PERFORMANCE MEASUREMENT OF OEE USING DATA ENVELOPMENT ANALYSIS (DEA) Muhamad Arifpin Mansor 1 and Ario Ohsato 2

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1 National Conference in Mechanical Engineering Reearch and Potgraduate Student (1 t NCMER 2010) MAY 2010, FKM Conference Hall, UMP, Kuantan, Pahang, Malayia; pp ISBN: (CD ROM); Editor: M.M. Rahan, M.M. Noor and K. Kadirgaa Univeriti Malayia Pahang PERFORMANCE MEASUREMENT OF OEE USING DATA ENVELOPMENT ANALYSIS (DEA) Muhaad Arifpin Manor 1 and Ario Ohato 2 1 Faculty of Mechanical Engineering, Univeriti Malayia Pahang Pekan, Pahang, Malayia 2 Departent of Inforation Science and Control Engineering Nagaoka Univerity of Technology Kaitoioka , Nagaoka , Japan ABSTRACT Buine procee uch a aintenance do the ae or iilar thing day after day and for that reaon, their perforance ut be eaured on a regular bai. Meaure of perforance are needed in order to deterine the productivity and the efficiency of an organization. Perforance eaureent alo play an iportant role in identifying and tracking progre againt organizational goal. Data Envelopent Analyi (DEA) i one of the excellent tool to eaure efficiency of buine procee and DEA ha been widely applied to perfor efficiency analyi in any ector. Keyword: Perforance eaureent, Overall Equipent Effectivene, Data Envelopent Analyi INTRODUCTION Every buine activity i a production proce and an organization i a coplex et of procee with ultiple input, production procee, output, and cutoer. Buine procee are uch like achine; they do the ae or iilar thing day after day and for that reaon, their perforance ut be eaured on a regular bai. Meauring work input and product output i neceary to deterine the work capacity and productivity of a proce. Meaure of perforance have been ued by anageent for centurie to review current operational capabilitie uch a departental and corporate perforance, a well a trend perforance achieved baed on organizational plan. Thee eaure are needed in order to deterine not only if reource and cot have been anaged accurately baed on achieved production and to deterine whether the aet or plant reain in good health.. Perforance eaureent alo play an iportant role in identifying and tracking progre againt organizational goal a well a to identifying opportunitie for iproveent (U.K Departent of Trade and Indutry, 2006). One of the excellent tool to eaure efficiency of buine procee i Data Envelopent Analyi (DEA). DEA ha been widely applied to perfor efficiency analyi in any ector including bank, univerity, hotel, power plant, and hopital etc (Schaffnit, Roen, Paradi, 1997; Petana Barro, 2005; Johne, 2006; Soerguter- Reichann, 2006; Balleteroa & Maldonado, 2004; Cooka & Green, 2005). DEA i a technique of analyzing the efficiency of the organization uing linear prograing. In DEA, the organization under tudy i called the DMU (Deciion Making unit). DMU refer to the collection of private fir, non-profit organization, departent, adinitrative unit, and group with the ae (or iilar) goal, function, tandard 65

2 Perforance Meaureent of OEE uing Data Envelopent Analyi (DEA) and arket egent. A DMU i regarded a the entity reponible for converting input into output and DEA eaure the efficiency of the converion proce. Rather than the conventional one input to one output, DEA evaluate ultiple input and ultiple output yte on the bai of what i ot excellent in the efficiency value. The DMU i ot efficient if the efficiency obtain a core of one and i inefficient if the core i le than one. Therefore, for every DEA calculation, the objective i to axiize the value of the efficiency. Meanwhile, Overall Equipent Effectivene (OEE) i a key eaureent of TPM. It indicate how effective the achine are running. OEE break the perforance of a achine into three eparate but eaurable coponent: Perforance Rate (PR), Quality Rate (QR) and Availability (A). Tracking OEE regularly can pot the pattern and influence that caue proble for the achine. Furtherore, eauring OEE can how u the reult of our effort to help the achine perfor better. (The productivity Developent Tea, 2004). Thi paper applie DEA to eaure the efficiency of eaurable coponent of OEE for the activity that had been conducted in ix period. The objective of thi paper are to oberve perforance trend of the activity over tie equence and to deterine the bet perforing period. Thi paper i organized a follow; Section two decribe the general knowledge about Data Envelopent Analyi. Section three applie DEA to eaure the efficiency of eaurable coponent of OEE in ix period. Finally, we conclude our work in ection four. DATA ENVELOPMENT ANAYSIS DEA i a technique of analyzing the efficiency of the organization uing linear prograing. Let, j : nuber of DMU being copared in the DEA analyi DMUj : DMU nuber j DMU 0 : target DMU θ: efficiency rating of the DMU being evaluated by DEA y rj : aount of output r ued by DMU j xij : aount of input i ued by DMUj i : nuber of input ued by the DMU r : nuber of output generated by the DMU : coefficient or weight aigned by DEA to output r : coefficient or weight aigned by DEA to input i where, j=1,2,..,n, r=1,2,,, i=1,2,, The DEA efficiency eaure for a DMU j i given by a ratio of weighted u of output to weighted u of input: j = r1 i 1 y rj x ij (1) 66

3 Muhaad Arifpin Manor and Ario Ohato Forally, the DEA efficiency eaure for a target DMU 0 i forulized by the following fractional prograing. ax o = r 1 i 1 y ro x io (2) ubject to r 1 i 1 y rj x ij 1 (j=1,...n) u 1,u 2,...,u 0, v 1,v 2,...,v 0 Replace above fractional prograing by the following linear prograing, ubject to i1 x io =1 y rj x ij 0, j 1,2,...,n r1 i1 0, r 1,2,..., 0, i 1,2,..., Max (= y ro ) (3) A dual proble for above linear prograing i forulated a, ubject to n o x io x ij j i 0, j 1 n y rj j 1 y ro j r 0 r1 Min o = o r i (4) j 0, r 0 (r 1,2,...,), i 0 (i 1,2,...,) where i a non-archiedean that i defined to be aller than real poitive nuber while i and r are the input and output lack, repectively. 67

4 Perforance Meaureent of OEE uing Data Envelopent Analyi (DEA) Window Analyi A DEA window analyi work on the principle of oving average (Charne et al.,1994; Yue,1992). And i ueful to detect perforance trend of a unit over tie. Each unit in a different period i treated a if it wa a different unit. In doing o, the perforance of a unit in a particular period i contrated with it own perforance in the other period in addition to the perforance of other unit. In thi ethod, conider N DMU (n=1,...,n) which are oberved in T period (t=1,...,t) and which all ue r input to produce output. The aple thu ha N X T obervation. The whole et of tie period, T, i divided into window or ub period. DMU whereby the width of each window, p, i alway equal. In the firt aeent, the window conit of n DMU within the tie period of (1,...,p). The econd window then ha period of (2,...,p+1) and thi goe on to the lat period (T-p+1,...,T). PERFORMANCE MEASUREMENT OF OEE USING DEA Manor et.al., (2008) propoed a general odel of DEA to eaure aintenance activity perforance by identified the general input and output baed on typical input for production yte and TPM eaureent indice. Thi odel could eaure aintenance perforance in aggregate becaue the odel include all the coniderable reource (input) ued in aintenance activitie againt all the coniderable outcoe (output) but require any data and take real effort and tie and cot for all and ediu enterprie. Therefore, in thi paper, we ue a iplet odel for aintenance; A odel with nuber of aintenance peronnel, aintenance cot and nuber of achine a the input data and quality rate (QR), availability (A), and perforance rate (PR) a the output. Aued that the are no change for input, we ued 1 ad the duy input and the value for the output i hown in Table 1. Table 1: Input and output data i/o data (I)reource (O)QR (O) A (O)PR Period t t t t t t We calculated the data in Table 1 uing Window analyi with the length of window i 2 and the reult i hown in Table 2. Next, we eaure the efficiency of the ae data in Table 1 to deterine the bet-perforing period uing CCR odel, the ot baic for of the DEA. We treated data for each period a an independent DMU, for exaple, t1 a DMU1, t2 a DMU2 and o on. The eaured reult i illutrated in graph a hown in Figure 3. 68

5 Muhaad Arifpin Manor and Ario Ohato Table 2: Reult t 1 t2 t3 t4 t5 t6 Average through window Average by ter Variation through Window t1-t2 t2-t3 t3-t4 t4-t5 t5-t6 Figure 1: Variation through Window Variation by Ter t1 t2 t3 t4 t5 t6 Figure 2: Variation by ter Table 3. Score and rank for each DMU DMU Score Rank t t t t t

6 Perforance Meaureent of OEE uing Data Envelopent Analyi (DEA) t6 1 1 Score t6 t5 t4 DMU t3 t2 t Efficiency Figure 3: Score for each DMU CONCLUSIONS AND DISCUSSION Figure 1 and Figure 2 how the trend of perforance where the efficiency of the activity wa not contant. Figure 3 indicate that t5 and t6 are the bet-perforing period while the efficiency of the activity in t 2 wa decreaed fro t 1 but keep increaing fro t 3. The anageent could thi inforation to invetigate why t 2 wa le efficient in coparing with the other. We have preented how enterprie can ue DEA ethod to eaure or evaluate their aintenance activitie a additional eaureent ethod to OEE. In thi aeent, the input and output are the ot iportant paraeter in aeing the organization though the identification of the input and output i a difficult a it i crucial. Without proper data, thi ethod could not be applied and it will take a certain period to anage and identify the neceary data if our data are not well anaged. The efficiency of the entire organization can be aeed eaily by certain indice uch a yearly profit but quite difficult for the efficiency of part of organization. However, the efficiency of certain part or function of organization uch a aintenance will alo contribute to the efficiency of an entire organization. Therefore, the efficiency of certain part or function of an organization i oething that we cannot ignore. DEA i aid to be coparative or relative efficiency eaureent becaue it require reference to oe other et of unit to copare againt. Selection of reference et i another iportant deciion that anager hould aware and taken into account. Thi ight be the firt thing that hould be decided before proceed with the ret of the tak. Reult obtained fro thi aeent ay be ued to undertand the tendency of proce and derive ueful inforation that ay help the organization to ake further iproveent in efficiency. We believed that the reaon why DEA i not popular in aintenance area are becaue due to difficulty to identify the input and output and lack of data to copare with. 70

7 Muhaad Arifpin Manor and Ario Ohato REFERENCES Balleteroa, E., Maldonado, J.A, (2004), Objective eaureent of efficiency: applying ingle price odel to rank hopital activitie, Coputer & Operation Reearch, 31, pp Barro, C.P., (2005), Meauring efficiency in the hotel ector, Annal of Touri Reearch, vol.32, no.2, pp Charne, A., Cooper, W. W., Lewin, A. Y., and Seiford, L. M., (1994), Data Envelopent Analyi: Theory, Methodology, and Application, Kluwer Acadeic Publiher, Boton. Cooka, W.D., Green, R.H., (2005), Evaluating power plant efficiency: a hierarchical odel, Coputer & Operation Reearch 32, pp Johne, 2006; Manor, M.A., Ohato A., Muhaad W.M.W., (2008), A Fraework For Maintenance Perforance Bencharking Uing Data Envelopent Analyi, The Proceeding Of The Second Engineering Conference Kuching, Sarawak, Malayia, pp Reichann, G., Soerguter-Reichann, M., (2006), Univerity library bencharking: An international coparion uing DEA, International Journal of Production Econoic 100, pp Schaffni,C., Roen,D., Paradi,J.C., (1997), Bet practice analyi of bank branche: An application of DEA in a large canadian bank, European Journal of operational reearch 98, pp United Kingdo Departent of trade and Indutry, (2006), acceed on July