THE T 2 MULTIVARIATE STATISTICAL CONTROL CHARTS CAPACITY WHEN APPLIED ON EQUIPMENTS CONTROL

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1 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 6-30 July 05 PAPER REF: 5448 THE T MULTIVARIATE STATISTICAL CONTROL CHARTS CAPACITY WHEN APPLIED ON EQUIPMENTS CONTROL Suzana Lamreia (*), Rui Parreira,, Vitor Lobo, Centro de Investigação Naval (CINAV), Lisbon, Portugal Portuguese Naval Academy, Lisbon, Portugal (*) suzanalamreia@gmail.com ABSTRACT The use of on-line monitoring on diesel engines can be decisive on critical equiment and when condition based maintenance is imlemented. A arameters database is crucial to equiment control and erformance. The monitoring of oil and fuel ressure, temerature and vibration allow the early detection of a robable failure so the technicians could decide when to do an intervention, on the right time, with the right environment and with the needed comonents and tools. The T multivariate statistics when alied on equiment control can enhance the data veracity, allowing desite the false alarms. In this aer we will wor with indeendent data, and four variables will be used. The used database has real data from a diesel engine on Phase. On Phase the data is simulated with MATLAB. This aer will aly T Modified Chart on equiment monitoring considered the data indeendence and its caacity will be tested. Keywords: Control Charts, Multivariate, Condition Maintenance, On-line Monitoring. INTRODUCTION The condition based maintenance allows the definition of a maintenance based on the equiment state. The use of on-line monitoring will allow the definition of maintenance in the resent time. The Statistical Process Control (SPC) is nown for control rocesses stability (Phaladiganon et al, 0), in this aer we roose a Statistical Equiment Control (SEC) to conduct a equiment on-line monitoring in order to define the erformance quality and now its state. The T modified control charts will have hases (Lamreia et al, 03). On hase the stabilization arameters will be verified on the hase the data with anomalies will be simulated on MATLAB. The defined variables to be study should allow the design of Modified T chart in hase (Oliveira et al, 009)), and be significant for the engine control. The caacity of the T modified chart aliance will be tested. T MODIFIED CONTROL CHARTS On hase the rocess arameters and the limits are estimated consider that the data is Normal, indeendent and the observations are individual. -83-

2 Trac_B Testing and Diagnostic In hase, the online data is monitored by Hotteling Modified T, and the control limits are calculated based on the samle number and rocess arameters estimated during hase (Pereira & Requeijo, 0). Phase - T multivariate control charts The selected variables to be monitored should contribute to a clear result in the Modified T chart in hase (Oliveira et al, 009)), and be significant for a diesel engine control. In this study the data from de diesel engine is indeendent, so only the indeendent subject will be resented. In hase, m individual observations X j ( j =,,, e =,,,m ) are collected. Based on the collected data the samle X j means, the samle variances and the samle S jh covariance s are estimated. The mean vector X, given by the equation () and the covariance matrix, given by equation (), are calculated. (Pereira & Requeijo, 0). ( ) T = () X X,X,,X S S S3 S S S S3 S.... S= S S S 3 S () Both the hase and hase uses T control charts, based on the statistic, defined for each by: ( ) ( ) T T X X S ( X X) = (3) The (LCL) and the (UCL) to the both hases are set as in Table. For more secifications Pereira & Requeijo (0) must be consulted. Table - Control limits for T charts Chart LCL UCL ( m ) Phase 0 m β α; / ; ( m ) / Phase 0 ( + )( m ) m( m ) m F α;;m -84-

3 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 6-30 July 05 Phase Modified T multivariate control charts In hase the vector X and the matrix S are calculated using the data collected in hase. The modification of T statistics is based, for each variable j, on the maximum accetable value T L. This value is calculated based on the maximum value admitted by the fabricant ( ) T, by the standard deviation and by a safety factor (assuming normal distributed L Standard data, we suggest = 3 ): ( L ) ( T ) = ( T ) σ (4) L j Standard j Then * ( ) ( ) T * T X TL S ( X TL) = (5) where * ( X TL) max ( 0; X TL) = (6) For the multivariate Modified T chart, two tyes of limits exist: Alert Level (AL), defined for α = % and the Uer Control Limit (UCL), defined for α = 0, %, for more detail see Table j. (Lamreia et al, 03) j Caacity of T Control Charts for equiment control. The caacity analysis is based in the technical secification range and the rocess range for α = 0, 7% comarison. The otential caacity index, C, comares the technical secification range ( USL LSL ) (USL-Uer secification level, LSL-Lower secification level) with the range normally considered to the rocess disersion (6σ), given to a X normal distributed in a univariate study. (Pereira & Requeijo, 0) In a caacity multivariate study the comarison between areas, volumes or other dimensional are done, considered a multivariate normal distributed N ( µ, ). The caacity index are C M, PV and LI. The C M (7) index comares the volume between the secification and the rocess, it is a otential caacity index. -85-

4 Trac_B Testing and Diagnostic C For a rocess: ( USLi LSLi) j= M = ( UPLi LPLi) j= For an equiment: C ( USLi LSLi) j= M = ( UELi LELi) j= (7) Where: UEL i = µ i + Χ α ; det ( i ), i,,..., = and LEL i = µ i Χ α ; det ( i ), i =,,..., The PV index comares the average rocess vector, µ, with the secification nominal values of T vector. ( ) N PV = PT > F, N N (8) The statistic T is defined by: ' ' ( ˆ µ ) ( ˆ µ ) ( ) ( ) (9) T = n T T = n X T S X T The LI (0) index analyses the regions between the secifications and the rocess, verifying if the rocess region (P) are in the secification region (S), necessary condition to the rocess be caable. And is defined by: LI { P S 0 other = (0) When characteristics are analyzed, a rocess is caable if C, 33, and PV is aroximately one, and LI =. For more detail Pereira & Requeijo (0) should be consulted. The caacity of the T modified chart aliance will be tested for the chosen variables. M METHODOLOGY a. In hase the data is collected considering the good functioning of the engine. b. Considered the variables indeendent, normal, and checing the equiment stability, the T chart should be built and the mean vector and covariance matrix are estimated. c. Test the T chart Caability. d. In hase built the Modified T to monitor the equiment erformance: -86-

5 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 6-30 July 05 Estimate the Uer Control Limit (UCL) and the Alert Value (AL) basis on the limits from fabricant. Establish rules for action on the system. The next are suggested: Execute an intervention to detect any anomalous situation when 4 consecutive oints above the AL are observed. Proceed to a maintenance intervention when consecutive oints above UCL are observed. RESULTS The alication of the T Modified Multivariate Control Charts can be seen of Fig.. Where all the observations are under control, so the conditions to define the functioning arameters are establish. In the T Modified the limits are defined based on fabricants and by normative instead of the mean. The data from the engine are indeendent and it was taen from hour intervals. Phase The X vector and the S e S - matrix are: 5, 7599, 008 X = 564, 4 560, 8 0, , , 043 0, 666 0, , , , 7897 S= 0, 043 0, , 460 3, , 666 0, , , 054 S 4, 6 0, 56 0, 009 0, 5 0, 559 4, 0 0, 003 0, 036 = 0, , 003 0, 0 0, 00 0, 5 0, 036 0, 00 0, 0 Fig. - T Modified multivariate Control Chart -87-

6 Trac_B Testing and Diagnostic Caacity of T Charts For the caacity index was obtained: C M =8,446, PV=0,7393 and LI=. So we conclude that the rocess is caable because C M,33, PV obtained a result close to e LI as a value of. Phase On hase the data was simulated in MATLAB, since the engine is from an oerational latform. For the first simulation, corresonding to data without anomalies non-observation was registered. Fig. - T on first Progression For the second rogression we can see four observations above the AL, so an investigation of the state of equiment should be made. Fig. 3 - T on Second Progression -88-

7 Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 6-30 July 05 For the third rogression two oints above the UCL were detected so a maintenance action allied to other diagnosis technics should be considered. Fig. 4 - T on Third Progression CONCLUSIONS This aer had alied the T Modified Multivariate Control Charts, where the conjunction of four variables increase the sensitivity data giving an integrate result of a diesel engine erformance. This aer shows the caacity of Modified Traditional Multivariate Control Chart. The T Modified Multivariate Control Charts can detect the tendency of a diesel engine functioning arameters. The use of Statistical Equiment Control methodology can contribute to avoid unlanned stos and allows the maintenance lanning. ACKNOWLEDGMENTS Portuguese Naval School and CINAV are indly acnowledged for the use of diesel engine database. REFERENCES []-Phaladiganon P, Kim SB, Chen VC, Bae JG, Par SK. Bootstra-Based T Multivariate Control Charts in Communications in Statistics Simulation and Comutation. Taylor & Francis, 0, 40, []-Lamreia SPGFS, Dias JM, Requeijo JG, Vairinhos VM. Monitorização da condição de turbinas a gás com cartas de controlo multivariadas T (Gas Turbine Monitoring with Multivariate T Control Charts), O Proulsor, 03, 54,

8 Trac_B Testing and Diagnostic [3]-Oliveira IK, Rocha WFC, Poi RJ. Alication of near infrared sectroscoy and multivariate control charts for monitoring biodiesel blends, Analytica Chimica Acta, 009, 64,. 7-. [4]-Pereira ZL, Requeijo JG, Qualidade: Planeamento e Controlo Estatístico de Processos (Quality: Statistical Process Control and Planning), Co-edição da Fundação da FCT/UNL e da Editora Prefácio, Lisboa,