Control Charts Limits Flexibility Based on the Equipment Conditions

Transcription

1 Conrol Chars Limis Flexibiliy Based on he quipmen Condiions S. Lampreia, V. Vairinhos, V. Lobo & R. Parreira 1, Cenro de Invesigação Naval (CINAV), Alfeie, 2810 Almada, Porugal J. G. Requeijo Faculy of Science and Technology of he Universidade Nova of Lisbon, Mechanical and Indusrial ngineer Deparmen, Lisbon , Caparica, Porugal ABSTRACT: Condiion Based Mainenance became an imporan developmen in indusrial and ranspor equipmen mainenance effors. Many saisical mehodologies have been applied in his area. These mehodologies are usually applied off-line: afer he daa is colleced. We propose an online, real-ime condiion monioring sysem based on a modified conrol char, applied o engine parameers. These chars should be flexible enough and is conrol limis should reflec he equipmen sae, he manufacurer specificaions and onboard meeorological condiions. In his sudy we will develop a mehodology o specify flexible char conrol limis. The experimenal equipmen is a combined diesel or gas propulsion sysem. Two phases will be assumed. In phase 1 he equipmen and hisorical daa are analyzed, sudying hisorical daa, which leads o he definiion of equipmen parameers. In phase 2, new daa is obained by simulaion, and he xponenially Weighed Moving Average chars are applied considering flexible limis. 1. INTRODUCTION 1.1 Applying conrol chars Conrol chars may be used in conjuncion wih Remaining Useful Life (RUL) - as an indicaor of equipmen condiion - o suppor mainenance decision making. See Rawa (2013). Boh radiional or Shewar chars assume wo phases. In phase 1, daa parameers are defined and esimaed, and on phase 2 he use of special conrol chars can enhance deecion sensiiviy. Applying Saisic Process Conrol (SPC) o equipmen -Saisical quipmen Conrol (SC) i is possible o deec ou of conrol evens (Lampreia, 2013) 1.2 The imporance of limis flexibiliy Flexible conrol char limis allow chars o adap (Schaeffers, 2016) o ships new operaional areas. For example: he operaion of a propulsion diesel engine in areas wih sea waer emperaure below 14ºC is no he same as he operaion in areas wih emperaures in he inerval 15-25ºC or above 25ºC. Bu even his flexibiliy should have limis. These limis are he ones imposed by he manufacurer. 2. CONTROL CHARTS 2.1 Phase 1 - Tradiional Conrol Chars Having enough daa o esimae he process parameers, phase 1 of SPC wih Shewhar chars is implemened. The volume of daa (number of samples (m)) needed o define he parameers on phase 1 depends on he sample dimension (n). Queensberry - see (Pereira & Requeijo, 2012) suggess, as can be seen in equaion 1, ha: 400 m (1) ( n 1) For individual For a single sample, he same auhor suggess ha 300 observaions should be used. Lampreia (2013), using experimenal equipmen daa uses 200 observaions on phase. In he presen work i is shown ha 200 observaions are enough. In his aricle individual observaion () and moving range (MR) conrol chars are implemened considering coninuous and independen daa. The conrol chars analysis mus show conrolled saisical equipmen. For independen daa, phase 1 should proceed and he Shewhar or radiional conrol chars are buil. Upper conrol limi (UCL), Lower conrol limi (LCL) and Cener line (CL) for hose chars, are calculaed using he formulas on he able 1.These cal-

2 culaions, based on he m (or m 1) sample dimensions are he saisics i m m 1 i1 m i1 MR MR i m 1, where MR. i i i1 Table 1. Tradiional Conrol Chars Limis, in phase 1 of SP (Pereira e Requeijo, 2012) Char LCL CL UCL MR (moving range) 3 3 D 3 MR MR D 4 MR and If he process is sabilized - under saisical conrol -is parameers should be esimaed by μˆ and ˆ MR d2. The consans D 3, D 4 and d 2 depend exclusively on he sample dimension. (Lampreia e al, 2012) For auo correlaed/dependen daa, since we are working in condiion based mainenance, a fied saisical model for he auocorrelaion should be applied. We sugges he ARIMA (Auoregressive Inegraed Moving Average) (p, d, q) Model. The saisics from individual observaion and Moving Range conrol chars are calculaed using he fied model residues for every observaion. (Lampreia e al, 2013). simaed -sampling - Auocorrelaion Funcion (ACF) and Parial Auo-Correlaion Funcion (PACF) are compared wih (ACF) and (PACF) of known dependence paerns in order o choose a specific model. quipmen parameers follows a ARIMA (p, d, q) model if d. The model defined by ARIMA (p,d,q): d B ( B) (3) p q 2 p p B (1 1B 2B pb ) (4) 2 q B (1 B B B ) (5) B q e q (6) ( ) p 1 j ( ) j1 (7) (8) Where B is he lag operaor, is he difference operaor, d is he differeniaion order o render a saionary process, is he observaion a ime, is he whie noise a ime, ΦB is he auoregressive polynomial of order p and ΘB is he moving average polynomial of order q. Using a defined model, he residues are esimaed by e ˆ, wih ˆ expeced value for he period. For more deails Pereira and Requeijo (2012) should be consuled. 2.2 Phase 2 - Modified WMA Char In phase 2, an WMA conrol char becomes suiable for equipmen monioring if he process has a change; T L represen he limi imposed by he manufacurer. The variable ha defines he Modified WMA is he exponenially weighed variable,, defined by he equaion (2) (Crowder & Hamilon, 1992). 1 L max 0,(1 ) T, 0< 1 (2) where, n,, (Zou & Tsung, 2010) TL TL S an dard S and S 1, wih 1 as a consan. In hese equaions is he sample mean a (Serel & Moskowiz, 2008), T L he maximum or minimum admissible for each variable or parameer, he variable sandard deviaion, n he sample dimension, λ he weigh consan (0 λ 1) and s he safey facor. The Modified WMA limis are Aler Level (AL) and Upper Conrol Level (UCL) for hese chars are given by equaions (3) and (4). (Lampreia e al, 2012) AL K1 (3) UCL K (4) where 2 2 (5) K 1 and K 2 are funcions of values of λ and ARL (for AL and UCL). To define he AL and UCL Crowder (1989) abacus are used, enering wih ARL (Average Run Lengh) value and he mean change, δ, where we obain K 1 and K 2. In his sudy 1% ( ARL 100 ) will be considered o define AL and 0,2% ( ARL 500) o define UCL. 3. MTHODOLOGY Depending on equipmen characerisics, we proposed a mehodology o be applied o repairable sysems monioring. For independen daa he seps should be as follows: Collec daa. A leas 200 observaions.

3 Wih he equipmen in good performance check for daa independence and Normaliy. simae is parameers; For online equipmen monioring, build he Modified WMA chars using he online colleced values. Define he change in he parameers mean ha mus be deeced. simae AL and UCL conrol limis, considering some meeorological sandards. Fix he inervenion rules: 6 consecuive poins are above he AL - Proceed o an inspecion. 3 consecuive poins are above he UCL - Proceed o a mainenance inervenion. Figure 1. Var1 - Normaliy Sudy 4. RSULTS 4.1 Phase 1 Tradiional Conrol Chars The variables under sudy are from a Combined Diesel or Gas propulsion sysem associaed o a pich propeller (PP). See Table 2 for he meaning of variables. Beween 0 o 500 of engine rpm PP is variable; afer ha value, for more speed, only he rpm of he engine is increased. Phase 1 sars wih he sudy of 200 observaions colleced from four parameers of an engine, a consan power. This sudy includes normaliy and independence checks and parameers definiion. Table 2. Variables in Sudy OP0155 Lub Oil Pressure OP0157 Pison Cooling Oil Pressure FP0163 Fuel Oil Pressure OT0114 Lub Oil Temperaure Figure 2. Var1 - ACF The Normaliy and he independence sudy explained in his aricle is for variable number 1. For variable 1, normaliy was esed wih he Kolmogorov-Smirnov es. See Figure 1, Figure 1, 0,886 0,886 where D Críico 0,06265 for 5%, N 200 and d= 0, Once d DCríico he normaliy condiion is acceped. (Pereira e Requeijo, 2012) Figure 3. Var1 - PACF All he variables were found o be normal and independen.

4 When building radiional conrol chars some ouliers were found. To esimae he parameers, ouliers mus be excluded or replaced, using some crieria; our decision was is replacemen wih he mean beween he preceding and he nex values. Using Saisica sofware, he following resuls were obained before replacing ouliers: Figure 4. Var 4 (Lub Oil Temperaure) Individual Conrol Char - Wihou Review Figure 5. Var 4 (Lub Oil Temperaure) Moving Range Conrol Char - Wihou Review The resuls afer replacing ouliers: Table 3. Variables parameers VAR 1 VAR 2 VAR 3 VAR 4 µ 6,3529 5,9947 0, ,99 σ 9 0, ,3778 0,512 T L 5,5 5,5 0, Phase 2 Modified WMA Conrol Chars Limis Flexibiliy To sum up: we observed ha for some operaing condiions, he ship diesel propulsion parameers show considerable variabiliy, so we will consider 3 limis according sea emperaure, a a cruise speed wih maximum pich propeller and 800 engine rpm. In wha follows, specifically for he limis flexibiliy we presen Var 4 (Lub oil emperaure) sudy in more deail, wih 3 disinc T L values ( lower, normal and higher namely 80, 85 and 95ºC). For his specific parameer, he ship sensor program has an alarm. I is considered imporan o deec evenual damage on he seleced variables wih σ hree levels of variaion. To es is sensibiliy, =[0,5σ; 1σ; 1,5σ], δ=[0,5; 1; 1,5], wih α = 1% (ARL = 100) in he definiion of AL and α = 0.2% (ARL = 500) in he definiion of UCL. Using he Crowder abacus (Pereira and Requeijo, 2012), we obained λ = 0.05, λ = 0,13 and λ = 0.25, respecively, and K = 2.7, K = 2.9 and K = 3. AL and he UCL values for each variable and each σ are obained using expressions 2 and 3, Figure 6. Var 4 (Lub Oil Temperaure) Individual Conrol Char - Reviewed Because his is a real engine, no induced damage is allowed, so he parameers wih anomalies were simulaed in he MATLAB, considering 0 o 3 progressions of he anomalies of he engine, and considering he limis flexibiliy For sea mean emperaure, wih T L =85ºC, for he 2 rd progression of a possible anomaly, considering 1% ( ARL 100 ) AL and 0,2% ( ARL 500) o UCL. WMA Modified 0,350 Figure 7. Figure 4. Moving Range Var 4 (Lub Oil Temperaure) - Reviewed 0,250 0,150 0,050 Applying he same procedure o ohers variables we obained he parameers esimaions for µ and σ. See resuls on Table 3., obained again wih Saisica. UCL AL Figure 8. Var4 - T L =85ºC wih =0,5σ - 2ªProgression

5 1,400 1,200 WMA Modified WMA Modified 1,000 0,800 UCL AL Figure 9. Var4 - T L =85ºC wih =1σ - 2ªProgression UCL AL Figure 14. Var4 - T L =95ºC wih =0,5σ 3ªProgression 1,800 1,600 1,400 1,200 1,000 0,800 WMA Modified UCL AL Figure 10. Var4 - T L =85ºC wih =1,5σ - 2ªProgression Comparing he resuls for each, we fixed =0,5σ as he more suiable for he variables characerisics and resuls. Analyzing figure 4, and using he defined mehodology, we should proceed o an invesigaion acion by he 40 h observaion. Wih T L =85ºC, for he 3 rd progression of a possible anomaly, figure 11: This means ha, wih he variaion on he T L value, he resuls change. If T L decreases, he resuls decreases; wih a T L increase here is a rise in he resuling values. To change he limis, he assumed ARL and δ should change. We simulaed several values, considering only δ wih 0.5, 1, and 1.5, given he Crowder abacus design. Considering 1% ( ARL 100 ) AL and 0,2% ( ARL 2000 ) o UCL, figure 15 and 16: 0,350 0,250 0,150 WMA Modified,5 WMA Modified 0,050 UCL AL Figure 15. Var4 - T L =85ºC wih =0,5σ - 2ªProgression - UCL- ARL=2000 UCL AL Figure 11. Var4 - T L =85ºC wih =1,5σ 3ªProgression WMA Modified, In figure 11 he char shows ha engine needs an invesigaion acion afer 31h observaion. Figure 12 shows an inervenion need afer 14h observaion. UCL AL Figure 16. Var4 - T L =85ºC wih =0,5σ - 3ªProgression - UCL- ARL=2000 0,500 WMA Modified Considering 1% ( ARL 100 ) AL and 0,2% ( ARL 1000 ) o UCL, figure 17 and 18: WMA Modified UCL AL Figure 12. Var4 - T L =85ºC wih =1σ 3ªProgression If we consider T L =80ºC, all he observaions will be ou of conrol; see figure 13. If we assume T L =95ºC all he observaions are under conrol. See figure 14. 0,350 0,250 0,150 0,050 UCL AL Figure 17. Var4 - T L =85ºC wih =0,5σ - 2ªProgression - UCL- ARL=1000 WMA Modified 1,000 WMA Modified,5 0,900 0,800 0,700 0,500 UCL AL Figure 13. Var4 - T L =80ºC wih =0,5σ 3ªProgression UCL AL Figure 18. Var4 - T L =85ºC wih =0,5σ - 3ªProgression - UCL- ARL=1000 For higher ARL values, he conrol char is less sensible. Assuming navigaion wih higher sea emperaures, he ARL limi can be higher; for lower

6 emperaures ARL can be lower, always respecing he manufacurer limis. 5. CONCLUSIONS For auo correlaed daa, an ARIMA model can be used for daa modeling. For independen daa, observaions are used direcly for conrol chars equipmen monioring. The auocorrelaion model is chosen comparing he ACF and PACF wih he ACF and PACF. In phase 1 he individual observaions and moving range conrol chars are used o define he working parameers values. The parameers are defined afer chars correcion for ouliers. I s possible o monioring equipmen daa wih he Modified WMA conrol chars. The Modified WMA is more sensible han he radiional chars. The variabiliy of influences he chars sensiiviy. For higher ARL values WMA he char sensiiviy decreases. The analyzed equipmen has shown parameers under saisical conrol. Rawa, Manish, Lad, Bhupesh (2013). Condiion Based Opimal Mainenance Sraegy for Muli-Componen Sysem. hp:// 20Jan2016. Lampreia, Suzana (2013). Manuenção Baseada no sado de Condição. Uma Abordagem Uilizando Caras de Conrolo Modificadas. Tese de Douorameno, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Seembro. Schaeffers, Marc (2016). Manage conrol limis when Implemening Saisical Process Conrol. hp:// ening-saisical-process-conrol 19Jan2016. Pereira, Z. L. and Requeijo, J. G. (2012), Qualidade: Planeameno e Conrolo saísico de Processos (Qualiy: Saisical Process Conrol and Planning), FCT/UNL Foundaion dior, Lisboa. Lampreia, S., Barbosa, P., & Requeijo, J. (2012). Manuenção Condicionada Baseada na Aplicação de Caras Conrolo WMA. Congresso Ibérico de Jovens ngenheiros - CIJ2012. Braga. Lampreia, Suzana, Requeijo, José, Dias, José, Vairinhos, Valer (2013). quipmen Condiion Monioring wih an Applicaion of MWMA Conrol Chars and Ohers Chars. ICOVP2013, Seembro de 2013, Lisboa. Crowder, S. V., & Hamilon, M. D. (1992). An WMA for monioring a process sandard Deviaion,Journal of Qualiy Technology,Vol. 24, pp Zou, C., & Tsung, F. (2010). Likelihood raio-based disribuion-free WMA conrol chars. Journal of Qualiy Technology, pp Serel, D. A., & Moskowiz, H. (2008). Join economicdesign of WMA conrol chars for mean and variance, uropean Journal of Operaional Research, pp Crowder, S.V., A Simple Mehod for Sudying Run Lengh Disribuions of xponenially Weighed Moving Average, Technomerics, Vol. 29, 1989, pp RCOMNDATIONS The simulaneous use of several echniques for equipmen condiion diagnosic is recommended. Tes he four variables daa wih MWMA Chars, and use flexibiliy concep in he chars design. Developmen of sofware o allow flexibiliy in he limis of online monioring wih conrol chars is needed. RFRNCS