Abstract: In this research, a methodology was proposed to select optimum maintenance strategy. The study suggested a methodology which applied various steps. This research considered developing a list of criteria with the recognition of patterns amongst those criteria. Having developed the hierarchy structure, then the paper illustrates the use of an AHP improved by Rough set to eliminate the inconsistency commonly existing in the AHP method. A case study is used to demonstrate the application of the various steps of the proposed methodology.
INTRODUCTION
Nowadays with increasing Technology`s development and develop Industry`s automation and increase of machinery`s quantity, volume of investment in organization`s physical assets and machineries have increased significantly. One of the fundamental items for these factories is the cost of maintenance that can reach 15-70% of production costs based on type of industry (Bevilacqua and Braglia, 2000). The amount of money spent on maintenance in a selected group of companies is estimated to be about 600 billion dollars in 1989 (Chan and Law, 2005). Annual maintenance cost in comparison with turn over in some of European countries, based on survey results of European Federation of National Maintenance Societies (EFNMS) in 1990 is: Belgium 4.8, France 4, Ireland 5.1, Italy 5.1, Netherlands 5, Spain 3.6 and UK 3.7%. Furthermore, maintenance plays a key role in reliability capability, availability, products quality, risk reduction, increasing efficiency, equipment safety and etc. In this regard, maintenance and its strategies are of special importance in Industry. In this research, we will go through the five most important kinds of strategies put forward that include: corrective, preventative, opportunistic, condition-based and predictive maintenance.
Implementation costs both in terms of fixed investments and assignment of people are high; hence, we don`t want to repeat it for some time. On the other hand, there exist multiple criteria and multiple perspectives that should be considered and taken heed of in this decision making. Decision making process and judgment regarding selection of maintenance strategy are often discontinuous, complex and unstructured (Hajshirmohammadi and Wedley, 2004) and it is necessary to be considered the great number of attributes and miscellaneous factors that some of them are intangible (Bevilacqua and Braglia, 2000).
To solve this kind of problems, some multiple criteria decision approaches have been suggested. In particular, Almeida and Bohoris (1995) considered the application of decision-making theory to maintenance paying special attention to the multiple attribute utility theory. Triantaphyllou et al. (1997) suggested the use of the analytical hierarchy process considering only four maintenance criteria: cost, repairability, reliability and availability. Azadivar and Shu (1999) presented the method to select a suitable maintenance strategy for each class of systems in a just-in-time environment, exploring 16 characteristic factors that could play a role in maintenance strategy selection. Bevilacqua and Braglia (2000) presented an application of the AHP technique for maintenance strategy selection in an Italian oil refinery processing plant, combining many features which are important in the selection of the maintenance policy: economic factors, applicability and costs, safety, etc. Al-Najjar and Alsyouf (2003) and Sharma et al. (2005) assessed the most popular maintenance strategies using the fuzzy inference theory and fuzzy multiple criteria decision making evaluation methodology. Okumura and Okino (2003) showed the methods to select the most effective maintenance strategy based on different production loss and maintenance costs incurred by different maintenance strategies. Mechefske and Wang (2003) proposed a model that evaluate and select the optimum maintenance strategy and condition monitoring technique making use of fuzzy linguistics. Hajshirmohammadi and Wedley (2004) proposed a systematic model for evaluating different maintenance organizational structures with respect to the objectives of a maintenance department. This model provided step by step guidelines for the maintenance management and decision makers to go through the evaluation process. Carnero (2005) proposed a model that carries out the decision making in relation to the selection of the diagnostic techniques and instrumentation in the predictive maintenance programs. Her model used a combination of tools belonging to operation research such as analytic hierarchy process and factor analysis. Bertolini and Bevilacqua (2006) presented a goal programming approach to define the best strategies for the maintenance of critical centrifugal pumps in an oil refinery. Wang (2007) proposed a model that helps management to select optimum maintenance strategies based on a fuzzy analysis hierarchy process.
In this research, we with the help of going over expertise of experts and their relevant specialized literature try to recognize variables and effective criteria in selecting maintenance strategy. Then, by using factor analysis, we will process the data so that we can designate fundamental variables and summarize them in some factors. Then after, we will apply the results from factors analysis for nomination of criteria in a hierarchy structure. Consequently, to choose best strategy, we will evaluate and determine weight of each maintenance strategy by improving AHP with rough set theory. By using rough set theory in AHP method the qualitative judgment can be qualified to make comparison more intuitionistic and reduce or eliminate assessment bias in pairwise comparison process.
MAINTENANCE STRATEGIES
In this research, we have gone through 5 types of maintenance strategies as fellows:
Corrective maintenance: This alternative maintenance strategy is also named as fire-fighting maintenance, failure based maintenance or breakdown maintenance. When the corrective maintenance strategy is applied, maintenance is not implemented until failure occurs (Swanson, 2001). Corrective maintenance is the original maintenance strategy appeared in industry (Chan and Lau, 2005; Wang, 2007). It is considered as a feasible strategy in the cases where profit margins are large (Sharma et al., 2005). However, such a fire-fighting mode of maintenance often causes serious damage of related facilities, personnel and environment. Furthermore, increasing global competition and small profit margins have forced maintenance managers to apply more effective and reliable maintenance strategies.
Preventative maintenance: This approach is based on component reliability characteristics. This data makes it possible to analyze the behavior of the element in question and allows the maintenance engineer to define a periodic maintenance program for the machine. The preventive maintenance policy tries to determine a series of checks, replacements and/or component revisions with a frequency related to the failure rate. In other words, preventive (periodic) maintenance is effective in overcoming the problems associated with the wearing of components. It is evident that, after a check, it is not always necessary to substitute the component: maintenance is often sufficient. For performing preventive maintenance, a decision support system is needed and it is often difficult to define the most effective maintenance intervals because of lacking sufficient historical data (Mann et al., 1995). In many cases when maintenance strategies are used, most machines are maintained with a significant amount of useful life remaining (Mechefske and Wang, 2003). This often leads to unnecessary maintenance, even deterioration of machines if incorrect maintenance is implemented.
Opportunistic maintenance: The possibility of using opportunistic maintenance is determined by the nearness or concurrence of control or substitution times for different components on the same machine or plant. This type of maintenance can lead to the whole plant being shut down at set times to perform all relevant maintenance interventions at the same time. Therefore, this maintenance strategy requires coordination and support from production`s personnel.
Condition-based maintenance: Maintenance decision is made depending on the measured data from a set of sensors system when using the condition-based maintenance strategy. To date a number of monitoring techniques are already available, such as vibration monitoring, lubricating analysis and ultrasonic testing. The monitored data of equipment parameters could tell engineers whether the situation is normal, allowing the maintenance staff to implement necessary maintenance before failure occurs. This maintenance strategy is often designed for rotating and reciprocating machines, e.g. turbines, centrifugal pumps and compressors. But limitations and deficiency in data coverage and quality reduce the effectiveness and accuracy of the condition-based maintenance strategy (Alnajjar and Alsyouf, 2003).
Predictive maintenance: Unlike the condition-based maintenance policy, in predictive maintenance the acquired controlled parameters data are analyzed to find a possible temporal trend. This makes it possible to predict when the controlled quantity value will reach or exceed the threshold values. The maintenance staff will then be able to plan when, depending on the operating conditions, the component substitution or revision is really unavoidable.
MAINTENANCE STRATEGY SELECTION CRITERIA
Selection of maintenance strategy in each organization depends on many criteria. This decision especially effects on how to allocate resource, technology selection, management and organization process, etc. Hence, to select suitable strategy, it is necessary to choose this decision commensurate with fact. Studying related articles to maintenance strategies (Alnajjar and Alsyouf, 2003; Bevilacqua and Braglia, 2000; Triantaphyllou et al., 1997; Wang, 2007) and also using expertise, we have recognized key and crucial criteria for selection of maintenance strategy; recognized criteria are as follow:
| Services quality | Risk |
| Equipment`s wear and tear | Personnel training |
| Product`s defect | Environmental effects |
| Equipment`s set up time | Personnel wage |
| Customer satisfaction | Equipments and personnel efficiency |
| Personnel damages | Product`s quality |
| Software cost | Reliability |
| Hardware facilities | Hardware cost |
| Software facilities | Equipment safety |
| Skillful human resources |
In order to take a suitable and accurate decision that satisfies organization`s requirements, paying attention to above mentioned criteria is crucial and vital.
MATERIALS AND METHODS
Proposed methodology comprises 5 steps. Generally this methodology after recognizing important criteria with the help of one of multivariate analysis techniques have formed the decision tree and with the application of AHP has improved by rough set theory has assessed each maintenance strategy. These steps have been detailed as it continues.
| Step 1: | We with the help of going over expertise of experts and their relevant specialized literature try to recognize 19 variables and effective Criteria in maintenance strategy selection |
| Step 2: | Since considering all criteria for maintenance strategy selection seems to be impossible it seems to be necessary to use a dimension decreasing technique for extracting pattern and summing up criteria. In this methodology due to considering mutual relation between factors for decreasing dimensions and recognition of patterns, factor analysis has been used as one of the most applicable and suitable techniques of multivariate analysis |
| Step 3: | With regard to the essence of each group criteria placed in each factor, we have labeled recognition factors in preceding stage. Then hierarchical tree is formed |
| Step 4: | With the improvement of AHP technique, by rough set theory it would become possible to reach to consistent comparison. By using rough set theory in AHP method the qualitative judgment can be qualified to make comparison more intuitionistic and reduce or eliminate assessment bias in pair wise comparison process |
| Step 5: | In order to calculate the final score of each supplier, the weight of criteria, sub criteria and maintenance strategy`s information should be combined. |
A short description of using techniques
Factor analysis (FA): Factor analysis is a general term that
is given to a group of statistical multivariate methods which their primary
goal is to define covert structure in data. In general terms by defining
a collection of joint covert dimensions that are referred to as factors,
it analysis relations structure (correlation) amongst great volume of
variables (Thompson, 2004). The aim of FA techniques is to find the synopsis
of available data in initial quantity of variables and conversion of them
to a smaller collection of dimensions or new combination factors with
less data missing (Lattin et al., 2003).
Improved AHP using rough set theory: AHP is a well known technique to help the analysts to organize the critical aspects of a problem into a hierarchical structure for making a decision (Saaty, 1980). In this technique, the Consistency Index (CI) is used as a measure of consistency of the judgments, where Cl = (λmax-n)/ (n-1), where λmax, is the biggest eigenvalue and n is dimension of the matrix. In AHP, the pairwise comparisons in a judgment matrix are considered to be adequately consistent if the corresponding Consistency Ratio (CR) is less than 10%. If the CR value is greater than 0.10, then a re-evaluation of the pairwise comparisons is recommended (Saaty, 1980).
Rough set theory, proposed by Pawlak (1982), is a new mathematical approach to data analysis. The basic idea behind this method is the classification of objects into similar classes (clusters) to find hidden patterns in the data (Nelson and Starzyk, 2001).
For the propose of reducing subjective extent of human judgment, we propose decision table approach for obtaining more objective weights. Conditional entropy and attribute significance concepts in rough sets theory can be used in AHP to improve the judgment consistency (Xia and Wu, 2007). We consider the use of the concept of attribute significance in rough sets theory proposed by Wang (2001) to eliminate evaluation bias problem in AHP. Some important concepts used in the proposed methodology are discussed below (Xia and Wu, 2007).
Formally, a data table is the 4-tuple S = {U,R,V,f}, where U is a finite set of objects (universe); R = C∪ D is a set of attributes, subsets C and D are the condition attribute set and the decision attribute set, respectively; Vr is the domain of the attribute r, V =∪ r∈R Vr and f: UxR→ V is a total function such that f (x,r)∈Vr for each r∈R, x∈U, called information function. To every non-empty subset B of attributes R (B ⊆ R) is associated an indiscernibility relation on U, denoted by IND (B):
IND (B) = {(x, y)| (x, y)∈UxU, ∀
b∈ B, (b (x) = b (y))} |
Clearly, the indiscernibility relation defined is an equivalence relation (reflexive, symmetric and transitive). The family of all the equivalence classes of the relation IND (B) is denoted by U|IND (B).
Definition 1: Entropy H (P) of knowledge P (attributes set) is defined as
where, p (Xi) = |Xi|/|U| and p (Xi) denotes the probability of Xi when P is on the partition
X = {X1, X2, ..., Xn} of universe U, i = 1, 2, ..., n.
Definition 2: Conditional entropy H (Q|P) which knowledge Q (U|IND (Q) = {Y1, Y2, ..., Ym}) is relative to knowledge P (U|IND (P) = {X1, X2, ..., Xn}) is defined as:
where, p (Yj|Xi) is conditional probability, i = 1, 2, ..., n, j = 1, 2, ..., m.
Definition 3: Suppose that decision table S = {U, R, V, f}, R = C∪ D, subsets C and D are the condition attribute set and the decision attribute set, respectively, attribute subset A ⊂ C. The attribute significance SGF (a, A, D) of attribute a (a∈C\A) is defined as SGF (a, A, D) = H (D|A)-H (D|A∪ {a}). Given attribute subset A, the greater the value of SGF (a, A, D), the more important attribute a is for decision D.
Application of factor analysis to identify key criteria in maintenance strategy selection: Here, we have introduced key criteria for decision making regarding selection of maintenance strategies. Taking into account all 19 criteria for decision making is a complicated and high error probable process. For the application of factor analysis we need data commensurate with facts that clarify the relation between criteria. For this reason a questionnaire was prepared and 96 experts in this field were queried so that required data was obtained.
After application of FA technique on data, following results were shown in Table 1; elements of the factor loading matrix pertinent to criteria for 4 factors after rotation (based on varimax method) have shown. In this methodology for extracting factors, method of eigenvalue bigger than 1 has been used.
| Table 1: | Results of FA after rotation |
| Fig. 1: | Decision tree and selection of maintenance strategy |
After factor rotation, allocation of criterion to factor is executed with higher accuracy and less error. For example, services quality criterion will be obviously allocated to factor 2.
Selection of these 4 factors has the capability of deducing 78.8% of data. Now, we make a distinction of allocated criteria in each factor. Obtain result have been shown in Table 2. This makes it easier to label factors.
Equipment tear and ware criterion, education of personnel, software cost, installation and set up timing of equipment, Hardware cost and personnel wages, all have been allocated to factor 1. Investigating these criteria, it is understood that all of them are cost and refer to cost calculation; therefore, we have named factor 1 as cost. We further label other 3 factors, which its results culminates in naming factor 2 as value added, factor 3 as execution capability and finally factor 4 as safety.
Making hierarchy tree: We proposed results obtained from factor analysis and connection between factors and criteria to a maintenance assessment team that includes experts in this field. After defining a general goal that was selection of maintenance strategy, we tried to visualize a hierarchical structure that included criteria, sub criteria and choices related to acquiring the general goal that its results have been shown in Fig. 1.
| Table 2: | Allocation criteria to suitable factor |
Goal is selecting the best maintenance strategy that includes 4 criteria; value added (A), Cost (B), safety (C) and execution capability (D). Value added criterion includes 2 sub criteria of products quality (A1) and equipment and personnel efficiency (A2). Criterion of cost constitutes 3 sub criteria of personnel training cost (B1), hardware costs (B2) and software costs (B3). Criterion of safety constitutes 3 sub-criteria of equipment safety (C1), personnel damages (C2) and environmental effects (C3). Criterion of execution capability includes 2 sub-criteria of Human resource (D1) and equipment and technology (D2). Five options of corrective maintenance (CM), preventative maintenance (PM), opportunistic maintenance (OM), condition-based maintenance (CBM) and predictive maintenance (PdM) have been considered for selection. This hierarchical structure can tremendously help in suitable and accurate decision making for selection of maintenance strategy in organizations.
CASE STUDY
Here, an industrial unit for the selection of best maintenance strategy with regard to stated methodology earlier has been studied. This industrial unit is active in producing standard parts. Most of produced productions in this complex constitute products such as screw basic and spring nut, gasket, different kinds of metal spangles (disks) and hinges in miscellaneous sizes. In the process of production of these productions, different equipments such as lathes, die and press, CNC, welding and are used. For the time being, maintenance strategy of this unit is corrective one and activity of maintenance unit is taken place only after equipments break down. In the past, due to high profit margin and exclusivity in the market, this strategy was applied by the management.
But currently considering the huge volume of production and necessity for diminution of stopping production line and converting the market to a competitive market, necessity for altering the maintenance strategy seems to be a vital issue. Because, an appropriate maintenance strategy results in reduction of over head costs, preserving reliability level, increase of product`s quality and customer satisfaction.
Management is willing to decide new maintenance strategy without huge amount of investment. With regard to methodology of mentioned earlier, goal is choosing the best strategy from amongst 5 strategies mentioned. Considering that steps 1, 2 and 3 have been applied in prior selections, in this part we only deal with application of steps 4, 5. In step 4, for assessment of criteria with the help of improved AHP by rough set theory, the procedure is as follows: initially for each of mentioned criterion in Fig. 1, a value such as the values of 1, 2 and 3 which are associated with low, middle, high or good, middle, poor is selected. These numerical quantities of scale are chosen in consideration of essence of criteria. In Table 3, these quantities have been mentioned for different criteria.
In next stage in order to evaluate criteria, a list of their different combinations is made.
| Table 3: | Identification of scale for the criteria |
We should pay attention that necessarily all possible combinations are not considered in this list. Different combinations are definable based on approach and view point of management of each organization. For example this list mentions Value added (A), cost (B), safety (C) and execution capability (D) criteria in Table 4.
Value of 1 in decision column for each row mentions selection of that row`s conditions and value of zero shows nonacceptance of that row`s conditions by the decision maker. For example, row 17 shows that if value added, cost, safety and execution capability are good, middle, high and middle, respectively, decision maker doesn`t have any willingness for realization of these conditions and values it as zero. For finding mentioned criteria weight in Table 4. In accordance with following process, it is done based on rough set theory.
U | IND{A, B, C, D} = {{1}, {2}, {3}, {4}, {5},
.., {43}, {44}} |
U | IND{d} = {{7, 8, 15, 16, 26, 27, 28, 30,
31, 32, 33, 34, 36, 40, 41, 43, 44}, {1, 2, 3, 4, 5, 6, 9, 10, 11,
12, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 35, 37, 38,
39, 42}} = {Y1, Y2} |
U | IND{ B, C, D} = {{1, 21, 38}, {2, 22, 39},
{3, 23}, {4, 24, 40}, {5, 25, 41}, {6, 26}, {7, 27}, {8, 28}, {9,
29, 42}, {10, 30, 43}, {11, 31}, {12, 32, 44}, {13, 33}, {14}, {15,
34}, {16}, {17, 35}, {18, 36}, {19, 37}, {20}} = {X1,
X2, X3, X4, X5, ...,
X19, X20} |
U | IND{A, C, D} = {{1, 9, 17}, {2, 10, 18},
{3, 11}, {4, 12, 19}, {5, 13, 20}, {6, 14}, {7, 15}, {8, 16}, {21,
29, 35}, {22, 30, 36}, {23, 31}, {24, 32, 37}, {25, 33}, {26}, {27,
34}, {28}, {38, 42}, {39, 43}, {40, 44}, {41}} = {K1,
K2, K3, K4, K5, ...,
K19, K20} |
U | IND{A, B, D} = {{1, 4, 7}, {2, 5, 8}, {3,
6}, {9, 12, 15}, {10, 13, 16}, {11, 14}, {17, 19}, {18, 20}, {21,
24, 27}, {22, 25, 28}, {23, 26}, {29, 32, 34}, {30, 33}, {31}, {35,
37}, {36}, {38, 40}, {39, 41}, {42, 44}, {43}} = {L1,
L2, L3, L4, L5, ...,
L19, L20} |
U | IND{A, B, C} = {{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, 41}, {42, 43}, {44}} = {V1,
V2, V3, V4, V5, ...,
V19, V20} |
| Table 4: | Decision table about value added (A), cost (B), safety (C) and execution capability (D) |
After definition of above set probabilities P (Xi), P (Yj|Xi) are calculated that results have been Shown in Table 5.
As it is shown in Table 6, importance of A, B, C and D criteria are 0. 1396, 0.0805, 0.2003 and 0.0698 respectively.
If superiority of importance of choices i and j are respectively as Wi and Wj, pairwise comparison matrix for these 4 criteria is formed as below:
| Table 5: | Probability values |
| Table 6: | Calculate the attribute significance |
| Table 7: | Result of local and global weight |
With the help of eigenvector method, weight of each criterion is calculated
based on above matrix. These weights are 0.283, 0.163, 0.412 and 0.142
for A, B, C and D criteria respectively. As it was mentioned earlier improved
AHP`s specifications with the help of rough set theory, doing pairwise
comparisons are completely consistent. In order to better understand this
subject, calculation of afore mentioned consistency index matrix is done,
in this matrix λmax equals 4 and considering that
Information of each of Maintenance strategy has been shown in Table 8.
| Table 8: | Maintenance strategy`s information |
| Table 9: | Maintenance strategy`s final weight |
After normalizing information and considering global weight in them, final weight of each supplier is calculated. Obtained results from final weight of each supplier have been shown in Table 9.
Amongst these 5 strategies, predictive maintenance strategy has the most weight and corrective maintenance strategy has the least weight. As a result, predictive maintenance strategy is selected as the best strategy for this technical unit.
CONCLUSION
In this study, one method has been provided for deciding best maintenance strategy. Five kinds of most important mentioned strategies that include corrective, preventative, opportunistic, condition based and predictive have been considered in this methodology. One optimal maintenance strategy could result in reduction of unnecessary maintenance costs and promotion of reliability and availability of equipments. Evaluation of these strategies is a decision making problem in multiple condition and numerous factors are effective in decision making.
In this methodology by utilizing the combination of two techniques of factor analysis and improved analytical hierarchy process by rough set theory, firstly we try to recognize key factors from amongst effective factors and then making a hierarchy structure and evaluation of strategies. Various steps of the methodology have been demonstrated using sample examples. These examples indicate industry specific use of the methodology as well as its being simple in application. One other important feature of the method as discussed in this paper is its capability to eliminate inconsistency in AHP application. In a case study it has been mentioned that this methodology can help us effectively for selecting optimal strategy.