1. INT R OD UC T ION 1.1 Applying control charts
C ontrol charts may be used in conjunction with R e-maining Useful L ife (R UL ) - as an indicator of equipment condition - to support maintenance deci-sion making. S ee R awat (2013). B oth traditional or S hewart charts assume two phases. In phase 1, data parameters are defined and estimated, and on phase 2 the use of special control charts can enhance detec-tion sensitivity. A pplying S tatistic Process C ontrol (S PC ) to equipment -S tatistical E quipment C ontrol (S E C ) – it is possible to detect out of control events (L ampreia, 2013)
1.2 T he importance of limits flexibility
F lexible control chart limits allow charts to adapt (S chaeffers, 2016) to ships new operational areas. F or example: the operation of a propulsion diesel engine in areas with sea water temperature below 14º C is not the same as the operation in areas with temperatures in the interval 15-25º C or above 25º C . B ut even this flexibility should have limits. T hese limits are the ones imposed by the manufacturer.
2. C ONT R OL C HA R T S
2.1 Phase 1 - T raditional C ontrol C harts
Having enough data to estimate the process parame-ters, phase 1 of S PC with Shewhart charts is imple-mented. T he volume of data (number of samples (m)) needed to define the parameters on phase 1 de-pends on the sample dimension (n). Queensberry - see (Pereira & R equeijo, 2012) – suggests, as can be seen in equation 1, that:
400 ( 1) m
n í
(1)
F or individual F or a single sample, the same author suggests that 300 observations should be used. L am-preia (2013), using experimental equipment data uses 200 observations on phase. In the present work it is shown that 200 observations are enough. In this article individual observation (X )and moving range (MR ) control charts are implemented consi-dering continuous and independent data. T he control charts analysis must show controlled statistical equipment.
F or independent data, phase 1 should proceed and the S hewhart or traditional control charts are built. Upper control limit (UC L ), L ower control limit (L C L ) and C enter line (C L ) for those charts, are culated using the formulas on the table 1.T hese
cal-C ontrol cal-C harts L imits F lexibility B ased on the E quipment cal-C onditions
S . L ampreia, V . V airinhos, V . L obo & R . Parreira
1, vlobo isegi.unl.pt, ribeiro.parreira marinha.pt, C entro de Investigaçã o Naval (C INAV ), Alfeite, 2810 Almada, Portugal
J . G. R equeijo
jfgr fct.unl.pt, F aculty of Science and T echnology of the Universidade Nova of L isbon,Mechanical and In-dustrial E ngineer D epartment, L isbon. 2829-516, C aparica, Portugal
culations, based on the m (or m-1) sample dimen-sions are the statistics
= = m i i m X X 1 and
(
)
-= -= 1 1 1 m i i m MRMR , where
1 -= i i
i X X
MR .
T able 1. T raditional C ontrol C harts L imits, in phase 1 of SPE ( Pereira e R equeijo, 2012)
C hart L C L C L UC L X
X
X - 3s X X 3 X
s
MR ( moving range)
MR D
3 MR D4MR
If the process is stabilized - under statistical con-trol -its parameters should be estimated by
X μ
ˆ = and
2
d MR ˆ =
s . T he constants
3
D ,
4
D and
2
d
depend exclusively on the sample dimension. (L am-preia et al, 2012)
F or auto correlated/dependent data, since we are working in condition based maintenance, a fitted sta-tistical model for the autocorrelation should be ap-plied. W e suggest the A R IMA (A utoregressive Inte-grated Moving A verage) (p, d, q) Model. T he statistics from individual observation and Moving R ange control charts are calculated using the fitted model residues for every observation. (L ampreia et al, 2013).
E stimated -sampling - A utocorrelation F unction (A C F ) and Partial A uto-C orrelation F unction (PA C F ) are compared with (A C F ) and (PA C F ) of known dependence patterns in order to choose a spe-cific model.
E quipment parameters follows a A R IMA (p, d, q) model if
t d
X
. T he model defined by A R IMA (p,d,q):
( ) ( )
d
p B Xt q B t
e
F = = Q (3)
( ) 2 1 2 (1 ) p p p
B fB f B f B
F = - - - - (4)
( ) 2 1 2 (1 ) q q q
B qB qB qB
Q = - - - - (5)
1 t t X B X -= e 1 t t t X X X
- = (6)
1 ( ) 1 p j j E X x m f = = = -
(7) ( ) E X =m(8)
W here B is the lag operator, is the difference operator, d is the differentiation order to render a sta-tionary process,
t
X is the observation at time t,
t
eis the white noise at time t, Φ(B) is the autoregressive polynomial of order p and Θ(B) is the moving aver-age polynomial of order q.
Using a defined model, the residues are estimated by ˆ
t t t
e =X - X , with ˆ
t
X expected value for the period t. F or more details Pereira and R equeijo (2012) should be consulted.
2.2 Phase 2 - Modified E WMA C hart
In phase 2, an E W MA control chart becomes suita-ble for equipment monitoring if the process has a change; TL represent the limit imposed by the
manu-facturer.
T he variable that defines the Modified E W MA is the exponentially weighted variable, E , defined by the equation (2) (C rowder & Hamilton, 1992).
(
)
(
1)
max 0, (1 ) E t , 0 1
t t L
E l l X T l
-= - - (2)
where, X
n
e
s =s ,
X
D=d s , (Z ou & T sung,
2010)
(
)
tan
L L S dard S
T = T - D andDS=d1s , with d1 as
a constant.
In these equations Xt is the sample mean at t
(Serel & Moskowitz, 2008), TL the maximum or
min-imum admissible for each variable or parameter, s E
the variable E standard deviation, n the sample di-mension, λ the weight constant (0 ≤ λ ≤ 1) and ∆s
the safety factor. T he Modified E W MA limits are A lert L evel (A L ) and Upper C ontrol L evel (UC L ) for these charts are given by equations (3) and (4). (L ampreia et al, 2012)
1
E E
A L = K s (3)
2
E E
U C L =K s (4)
where 2 E X l s s l = (5)
K1 and K2 are functions of values of λ and A R L
(for A L and UC L ). T o define the A L and UC L C rowder (1989) abacus are used, entering with A R L (A verage R un L ength) value and the mean change, δ , where we obtain K1 and K2. In this study a =1%
(ARL=100) will be considered to define A L and %
2 , 0 =
a (ARL=500) to define UC L . 3. ME T HODOL OGY
D epending on equipment characteristics, we pro-posed a methodology to be applied to repairable sys-tems monitoring.
F or independent data the steps should be as fol-lows:
W ith the equipment in good performance check for data independence and Normality. E stimate its parameters;
- F or online equipment monitoring, build the Modified E WMA charts using the online collected values.
- D efine the change in the parameters mean that must be detected.
- E stimate AL and UC L control limits, con-sidering some meteorological standards.
- F ix the intervention rules:
6 consecutive points are above the AL - Proceed to an inspection.
3 consecutive points are above the UC L - Proceed to a maintenance intervention. 4. R E S UL T S
4.1 Phase 1 – T raditional C ontrol C harts
T he variables under study are from a C ombined D i-esel or Gas propulsion system associated to a pitch propeller (PP) . S ee T able 2 for the meaning of va-riables. B etween 0 to 500 of engine rpm PP is varia-ble; after that value, for more speed, only the rpm of the engine is increased.
Phase 1 starts with the study of 200 observations collected from four parameters of an engine, at con-stant power. T his study includes normality and inde-pendence checks and parameters definition.
T able 2. V ariables in S tudy
OP0155 L ub Oil Pressure OP0157 Piston C ooling Oil Pressure F P0163 F uel Oil Pressure OT 0114 L ub Oil T emperature
T he Normality and the independence study ex-plained in this article is for variable number 1.
F or variable 1, normality was tested with the K
olmo-gorov-Smirnov test. See F igure 1, F igure 1,
where
C rítico
0,886 0, 886
D 0,06265
N 200
= = = for a =5%,
and d= 0,03627. Once
C rítico
dD the normality con-dition is accepted. (Pereira e R equeijo, 2012)
F igure 1. V ar1 - Normality S tudy
F igure 2. V ar1 - A C F
F igure 3. V ar1 - PA C F
W hen building traditional control charts some outliers were found. T o estimate the parameters, out-liers must be excluded or replaced, using some crite-ria; our decision was its replacement with the mean between the preceding and the next values.
Using S tatistica software, the following results were obtained before replacing outliers:
F igure 4. V ar 4 ( L ub Oil T emperature) – Individual C ontrol C hart - W ithout R eview
F igure 5. V ar 4 ( L ub Oil T emperature) – Moving R ange C ontrol C hart - W ithout R eview
T he results after replacing outliers:
F igure 6. V ar 4 ( L ub Oil T emperature) – Individual C ontrol C hart - R eviewed
F igure 7. F igure 4. Moving R ange V ar 4 ( L ub Oil T empera-ture) - R eviewed
A pplying the same procedure to others variables we obtained the parameters estimations for µ and σ . S ee results on T able 3., obtained again with S tatisti-ca.
T able 3. V ariables parameters
V A R 1 V A R 2 V A R 3 V A R 4
µ 6,3529 5,9947 0,79116 70,99
σ 0,0009 0,06856 0,3778 0,512
TL 5,5 5,5 0,5 95
4.2 Phase 2 – Modified E WMA C ontrol C harts L im -its F lexibility
T o sum up: we observed that for some operating conditions, the ship diesel propulsion parameters show considerable variability, so we will consider 3 limits according sea temperature, at a cruise speed with maximum pitch propeller and 800 engine rpm. In what follows, specifically for the limits flexibility we present V ar 4 (L ub oil temperature) study in more detail, with 3 distinct TL values ( lower,
nor-mal and higher namely 80, 85 and 95º C ). F or this specific parameter, the ship sensor program has an alarm.
It is considered important to detect eventual dam-age on the selected variables with σ three levels of variation. T o test its sensibility, ∆ =L 0,5σ ; 1σ ; 1,5σ ], δ =L0,5; 1; 1,5] , with α = 1% (A R L = 100) in the de-finition of A L and α = 0.2% (A R L = 500) in the de-finition of UC L . Using the C rowder abacus (Pereira and R equeijo, 2012), we obtained λ = 0.05, λ = 0,13 and λ = 0.25, respectively, and K = 2.7, K = 2.9 and K = 3.
A L and the UC L values for each variable and each σ are obtained using expressions 2 and 3,
B ecause this is a real engine, no induced damage is allowed, so the parameters with anomalies were simulated in the MA T L A B , considering 0 to 3 pro-gressions of the anomalies of the engine, and consi-dering the limits flexibility
F or sea mean temperature, with TL=85º C , for the
2
rd
progression of a possible anomaly, considering
% 1 =
a (ARL=100) A L and a =0,2% (ARL=500) to UC L .
0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d 37 0
9 U / L AL
0,000 0,200 0,400 0,600 0,800 1,000 1,200 1,400
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA a odifie d 28 000
9 U / L AL
F igure 9. V ar4 - TL=85º C with ∆ =1σ - 2ªProgression
0,000 0,200 0,400 0,600 0,800 1,000 1,200 1,400 1,600 1,800
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9ía A aodifie d 0
9 U / L AL
F igure 10. V ar4 - TL=85º C with ∆ =1,5σ - 2ªProgression
C omparing the results for each ∆ , we fixed ∆ =0,5σ as the more suitable for the variables charac-teristics and results. A nalyzing figure 4, and using the defined methodology, we should proceed to an investigation action by the 40
th
observation. W ith TL=85º C , for the 3
rd
progression of a possi-ble anomaly, figure 11:
0,000 0,100 0,200 0,300
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d 1 D2
9 U / L AL
F igure 11. V ar4 - TL=85º C with ∆ =1,5σ – 3ªProgression
In figure 11 the chart shows that engine needs an investigation action after 31th observation.
F igure 12 shows an intervention need after 14th ob-servation. 0,000 0,100 0,200 0,300 0,400 0,500 0,600
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d ( D=1s )
9 U / L A L
F igure 12. V ar4 - TL=85º C with ∆ =1σ – 3ªProgression
If we consider TL=80º C , all the observations will
be out of control; see figure 13. If we assume TL=95º C all the observations are under control. S ee
figure 14. 0,000 0,100 0,200 0,300 0,400 0,500 0,600 0,700 0,800 0,900 1,000
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d ( D=0,5s )
9 U / L A L
F igure 13. V ar4 - TL=80º C with ∆ =0,5σ – 3ªProgression
F igure 14. V ar4 - TL=95º C with ∆ =0,5σ – 3ªProgression
T his means that, with the variation on the TL
val-ue, the results change. If TL decreases, the results
decreases; with a TL increase there is a rise in the
resulting values.
T o change the limits, the assumed A R L and δ should change. W e simulated several values, considering only δ with 0.5, 1, and 1.5, given the C rowder abacus design.
C onsidering a =1% (ARL=100) AL and %
2 , 0 =
a (ARL =2000) to UC L , figure 15 and 16:
0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d ( D=0,5s )
9 U / L A L
F igure 15. V ar4 - TL=85º C with ∆ =0,5σ - 2ªProgression UC L
-A R L =2000
0,000 0,100 0,200 0,300
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d 0,100
9 U / L AL
F igure 16. V ar4 - TL=85º C with ∆ =0,5σ - 3ªProgression UC L
-A R L =2000
C onsidering a =1% (ARL=100) A L and %
2 , 0 =
a (ARL =1000) to UC L , figure 17 and 18:
0,000 0,050 0,100 0,150 0,200 0,250 0,300 0,350 0,400
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d
9 U / L AL
F igure 17. V ar4 - TL=85º C with ∆ =0,5σ - 2ªProgression UC L
-A R L =1000
0,000 0,100 0,200 0,300
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
9
h b se rvation nr
9íaA aodifie d 19 D2
9 U / L AL
F igure 18. V ar4 - TL=85º C with ∆ =0,5σ - 3ªProgression UC L
-A R L =1000
F or higher A R L values, the control chart is less sensible. A ssuming navigation with higher sea tem-peratures, the A R L limit can be higher; for lower
0,000 0,100 0,200 0,300
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 9
h b se rvation nr 9íaA aodifie d13
temperatures A R L can be lower, always respecting the manufacturer limits.
5. C ONC L US IONS
F or auto correlated data, an A R IMA model can be used for data modeling. F or independent data, obser-vations are used directly for control charts equip-ment monitoring.
T he autocorrelation model is chosen comparing the A C F and PA C F with the E A C F and E PA C F .
In phase 1 the individual observations and mov-ing range control charts are used to define the work-ing parameters values. T he parameters are defined after charts correction for outliers.
It’s possible to monitoring equipment data with the Modified E W MA control charts.
T he Modified E W MA is more sensible than the traditional charts.
T he variability of ∆ influences the charts sensitiv-ity.
F or higher A R L values E W MA the chart sensitiv-ity decreases.
T he analyzed equipment has shown parameters under statistical control.
6. R E C OME NDA T IONS
T he simultaneous use of several techniques for equipment condition diagnostic is recommended.
T est the four variables data with ME W MA C harts, and use flexibility concept in the charts de-sign.
D evelopment of software to allow flexibility in the limits of online monitoring with control charts is needed.
R E F E R E NC E S
R awat, Manish, L ad, B hupesh ( 2013) . C ondition B ased Opti-mal Maintenance Strategy for Multi-C omponent System. http://www.researchgate.net/publication/25844583,
20J an2016.
L ampreia, Suzana ( 2013) . Manutençã o B aseada no E stado de C ondiçã o. Uma A bordagem Utilizando C artas de C ontrolo Modificadas. T ese de D outoramento, F aculdade de C iê ncias e T ecnologia da Universidade Nova de L isboa, S etembro. Schaeffers, Marc ( 2016) . Manage control limits when
Imple-menting S tatistical Process C ontrol.
http://www.isixsigma.com/tools-templates/control-charts/manage-control-limits-when-implem-
enting-statistical-process-control 19J an2016.
Pereira, Z . L . and R equeijo, J . G. ( 2012) , Qualidade: Planea-mento e C ontrolo E statístico de Processos ( Quality: Statis-tical Process C ontrol and Planning) , F C T /UNL F oundation E ditor, L isboa.
L ampreia, S., B arbosa, P., & R equeijo, J . ( 2012) . Manutençã o C ondicionada B aseada na A plicaçã o de C artas C ontrolo E WMA. C ongresso Ibérico de J ovens E ngenheiros - C IJ E 2012. B raga.
L ampreia, Suzana, R equeijo, J osé, D ias, J osé, V airinhos, V alter ( 2013) . E quipment C ondition Monitoring with an A pplica-tion of ME W MA C ontrol C harts and Others C harts. IC OV P2013, Setembro de 2013, L isboa.
C rowder, S. V ., & Hamilton, M. D . (1992) . A n E WMA for monitoring a process standard D eviation,J ournal of Quality Technology,V ol. 24, pp. 12-21.
Z ou, C ., & T sung, F . ( 2010) . L ikelihood ratio-based distribu-tion-free E WMA control charts. J ournal of Quality T ech-nology, pp. 174-196.
Serel, D . A ., & Moskowitz, H. (2008). J oint economicdesign of E WMA control charts for mean and variance, E uropean J ournal of Operational Research, pp. 157-168.
