THE CUSUM VERSUS MCUSUM MODIFIED CONTROL CHARTS WHEN APPLIED ON DIESEL ENGINES PARAMETERS CONTROL

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1 Proceedings of he 6h Inernaional Conference on Mechanics and Maerials in Design, Ediors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 PAPER REF: 5649 THE CUSUM VERSUS MCUSUM MODIFIED CONTROL CHARTS WHEN APPLIED ON DIESEL ENGINES PARAMETERS CONTROL Suzana Lampreia 1(), Rui Parreira 1,2, José Requeijo 3, Vior Lobo 1,2 1 Cenro de Invesigação Naval (CINAV), Porugal 2 Poruguese Naval Academy, Lisbon, Porugal 3 Faculy of Science and Technology of he Universidade Nova of Lisbon, Porugal () suzanalampreia@gmail.com ABSTRACT The equipmen condiion monioring has been developed in order o improve he equipmen performance, obaining more availabiliy wih less immobiliy beween operaional cycles. The online equipmen condiion monioring allied o saisical echniques can widely conribue o a lean mainenance managemen. Some sudies had demonsrae ha CUSUM and MCUSUM conrol chars can be applied on equipmen condiion monioring. In his aricle we will demonsrae he applicaion of boh modified chars o funcioning parameers of a diesel engine. And will idenify he consrains of is applicaion. The basis parameers were obained from an engine wih a good performance, so i will be use o define he char mean and sandard deviaion in phase 1. In phase 2 he daa will be simulaed. Alhough he applicaion of he CUSUM and MCUSUM char when in pracice i is applied, he implemened saisical sysem mus be flexible and i should be considered in which sage of he cycle he equipmen are and he characerisics of he parameers mus be well known. Keywords: Conrol Chars, Cumulaive Sum, Condiion Monioring. INTRODUCTION The use of saisical conrol in equipmen s monioring may conribue o he implemenaion of equipmen s lean mainenance managemen, allowing he advance or delay he decision of a mainenance inervenion. The CUSUM chars shows higher sensiiviy han he radiional chars (Pereira & Requeijo, 2012). I will be considered wo phases in he implemenaion of he chars. In phase 1 he radiional chars are used, and in he phase 2 he modified CUSUM and MCUSUM are implemen o parameers equipmen. In he phase 2 he daa is simulaed demonsraing he online parameers monioring. I will be possible o observe he difference of sensibiliy beween hem. The opimizaion of he CUSUM conrol chars should be full considered (Wu e al, 2009) wih he equipmen cycle evoluion. Phase 1 Because of variables characerisics, in his sudy only he chars o independen daa would be invesigaed. For more deails Pereira & Requeijo (2012) should be consuled

2 Symposium_9 Sysemaic Innovaion and Lean Approach in Engineering Univariae Chars X and MR Chars In phase 1 he X and MR char will be used o define he equipmen parameers. The chars analysis should reveal equipmen s under saisical conrol. The chars inerpreaion is based on evenual random paerns (Norma ISO 8258:1991), considering he daa independen and Normal. The under conrol limi (UCL), he lower conrol limi (LCL) and he cenral line (CL) are calculaed by he equaions on Table 1: Table 1 Shewhar chars phase 1 Cara LIC LC LSC X (individual X observaion) d2 3MR X 3MR X+ d 2 MR (moving range) D 3 MR MR D 4 MR The X and MR in able 1 are calculaed based on he m (or m 1) sample saisics calculaed from: X = m i= 1 X i m m 1 i= 1 e = MR i ( m 1) MR, where MR i = X i X i 1. If he resuls shows an under conrol equipmen, he parameers are esimaed by ˆ = σ MR d 2. The consans 3 µˆ = X and D, D 4 and d 2 depend exclusively from he sample dimension. Mulivariae Char - T 2 Tradiional Conrol Chars T 2 chars are applied when he number of variables is greaer han one. If he observaions of p variables in conrol are independen, we have, X ij = µ j+ εij where X ij is he observaion i for variable j, µ j is he process mean for he variable j, and are iid normal random variables wih mean zero and sandard deviaion (whie noise). The mean vecor ( X ) and he covariance marix (S) are calculaed using daa from phase 1, and are respecively given by: =,,, and = (1) The T 2 conrol chars for each k, are based on he saisic: 2 ( ) ( ) T 1 T X k X S ( X k X) k = (2)

3 Proceedings of he 6h Inernaional Conference on Mechanics and Maerials in Design, Ediors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 The LCL and he UCL o phase 1 are consan in Table 2. Table 2 - T 2 Conrol Char Limis Char LCL UCL Phase I 0 ( m 1) m 2 β α; p / 2; ( m p 1) / 2 Phase 2 - Univariae Char - Modified CUSUM Char The modified CUSUM (M-CUSUM) char is based in a saisic wih memory, because he presen saisic is based in he las observaion. (Pereira & Requeijo (2012) The modified CUSUM char is buil based on he cumulaive sum, C, and i is defined by: C (, C + ( Z k) ) ; 0 = max 0 1 C0 = (3) ( 0, ( )) T = min T + Z + k ; T 0 = 0 (4) 1 where Z ( X T ) σ ) = L, σ = σ n, =δ σ X, =δ 2 X X T = and k, L ( T L ) S S = δ 1σ, where δ 1 is a consan. In his equaion X is he mean of he sample, T L is he maximum value defined by he equipmen fabrican, σ is he sandard deviaion from he equipmen parameers, n he sample dimension, Z he Normal reduced variable referee o X, k he reference value and S he securiy facor. For he design of he modified CUSUM char, he aler level (AL) and he upper conrol level (UCL) limis are considered. The limis are calculaed based on Gan (1991), and are funcion of he ARL (Average Run Lengh) value and k. Norma Mulivariae Char - Modified MCUSUM Char When a seleced equipmen is under sudy he modified cumulaive mulivariae char should be considered for some specific variables. I will be more sensiive o lile changes and accurae on he observed equipmen parameers. The modified MCUSUM (M-MCUSUM) Char o conrol he mean vecor is represened by (Villalobos, 2005):

4 Symposium_9 Sysemaic Innovaion and Lean Approach in Engineering 1 ( ) 1/2 Y = C C ; C = 0 if For independen daa: C k C = ( C 1 + X TL) 1 ; C k (5) C (( ) 1 ( )) 1/2 1 1 > k (6) C = C + X TL C + X TL ; C 0 = 0 and k> 0 (7) The modified MCUSUM conrol chars depend eiher on he ARL InConrol value, if he values > h, where h is he conrol limi, he siuaion is ou of conrol. (Pereira & Requeijo, 2012). Y METHODOLOGY a. In phase 1 he daa is colleced considering he good funcioning of he engine. b. Considered he variables independen, normal, and checking he equipmen sabiliy, he X and MR or T 2 chars should be buil and he mean/covariance and he mean vecor/covariance marix are respecively esimaed. c. In phase 2 buil he modified CUSUM or he modified T 2 o monior he equipmen performance, and wach each sensiiviy: Esimae he Upper Conrol Limi (UCL) and he Aler Value (AL) basis on he limis from fabrican. Esablish rules for acion on he sysem. The nex are suggesed: Execue an inervenion o deec any anomalous siuaion when 4 consecuive poins above he AL are observed. Proceed o a mainenance inervenion when 2 consecuive poins above UCL are observed. RESULTS Phase 1 Univariae Chars In phase 1 for univariae sudy he radiional chars will be used (Figure 1)

5 Proceedings of he 6h Inernaional Conference on Mechanics and Maerials in Design, Ediors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 Fig. 1 Phase 1 MR Char Because he chars represens an under conrol equipmen he parameers are calculaed and X=5.76 and σ=0.16 are obained. Phase 1 - Mulivariae Char The applicaion of modified T 2 char shows equipmen under conrol so he X vecor, he S and S -1 marix can be calculaed: 5, , 0108 X = 564, , 18 0, , , , , , , , S= 0, , , , , , , , S 1 42, 6 0, 156 0, 009 0, 125 0, , 0 0, , 0136 = 0, , , 02 0, 001 0, 125 0, , 001 0, 02 The T 2 char shows an under conrol equipmen so he parameers can be defined. Fig. 2 - Phase 1 T 2 char

6 Symposium_9 Sysemaic Innovaion and Lean Approach in Engineering Phase 2 - Univariae Char For he modified CUSUM chars o define he conrol limis α = 1% ( ARL = 100 ) for he AL and α = 0,2% ( ARL = 500) for he UCL are considered. Considering he modified CUSUM for equipmen monioring wih =0,5σ i represens lower observaions values han for =1σ. For lower he sensiiviy is higher (Fig. 3 and Fig. 4). Fig. 3 - Phase 2 Modified CUSUM Char - 2 nd Progression ( =0,5σ) Fig. 4 - Phase 2 Modified CUSUM Char - 2 nd Progression ( =1,5σ) Mulivariae Char - Modified MCUSUM Char From zero o he second progression non observaion are regisered. Since he M- MCUSUM represens he resuls of he combinaion of various variables and on he previous observaion values, alhough he applicaion of he modified MCUSUM Char, he variables should be sudy individual

7 Proceedings of he 6h Inernaional Conference on Mechanics and Maerials in Design, Ediors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, July 2015 Fig. 5 - Phase 2 Modified MCUSUM Char - 3 rd Progression For he hird progression grea sensiiviy has been shown. CONCLUSIONS I is possible o implemen he modified CUSUM and MCUSUM conrol chars in condiion monioring. The parameers choice o be used wih he M-MCUSUM chars mus be based in is relaion. To choose he variables for mulivariae chars his sudy had considered he relaion beween hem. The M-CUSUM chars are more sensiiviy han he Shewhar chars. If he M-MCUSUM char is applied, in spie of is sensibiliy, he resuls congregae various variables, so he analysis should be made wih cauion, and individual variables sudy should be considered. I should be considered he adjusmen of he Gan abacus for he M-MCUSUM chars. The M-CUSUM and M-MCUSUM chars can probably be use in equipmen condiion monioring (Requeijo e al, 2012), alhough he implemened saisical sysems mus be flexible and be adaped according he equipmen and i s cycle. ACKNOWLEDGMENTS Poruguese Naval School and CINAV are kindly acknowledged for he use of diesel engine daabase and also for he fruiful collaboraion of he Faculy of Science and Technology from he Universidade Nova of Lisbon

8 Symposium_9 Sysemaic Innovaion and Lean Approach in Engineering REFERENCES [1]-Wu Z, Yang M, Khoo MBC, Yu FJ. Opimizaion Designs and Performance Comparison of Two CUSUM Schemes for Monioring Process Shifs in Mean and Variance in European Journal of Operaional Research. Elsevier, 2009, 205, p [2]-Pereira ZL, Requeijo J. Qualidade: Planeameno e Conrolo Esaísico de Processos (Qualiy: Planning and Saisical Process Conrol), 2012, FCT/UNL, Prefácio, Lisboa. [3]-Requeijo J, Lampreia S, Barbosa P, Dias J, Conrolo de Condição de equipamenos mecânicos por análise de vibrações com dados auocorrelacionados (Conrol provided by mechanical vibraion analysis wih auocorrelaed daa), Riscos, Segurança e Fiabilidade (Risks, Safey and Reliabiliy), 2012, Salamandra, Lisboa, 1, p [4]-Villalobos JR, Munoz L, Guierrez MA (2005). Using Fixed and Adapaive Mulivariae SPC Chars for Online SMD Assembly Monioring. Inernaional Journal of Producion Economics, Vol.95, pp [5]-Crosier RB (1988). Mulivariae Generalizaions of Cumulaive Sum Qualiy Conrol Schemes. Technomerics, 30,