

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regarded as a necessary expense that belongs to the operating budget. It is a common item on the list of cost-reduction programs. However, maintenance, as a support function in businesses, plays an important role in backing up any emerging business and operation strategies (e.g., lean manufacturing, just-in-time production and six sigma programs). The effectiveness of maintenance management depends significantly on proper deployment of resources in the form of spare parts and other maintenance materials, manpower, necessary tools and instruments, and ultimately life cycle profit for an organization (Sherwin, 2000). But since, organizational resources are limited and scarce, prioritizing equipments for assigning resources is essential. Recently, Developments in micro-technology and artificial intelligence (AI) have driven the trend towards more extensive maintenance management. Recent systems have relied on artificial intelligence techniques to strengthen the robustness of maintenance management. Four AI techniques have been widely applied: 1. 2. 3. 4.

Expert systems; Neural networks; Fuzzy logic; Model-based systems.

In this paper, fuzzy rules as an AI tool used to determine priority of activities. For achieving this goal, paper is organized as follows. First, maintenance activities and its importance and types will be described. Then, intelligent techniques and their applications in maintenance management will be presented. In the next section, the fuzzy rules will be explained together with the main concepts; the decision-making algorithm implemented to solve the priority determining problem and the details of the implementation. Finally, the last section establishes the conclusion giving general remarks on this work, limitations of the study and directions for future research. 2. Maintenance management Business leaders increasingly realize the strategic importance of the maintenance function for organizations, which have significant investments in physical assets, and so is a necessary expense in the operating budget. In other words, reliability has become a critical issue in capital-intensive operations (Eti, Ogaji, & Probert, 2006). Overall, the goal for an organization is to increase profitability. The maintenance and asset-management functions can increase profits in two main ways, i.e., by decreasing running costs and increasing capability. If the annual maintenance cost exceeds 5% of the asset value, the organization is probably in financial difficulties. The total maintenance cost depends on the quality of the equipment, the way it is used, the maintenance policy and the business strategy. The wise business owner buys equipment that will subsequently need little maintenance, i.e., is highly unlikely to fail (Sondalini, 2000). Maintenance activities fall into two broad categories, namely corrective maintenance and preventive maintenance (Duffuaa, Ben-Daya, Al-Sultan, & Andijani, 2001). Corrective maintenance, also known as fireman maintenance, is performed when action is taken to restore the functional capabilities of failed or malfunctioned systems. This is a reactive approach to maintenance because the action is started when the unscheduled event of an equipment failure happens. Nowadays, in small and medium enterprises (SME), the maintenance activities are moving from the reactive and expensive mode (e.g., breakdown maintenance, failure-finding maintenance and corrective maintenance) to proactive-based, cost effective and high service maintenance techniques and approaches are adopted by enterprises in one form or another. Some of the most important maintenance techniques and approaches are (Pun, Chin, Chow, & Chow, 2002): • Preventive maintenance. Use of overhaul or preventive replacement procedures; predictive maintenance and condition-based maintenance. Use of advanced monitoring sensors to keep track of the condition of equipment; • Proactive maintenance. Identifies and solves specific maintenance problems;

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• Total productive maintenance. Maximizes equipment effectiveness through employee involvement, and incorporates the use of autonomous maintenance and small group activities to improve equipment reliability, maintainability and productivity; profit-centered maintenance. Insists on the reduction of the need for maintenance and the re-engineering of maintenance practices, thereby eliminating non-value-adding activities and reducing maintenance costs; and • Reliability-centered maintenance. Methodology for determining what preventive maintenance is required to maximize the reliability of equipment and systems. The focus of this paper is on preventive maintenance (PM) activities. PM involves the repair, replacement, and maintenance of equipment in order to avoid unexpected failure during use (Mann, Saxena, & Knapp, 1995). PM is performed to retain the equipment in a satisfactory operational condition: it is divided into time-based and condition-based maintenance. Time-based maintenance is performed after fixed time intervals, whether a problem is apparent or not, in order to avoid failure of the items during operation. Time-based maintenance incurs a large cost for the user in maintaining the required level of reliability, because the majority of items are replaced prematurely despite still having useful lives remaining. Condition-based maintenance is applicable to components which tend to deteriorate rapidly with time. However, it is usually not cost effective to monitor the condition of each component: some will be relatively inaccessible for monitoring (Eti et al., 2006). The objective of any PM program is the minimization of the total cost of inspection and repair, and equipment downtime (measured in terms of lost production capacity or reduced product quality) (Gento, 2004). Preventive maintenance of a system is taking into account expert knowledge, feedback observations and degradations in order • to model the system lifetime and to quantify the degradation or failure probability, • to detect important variables involved in the degradation process and to design maintenance tasks in order to differ or eliminate ageing, • to quantify the effect of maintenance actions on the system behavior, • to propose diagnosis and decision help, • to propose data mining and sensibility analysis (Celeux, Corset, Lannoy, & Ricard, 2006). Preventive maintenance consists of a set of technical, administrative and management actions to decrease the component ages in order to improve the availability (and the reliability) of a system (reduction of probability failure or the degradation level of a system’s component). These actions can be characterized by their effects on the component age: the component becomes ‘‘as good as new’’, the component age is reduced, or the state of the component is lightly affected only to ensure its necessary operating conditions, the component remaining appears to be ‘‘as bad as old’’. PM policy has been the subject of many studies in recent years. Those studies take into consideration several criterions like cost, economic life, risk or a combination of the above stated criteria (Samrout, Yalaoui, Chaˆtelet, & Chebbo, 2005). As mentioned, PM activity is relying on planning and scheduling. Preventive maintenance (PM) planning is among the most common and significant problems faced by the manufacturing industry. Production schedules are often interrupted by equipment failures, which could be prevented by proper preventive maintenance (Sortrakul, Nachtmann, & Cassady, 2005). Equipment maintenance management must primarily provide operational or short-term (daily) planning and long-term planning. Pragmatically speaking, maintenance management is done to minimize downtime. Management boils down to making a series of decisions concerning the following: (1) If, or why perform maintenance; (2) The average interval between component failures, or when to perform preventative maintenance; (3) Which actions are required, or what to do on the equipment; (4) How to do it (macro-technologically); (5) Where to do it; (6) How long it takes (Fig. 1). Some researchers attempted to solve PM planning and scheduling problem, Graves and Lee (1999) presented a single-machine scheduling problem with the objective to minimize the total weighted completion time of jobs. However, only one maintenance activity can be performed during the planning horizon (Sortrakul et al., 2005). Lee and Chen (2000) extended Graves and Lee’s research to parallel machines. Qi, Chen, and Tu (1999) considered a similar single-machine problem with the possibility for multiple maintenance actions, but the risk of not performing maintenance is not explicitly included in the model.

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Maintenance Management Problem

When

Why

What Where

How

How long

Fig. 1. Decision making in maintenance (Knezevic et al., 1997).

3. Artificial intelligence in maintenance decisions Artificial intelligence has been frequently applied in maintenance decisions at several ways and different problems. Gopalakrishnan, Mohan, and He (2001) presented a tabu search based heuristic for the preventive maintenance (PM) scheduling problem. They have tested their heuristic on 60 problems. The aim was to maximize the total priority of the scheduled tasks subject to resource availability constraints. Cavory, Dupas, and Goncalves (2001) presented article deals with optimizing the schedule of maintenance tasks of all the machines in a single product manufacturing production line. This study was made in the context of one machine assigned to one operator. This operator intervenes to change tools during a stoppage. Their approach to the scheduling of maintenance tasks was validated upon an actual production line of car engines. They focused their study on the setting of parameters of a genetic algorithm. They proceeded with a systematic approach inspired by the Taguchi method to find the best combination of levels for each studied parameter and performed a statistical confirmation of the results. Finally they validated the genetic approach as against naive optimization. Chen, Yang, Lee, and Ni (2002) dedicated a web-enabled intelligent maintenance optimization platform which can adjust itself to make the various suggestions in the particular time interval, to make decision of maintenance action for key components and to make schedule for the parallel or series systems within limited maintenance resources. Gento (2004) shows the power of rough sets contains a real case of a plastic injection installation for the analysis. He used this theory to facilitate extracting knowledge from the great amounts of information by detecting those parameters that are truly significant for establishing the decision rules of the maintenance. Samrout et al. (2005) used genetic algorithm to minimize preventive maintenance cost problem for the series–parallel systems. Their work is based on another technique, the ant colony optimization (ACO). Sortrakul et al. (2005) developed heuristics based on genetic algorithms to solve an integrated optimization model for production scheduling and preventive maintenance planning. Quan, Greenwood, Liu, and Hu (2006) used evolutionary algorithms to solve multiobjective problem, should the workforce be small to reduce idle time or should it be large so more maintenance can be performed each hour?, they rather than conducting a conventional dominance-based Pareto search, introduce a form of utility theory to find Pareto optimal solutions. Ciarapica and Giacchetta (2006) experimentally used neural nets and neuro-fuzzy systems to forecast activities in the maintenance cycle achieved the dual goal of identifying any need for measures ahead of the deadlines established for routine preventive maintenance in the event of alarm conditions being detected, and of postponing any scheduled measures in the event of the components in question still being in good condition.

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Using these tools enabled an accurate prediction of the values of the vibrations on rotating machinery based on the values of the operating parameters given as input. Al-Garni, Jamal, Ahmad, Al-Garni, and Tozan (2006) used an artificial neural network (ANN) model for predicting the failure rate of one type of airplane tires utilizing the two layered feed-forward backpropagation algorithm as a learning rule is developed. The results show that the failure rate predicted by the ANN is closer in agreement with the actual data than the failure rate predicted by the Weibull model (a model in this area). Lapa, Pereira, and Barros (2006) present a novel methodology for preventive maintenance policy evaluation based upon a cost–reliability model, which allows the use of flexible intervals between maintenance interventions. Such innovative features represent an advantage over the traditional methodologies as it allows a continuous fitting of the schedules in order to better deal with the components failure rates. This methodology is to automatically optimize the preventive maintenance policies, considering the proposed methodology for systems evaluation. They used genetic algorithm in order to evaluate the proposed methodology, the High Pressure Injection System (HPIS) of a typical 4-loop PWR was used as a case study. As authors claimed, the results obtained by this methodology outline its good performance, allowing specific analysis on the weighting factors of the objective function. The results of mentioned researches show the power of AI techniques for solving maintenance problems. But these approaches are simplified and cannot solve real world problems completely yet. So there need more works on maintenance decisions, specifically, in PM planning. 4. Fuzzy logic in maintenance According to Sweeney and Petrovic (1991), there are noisy data, lexical imprecision, descriptive language, random processes, incomplete data, contradictory data, uncertain knowledge, aggregation of rules from different knowledge sources and experts. Many of these are met when managing equipment maintenance. Other data used for purposes of maintenance management include those about vehicles and their main assemblies, spare parts, labor force, maintenance capacity, schedules of vehicle utilization and preventive maintenance. Data are extracted from ‘‘source documents’’ (travel orders, reports on preventive maintenance, occurrence of faults, diagnostic examination, corrective maintenance and the like), and fed into a computer. Various classes of data obviously result from corresponding segments or stages in the process of maintenance (and operation) of vehicles. These stages are characterized by their entities, characteristics and transformations, each laden with imprecise and uncertain data. Also, values of certain attributes describing entities are expressed as intervals. Furthermore, these values have different limits in different situations (Knezevic, Papic, & Vasic, 1997). In the fuzzy set theory, uncertainty is viewed as a degree of set membership (e.g., the degree of presence of a symptom). Degrees of membership are numerical values in the interval [0, 1], where 1 means that an object is a member, 0 means that an object is not a member, and an intermediate value means that an object is a partial member. In recent years, many research papers using fuzzy set theory in problem solving have appeared in magazines and at meetings. Maintenance is rarely mentioned in such papers, mostly when discussing simple examples of fuzzy logic application in modeling rules of the so-called ‘‘approximate reasoning’’ (for example Onisawa (1990) states: ‘‘If the quality of maintenance is good, then equipment reliability is high’’; and ‘‘If the quality of maintenance is bad, then equipment reliability is low’’). However, the approach based on fuzzy logic and decision making under uncertainty is very logical and fully convenient. When we refer to operations and maintenance, special difficulties arise from the fact that some data are insufficiently precise or uncertain. Such data are often very important for management decision making and must not be disregarded. In this paper, uncertainty is treated under the fuzzy set theory. In other words, along with the well-known application of fuzzy logic in ES bases of rules for accessing knowledge from knowledge bases, this paper points to the possibility of feeding verbal expressions and observations about the state of the equipments and the history of failures into IS databases. These observations are noted in operation and maintenance documents by drivers, controllers, maintenance workers and other persons. Such verbal expressions, which cannot be explicitly analyzed or statistically expressed, are herein quantified and used in decision making.

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5. Prioritizing equipments using fuzzy rules Since time and resources are scarce, experts in large factories prioritize equipments to repair or replace. But when ask them to explain how they prioritize equipments; they answer with impersipcuous and vague terms. In fact, they are not able to express their knowledge and experiences with crisp and precise sentences or formulas. Some data in maintenance database are also insufficiently precise or uncertain. Therefore, if you are to extract rules of prioritizing, need to apply a technique to model linguistic rules and imprecise data. As shown later, one of these techniques is if-then fuzzy rule. These rules comprise the knowledge base of the fuzzy inference module. A single fuzzy if-then rule assumes the form: If x is A then y is B (z), Where A and B are linguistic values defined by fuzzy sets on the ranges (universes of discourse) x and y, respectively. The if-part of the rule ‘‘x is A’’ is called the antecedent or premise, while the then-part of the rule ‘‘y is B’’ is called the consequent or conclusion. It must be noted that the antecedent is an interpretation that returns a single number between 0 and 1, whereas the consequent is an assignment that assigns the entire fuzzy set B to the output variable y. The number (z) in the parentheses above represents a weight factor between 0 and 1 that can be applied to the rule if desired. The weights are used to describe the uncertainty of expert’s assessment on the rules. In this paper, for simplifying, the weights of the rules assumed as 1. All the rules that have any truth in their antecedent will ‘‘fire’’ and contribute to the fuzzy conclusion set. If the antecedent is true to some degree of membership, the consequent is also true to that same degree. This point leads a natural way to combine multiple qualitative assessments (Zafiropoulos & Dialynas, 2005). The fuzzy inference uses the method of min–max implication–aggregation inference. The defuzzification of the output is made using the center of area method. The process of fuzzification, inference and defuzzification is demonstrated in Fig. 2 by using a generic example with two inputs and a single output. Three rules (1–3) are fired applying nine membership functions (A1–A3, B1–B3, C1–C3) while (z1), (z2) and (z3) are the weight factors for these three rules. The process has the following five stages where the inputs are x and y (x and y are crisp values): (1) Fuzzification of inputs: • Fuzzification of the variables in rule 1 results in: A1(x), B1(y); • Fuzzification of the variables in rule 2 results in: A2(x), B2(y); • Fuzzification of the variables in rule 3 results in: A3(x), B3(y). (2) Application of fuzzy operation (and = min, or = max): • Fuzzy operation for rule 1 is: max (A1(x), B1(y)); • Fuzzy operation for rule 2 is: min (A2(x), B2(y)); • Fuzzy operation for rule 3 is: max (A3(x), B3(y)).

A1

B1

1)

C1 IF X=A1 OR Y=B1 THEN Z=C1

2)

A2

B2

IF X=A2 OR Y=B2 THEN Z=C2

3)

A3

B3

C2

C3

IF X=A3 OR Y=B3 THEN Z=C3

COA

Fig. 2. Generic example of fuzzy inference process (Zafiropoulos & Dialynas, 2005).

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(3) Application of implication method (min): • Implication for rule 1 is: C1 = min (C1(max (A1(x), B1(y)))); • Implication for rule 2 is: C2 = min (C2(min (A2(x), B2(y)))); • Implication for rule 3 is: C3 = min (C3(max (A3(x), B3(y)))); (4) Application of aggregation method (max). The result of the aggregation method is the area E = max(z1 · C1, z2 · C2, z3 · C3). (5) Application of defuzzification (the center of area COA). The result of the defuzzification is the center of the area E which is calculated as: R EðxÞxdx C¼ R EðxÞdx In this paper, a fuzzy system has been applied for prioritizing PM activities. This work is more important for a factory with limited resources that preventive activities must be prioritized. To prioritize equipments for PM activities, we identified six criteria through interviews with PM experts in a factory. These criterions are following as: • Sensitivity of Operation (SO): that is degree of critically of an equipment operation in the production line that may led to bottleneck, it can consider production costs, opportunity costs of stopped production and so on. • Mean Time between Failures (MTBF): is equal to sum of the working time of given equipment divide on sum of the failures. • Mean Time to Repair (MTTR): is equal to sum of the down time of given equipment divide on working time. • Availability of Required Parts (ARPa): that can be defined as mean of time between requesting and receiving parts for repair activities on given equipment. Note: The greater ratio causes to decrease priority of equipment for preventive maintenance. • Availability of Repair Personnel (ARPe): that can be defined as repair personnel ratio where; repair personnel ratio is total time of repair personnel to total time of personnel. Note: The greater ratio causes to decrease priority of equipment for preventive maintenance. • Work Load (WL): is considered as; Work Load = actual capacity of equipment in the last duration/length of equipment work time in the last duration * nominal daily capacity of equipment. The first step in this process (using fuzzy rules) is fuzzification of the variables. In this step, the variables are changed to linguistic variables. In this case, the variables’ values are defined as high, medium and low regard to given values to variables. Membership functions are determined from experts’ point of views about type of the variables (Figs. 3–9). Using direct approach and based on experts explanations about variables, triangular and trapezoidal membership functions are used to represent the fuzzy variables. The overlaps between adjacent membership functions allow for a smooth interpolation of the inputs across membership functions. This approach is more qualitative, flexible and interactive in respect of indirect approach that rules are extracted from data via tools like clustering, neural network. Furthermore, the qualitative assessment of the variable type can be expressed more effectively. Meanwhile, in this case like many other factories, maintenance database was unreliable that forced to use direct approach and knowledge extraction from experts. In Table 1, the values of defined variables (criterions) and their related membership functions are depicted. The assigned values are the average of values which experts assigned to. Based on values which depicted in Table 1, a fuzzy rule base was developed that includes rules such as:

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Fig. 3. MF of Sensitivity of Operation.

Fig. 4. MF of MTBF.

Fig. 5. MF of MTTR.

If (Sensitivity of Operation is High) and (MTBF is Medium) and (MTTR is Medium) and (Availability of Required Parts is Low) and (Availability of Repair Personnel is Low) and (Work Load is Medium) then (Priority is Medium). Based on above information about six instance equipments in the factory, 48 rules were extracted; these rules are ones that membership functions of their all variables have a value more than 0. Among them, there are 16 similar rules contains 8 pairs of rules (similar rules have same number in the right column of Table 2). Then, the validity of rules is calculated as: ValidityðRulei Þ ¼

6 Y j¼1

MF ðvariablej Þ

A. Khanlari et al. / Computers & Industrial Engineering 54 (2008) 169–184

Fig. 6. MF of Availability of Required Parts.

Fig. 7. MF of Availability of Repair Personnel.

Fig. 8. MF of Work Load.

Fig. 9. MF of priority (output).

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Table 1 Variables’ values of per equipment Criteria

Equip1

Equip2

Equip3

Equip4

2.5 0.5 0.5 0

1 0 0 1

MTBF High Medium Low

8 0 1 0

7 0 0.5 0.5

9 0 1 0

MTTR High Medium Low

1 0 0.77 0

1.3 0 0.875 0

1.2 0 1 0

1.9 0.36 0.13 0

0.25 0 0 1

Availability of Required Parts High Medium Low

1.5 0 0 0.33

1.8 0 0.3 0.3

0.25 0 0 0.88

0.5 0 0 0.77

7 1 0 0

12 1 0 0

Availability of Repair Personnel High Medium Low

0.25 0 0 0.88

1.5 0 0 0.33

8 1 0 0

13 1 0 0

9 1 0 0

10 1 0 0

33 0 0.42 0.42

5 0 0 1

18 0 0 1

70 0.5 0.5 0

45 0 1 0

Priority High Medium Low

11.19 0 0.865 0.135

10.25 0 0.72 0.28

15 0 0 1 9.65 0 0.61 0.39

10 0 1 0

9.42 0 0.57 0.43

0.75 0 0 0.75

Equip6

3.5 0.5 0.5 0

Work Load High Medium Low

1.5 0 0.5 0.5

Equip5

Sensitivity of Operation High Medium Low

13 1 0 0

7.75 0 0.29 0.71

1.5 0 0.5 0.5 16 1 0 0 0.1 0 0 1

8.5 0 0.42 0.58

The validities of similar rules are summed and considered as a single validity. For example, as depicted in following table (Table 3), since rules 3 and 11 are similar, the validities summed and represented only in rule 3. When the validities calculated, the resulted rule base used to apply for an instance that contains three equipments. In the next step, the membership functions of these equipments calculated based on the values which experts assigned to the variables (Table 4). The extracted data fired 16 rules that are mentioned in Table 5. Intersection between membership function of inputs calculated with min operator. IntersectionðRulei Þ ¼ minðMF ij Þ i ¼ 1; 2; . . . ; 16 j ¼ 1; . . . ; 6

In the next step, the intersection results multiplied by the rules validities that depicted in the Correctness Degree column of Table 5. And finally in the last step, priority results of fired rules aggregated using max operator (Table 6). For example, in case equipment 1, aggregation of medium priority considered as follows: max(0.0048, 0192) = 0.0192. After normalization of the obtained results (the right column of each equipment result in Table 6), the priorities of equipments calculated as:

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Table 2 Extracted rules Equipment

Rule/criteria

SO

MTBF

MTTR

ARPa

ARPe

WL

P (output)

Similar rules

Equipment 1

Rule Rule Rule Rule Rule Rule Rule Rule

1 2 3 4 5 6 7 8

H H H H M M M M

M M M M M M M M

M M M M M M M M

L L L L L L L L

L L L L L L L L

H H M M M M H H

M L M L M L M L

1 2 3 4

Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

H H H H M L M M H H H H M L M M

L L M M L M M M L L M M L M M M

M M M M M M M M M M M M M M M M

L M L M L M M L L M L M L M M L

L L L L L L L L L L L L L L L L

M M M M M M M M M M M M M M M M

M M M M M M M M L L L L L L L L

Equipment 2

Equipment 3

Rule 25 Rule 26

L L

M M

M M

L L

H H

L L

M L

Equipment 4

Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule

L L L L M M M M L L L L M M M M

M M M M M M M M M M M M M M M M

H H M M H H M M H H M M H H M M

H L L L L L L L H L L L L L L L

H H H H H H H H H H H H H H H H

L M L M L M L M L M L M L M L M

L L L L L L L L M M M M M M M M

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

1

3

2

4 5 6

6

5

Equipment 5

Rule 43 Rule 44

L L

H H

L L

H H

H H

L L

M L

7 8

Equipment 6

Rule Rule Rule Rule

L M L M

H H H H

L L L L

H H H H

H H H H

L L L L

M M L L

7

45 46 47 48

H, high, M, medium, L, low.

PriorityðEquipi Þ ¼

3 X

NVij  MeanðMF J Þ

j¼1

NV, normalized value of priority (output)

8

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Table 3 Calculated rules validities Rules

Equip1

Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule Rule

0.048 0.008 0.048 0.008 0.048 0.068

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.048

0.068

Equip2

Equip3

Equip4

Equip5

Equip6

Validity

0.21 0.29 0.21 0.29

0.048 0.008 0.064 0.014 0.048 0.068 0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.054 0.006 0.006 0.006 0.006 0.006 0.006 0.552 0.417 0.025 0.025 0.009 0.025 0.025 0.009 0.009 0.033 0.033 0.012 0.033 0.033 0.012 0.012 0.428 0.823 0.21 0.29

0.016 0.006

0.016 0.016 0.016 0.016 0.016 0.016 0.016 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.54 0.34

0.012 0.009 0.025 0.025 0.009 0.025 0.025 0.009 0.009 0.033 0.033 0.012 0.033 0.033 0.012 0.012 0.218 0.533

PriorityðEquip1Þ ¼ 0:979  12 þ 0:021  6 ¼ 11:874 PriorityðEquip2Þ ¼ 0:613  12 þ 0:387  6 ¼ 9:678 PriorityðEquip3Þ ¼ 0:42  12 þ 0:58  6 ¼ 8:52 According to calculations, equipment 1, equipment 2 and equipment 3 got the first, second and third priority, respectively. Therefore, PM activities should be performed based on these obtained priorities. For more confidence to approach results, the priorities presented to PM experts of given factory and they approved such priorities. 6. Conclusions and limitations Prioritizing equipments for PM activities regarded to scarce resources in organizations is essential. As mentioned earlier, when we refer to operations and maintenance, special difficulties arise from the fact that some data are insufficiently precise or uncertain. Such data are often very important for management decision mak-

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Table 4 Variables’ values for test Equipments Criteria

Equip1

Equip2

Equip3

Sensitivity of Operation High Medium Low

3.2 1 0 0

1.5 0 0.5 0.5

MTBF High Medium Low

9 0 1 0

9.7 0 1 0

MTTR High Medium Low

1.2 0 1 0

1.3 0 .875 0

0.1 0 0 1

Availability of Required Parts High Medium Low

1.8 0 0.3 0.3

0.25 0 0 0.88

6 1 0 0

Availability of Repair Personnel High Medium Low

1.5 0 0 0.33

7 1 0 0

5.5 1 0 0

Work Load High Medium Low

43 0 1 0

33 0 0.42 0.42

1.8 0 0.75 0.25 13 1 0 0

2 0 0 1

ing and must not be disregarded. We may conclude that fuzzy rules provide very convenient tools for analyzing maintenance and understanding procedures of decision making under uncertainty and vagueness. The approach suggested in this paper gives a possible solution to maintenance planning problems in the area of prioritizing equipments for PM activities. This approach systematically formulates expert’s knowledge about equipments prioritizing. In this paper for implementing this approach in a real world case, prioritizing rules extracted through interview with PM experts of a factory and gathering data about six sample equipments. After processing gathered data, three sample equipments prioritized based on six PM criterions which have been used in extracted rules. Then for more confidence, priority results presented to PM experts of given factory and they approved such priorities. As shown, with regard to mentioned problems, prioritizing using this approach will be more systematic and precise and in consideration of its ease of use and efficiency, it can also be used for prioritizing much more equipments and maintenance criteria in the real world. But in spite of this contribution, knowledge acquisition via this approach may be a slow process with much iteration (for verification and learning purposes). The process is expensive and even unreliable because the experts may find it difficult to contribute their knowledge via the knowledge engineer. This approach has some other important problems which are the identification of aware experts, difficulties in verbalizing knowledge and providing irrelevant, incomplete, inconsistent and incorrect knowledge. However, knowledge engineer must be able and willing to commit a substantial amount of time to knowledge acquisition and validation of extracted knowledge. Furthermore, the number of selected equipments in given factory was limited, fuzzy operators were also simplified; intersection, aggregation and defuzzification methods were the simplest methods which can compare with other methods. But despite all these limitations, the information provided in this paper is significant in that it gives researchers and practitioners a better understanding of PM scheduling especially in determining priorities.

182

Equip1

Equip2

Equip3

Sensitivity of Operation

MTBF

High

Med

1

Med

0.5

Low

0.5

Med

0.75

Low

0.25

Med

High

MTTR 1

1

1

Med

Med

Low

1

0.875

1

Availability of Required Parts

Availability of Repair Personnel

Work Load

Intersection (min)

Priority

Validity

Correctness Degree

Med

0.3

Low

0.33

Med

1

Low

0.3

0.3 0.3 0.3 0.3

M L M L

0.016 0.006 0.064 0.014

0.0048 0.0018 0.0192 0.0042

Low

0.88

High

1

Med

0.42

Low

0.42

0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42

M L M L M L M L

0.012 0.009 0.012 0.009 0.012 0.009 0.552 0.349

0.00504 0.00378 0.00504 0.00378 0.00504 0.00378 0.23184 0.14658

Low

1

0.75 0.75 0.25 0.25

M L M L

0.21 0.29 0.428 0.823

0.1575 0.2175 0.107 0.20575

High

1

High

1

A. Khanlari et al. / Computers & Industrial Engineering 54 (2008) 169–184

Table 5 Intersection and correctness of rules

A. Khanlari et al. / Computers & Industrial Engineering 54 (2008) 169–184

183

Table 6 Aggregation results Priority

Equip1

Normalized

Equip2

Normalized

Equip3

Normalized

High Med Low Sum

0 0.192 0.0042 0.1962

0 0.979 0.021 1

0 0.23184 0.14658 0.37842

0 0.613 0.387 1

0 0.1575 0.2175 0.3750

0.42 0.58 1

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