501
1 INTRODUCTION
Accidents due to the malfunction of the ship
propulsion system may occur when the ship is in
heavytrafficsealane,orwhentheshipisunderberth
maneuvering. Aging effects increase the likelihood
malfunction. In that respect, additional premium is
appliedforshipsolderthan15yearsintheinsurance
ofthecargo[1].Sincethedemandforecast
ingofthe
numberofshipsasafunctionoftimeisdifficult,there
is a wide age distribution of available vessels.
Figure 1 shows the age distribution of handy size
bulkers worldwide as an example [2] and indicates
that while the number av
ailable decreases with
increasing age, in general, there are still more than
1400 handy size bulkers older than 25 years. Most
these older ships are operated by minor marine
transportation companies because major marine
transportationcompaniesusuallyselltheshipswhen
theship’sagereaches20to25years.Ifanagingship
isoperatedbyminorma
rinetransportationcompany,
there is a higher likelihood that the ship propulsion
systemisnotmaintainedproperlyduetocostfactors.
Therefore,theunavailabilityofpropulsionsystemof
aging ship may not only be increased due to aging
effectsbutalsoduetoimpropermaintenance.
0-4
5-9
10-14
15-19
20-24
25-29
30-
0 200 400 600 800 1000
Number of ships
Age [year]
Figure1.Agedistributionofhandysizebulkersin2011.[2]
Ingeneral,toobtainsystemunavailability,failure
rate of each component in the system is handled as
constant value. However, to obtain system
unavailability under aging effects, time‐dependent
failurerateofeachcomponentneedsobeconsidered.
Relativelyfewstudieshavebeenperformedthattake
aging effects into account [6][7]. However, these
Case Study on the Unavailability of a Ship Propulsion
System under Aging Effects and Maintenance
T.Okazaki
TokyoUniversityofMarineScienceandTechnology,Tokyo,Japan
ABSTRACT: Unavailability of a ship propulsion system under aging effects and proper maintenance is
estimatedusingGO‐FLOW.GO‐FLOWisaneffectivesoftwaretoolfortheunavailabilityanalysisofcomplex
systems. Aging effects are incorporated into GO‐FLOW using a time‐dependent technique and assuming a
linearagingmodel.Theresultsshowtha
ttheagingeffectsandimpropermaintenancecanpotentiallyincrease
thefrequencyofaccidentsduetoamalfunctionofthepropulsionsystembyafactorofthree.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 10
Number 3
September 2016
DOI:10.12716/1001.10.03.16
502
papers did not treat ship propulsion system.
Availability of ship propulsion system without
accounting for aging effects has been estimated by
Kiriya[8]usingtheGO‐FLOWmethodology[9](also
seeSection3).GO‐FLOWissystemanalysissoftware
which has a friendly Graphical User Interface (GUI)
that allows constructing
a system model without
specifyingequations.Thisstudyillustrateshowaging
effects as well as maintenance can be incorporated
into GO‐FLOW by using the time‐dependent
technique described in [4]. Sections 2 and 3,
respectively, provide an overviews of the example
propulsion system under consideration and its
correspondingGO‐
FLOWmodelwithoutconsidering
agingeffects.Section4describeshowthismodelcan
beaugmentedtoaccountforagingandmaintenance
withthemethodologyof[4].Theunavailabilityof
the propulsion system under aging effect and
improper maintenance is estimated using the
augmentedGO‐FLOWinSection5.Section6reports
theresultsandSection7gives theconclusionsofthe
study.
2 SHIPPROPULSIONSYSTEM
Ingeneral,theshippropulsionsystemconsistsoffuel
oilsystem(F.O. system), lubricatingoil system (L.O.
System), cooling system, main engine (M/E) system,
anddrivelinesystem(seeFig.2)withthepictureof
thepiston
andcylinder.Themainengineoftheshipis
large diesel engine with combustion chamber and
inner mechanism, power transmission equipment,
and fittings and accessories. The driveline system
shown at the right hand side of Fig.2 delivers the
drivingforce generated bythe M/E to the propeller.
The driveline system has
a propeller, a shaft,
intermediateshaftbearings, sterntubebearings,and
sterntubesealbearings.
L.O. System
Cooling System
• Fittings and Accessories
• Combustion Chamber and
Inner Mechanism
• Power Transmission
Equipment
•Shafts
• Intermediate Shaft Bearing
• Stern Tube Bearing
• Stern Tube Seal Bearing
• Propeller
M/E System
Driveline System
F.O. System
Seawater
Coolant
water
Figure2.Outlineofshippropulsionsystem
TheF.O.systemisthesystemthatsuppliesthefuel
oil to the main engine. Conceptual diagram for F.O.
system is shown in Fig.3. The fuel oil is the crude
petroleum stored at service tank (1). Sludge in the
F.O. is removed with F.O. strainer (2). The F.O. is
collected by
the chamber via F.O. supply pump (3).
The F.O. collected by the chamber is sent to F.O.
heater via F.O. booster pump (4). Pressure of F.O.
riseswiththeboosterpump(5).TheF.O.isheatedup
toappropriatetemperaturewithFOheater(6).Sludge
in the F.O. is removed
with strainer, again (7). The
F.O. is sent to the F.O. injection pump and put on
high pressure (8). The F.O. is jetted from the fuel
injection valve to the piston chamber (9). The
numbersinparenthesescorrespondtothoseinFig.3.
(6) F.O.
Heater
(7) Strainer
(3) F.O. Supply Pump
(2) F.O.
Strainer
(1) F.O. Service Tank
(4) F.O.
Chamber
(5) F.O. Booster Pump
(9) Fuel
Injection
Valve
(8) Fuel Injection Pump
M/E
Figure3.ConceptualdiagramforF.O.system
The L.O system is a system that offers the
lubricating oil to the operation part of the main
engineblock.ConceptualdiagramforL.O.systemis
showninFig.4.TheL.O.isstoredinL.O.servicetank
(1)andL.O.gravitytank(2),andsenttotheM/E.The
L.O.at
M/EiscollectedandsenttoL.O.cooler(4)by
L.O. pump (3). Then cooled L.O. is returned to the
L.O.servicetank.
(4) L.O. Cooler
(3) L.O. Pump
(2) L.O. Gravity Tank
(1) L.O. Service Tank
M/E
Figure4.ConceptualdiagramforL.O.system
The cooling system makes the coolant water
circulatein the main engineblock, and prevents the
enginefromoverheating.Thecoolingsystemconsists
of freshwater (F.W.) cooling system and seawater
(S.W.) cooling system. Conceptual diagram for
coolingsystemisshowninFig.5.TheF.W.isstoredin
F.W.tank(1)as
coolantforM/E.TheF.W.issentto
F.W.cooler(3)byF.W.pump(2).AttheF.W.cooler,
F.W is cooled by seawater which comes from S.W.
coolingsystem(seeFig.2).ThenF.W.cools theM/Eby
passingovertheinsideofengineblock.Thewarmed
F.W. from M/E
returns to F.W. tank. In the S.W.
cooling system, seawater outboard is absorbed by
S.W. pump (2) via the S.W. suction valve. The S.W.
cools F.W. at F.W. cooler, and is exhausted to
outboard.
503
(3) F.W. Cooler
(2) F.W. Pump
(6) S.W. drainage valve
(1) F.W. Service Tank
(4) S.W. Suction valve
(5) S.W. Pump
M/E
Seawater
Freshwater
Figure5.Conceptualdiagramforcoolingsystem
The M/E system and the driveline system are
large,mainsubsystemsoftheshippropulsionsystem
and there are no backups. On the other hand, F.O.
system, L.O. system, and cooling system are small
auxiliary subsystems and each of them typically
consistsoftwoorthreetrains.
3 DESCRIPTIONOFGO
‐FLOW
GO‐FLOWisa success‐oriented systemanalysistool
forevaluatingsystemreliabilityandavailability.GO‐
FLOWusesasetofstandardizedoperatorsshownin
Table 1 to describe the logic operation, interaction,
andcombinationofphysicalequipment.Asystemis
modeledbyselectingoperatorsandconnectingthem
by
signal lines. The signal represents some physical
quantityorinformation.InGO‐FLOW,threetypesof
signalsareconnectedtoanoperator;the ma in input
signal(s), the sub‐input signal(s), and the output
signal. The intensity of a signal represents the
probability of the actual or potential existence of a
physical
quantity or the probability of some
information transmission or mission. The output
signalintensityofeachoperatorisshowninTable1.
By using GO‐FLOW, F.O. system of ship
propulsionsystemdescribedinFig.3wasmodeledas
showninFig.6.InFig.6,thesignalisflowofF.O.and
startsfromOperator1 whicha signal generator(see
Table1).InGO‐FLOW,systemoperationsequenceis
expressedintermsofafinitenumberofdiscretetime
points (TP) and signal intensity (SI) of signal
generator. Table 2 shows the sequence of operation
forthesysteminFig.6.No.1F.O.
servicetankinFig.6
is modeled with Operator 3 which is a Type 26
operator (see Table 1). Although Type 26 operator
usuallyrepresentsanormallyclosedvalveasshown
inTable1,inconjunctionwithOperator2whichisa
signalgenerator(seeTable1)itisusedto
modelthe
process of opening the valve of service tank that is
closedattheinitialstate(TP1inTable2).FromTable
2,theSIofOperator 2turnsfrom 0to 1 atTP2and
hence initiates the F.O. flow through Operator 3
whichemulatestheopeningthe
valve.ThentheF.O.
flows to Operator 5.Operator 5 models No.1 F.O.
strainer by Type 21 operator which represents a
good/bad component. If the component does not
work, F.O. is not supplied to downstream of the
component.TheF.O.systemhastwotrainsandeach
pumphasselectablefunction.
Thereforethesignalat
the upstream of the pump and downstream of the
pump was connected by OR gate. Then, the GO‐
FLOW outputs the availability of the F.O system as
theintensityoffinalsignal.ThefinalsignalinFig.6is
theinputlineoftheTerminal.
Table1.OperatorsinGO‐FLOWmethodology
__________________________________________________________________________________________________
Operator Symbol Model OutputSignalIntensity
__________________________________________________________________________________________________
Type21 Two‐StateComponent
() ()
og
Ri Si P
Type22
ORGateProbabilitythatatleastoneinputsignalexists
Type23
NOTGate
() 1 ()
o
Ri Si
Type25
SignalGeneratorProbabilityofademandortimedurationinhours
Type26 NormallyClosedValve
1
() () (), () ( ) [1 ( )] () , ( )
o gp
R
iSiOiOiOi OiViP Oi P
Type27
NormallyOpenValve
1
() () (), () ( ) [1 () ], ( ) 1
ogp
R
iSiOiOiOi ViP Oi P
Type30
ANDGateProbabilitythatalltheinputsignalexist
__________________________________________________________________________________________________
*Inthistable,S(i)isthemaininputsignal,V(i)isthesub‐inputsignal,Ro(i)istheoutputsignal,Pgistheprobabilityfor
successfuloperation,O(i)istheprobabilityforavalvetobe intheopenstate,P
pistheprobabilityforprematureoperation,
iisthetimepointwithsubscriptdenotingtheordinal,i’isthetimepointimmediatelybeforethetimepointi.
504
Figure6.GO‐FLOWchartofF.O.system
Table2.Exampleofoperationsequence
_______________________________________________
TimePoint(TP) Sequence Signalintensity(SI)
Operator1 Operator2
_______________________________________________
1 F.Oflows fromupstream.10
2 Valveopen.11
_______________________________________________
Figure 7 shows GO‐FLOW chart of L.O. system
describedinFig.4.InFig.7,thesignalisflowofL.O.
Then the signal intensity at Terminal in Fig.7
describestheavailabilityofL.O.system.
Fig.8 shows GO‐FLOW chart of cooling system
describedinFig.5.Uppersideofthefigureindicates
flow of freash water in cooling system and lower
sinde of the figure indicates flow of sea water in
coolingsystem. Thesignalfromuppersideandsignal
fromlowersideareconnectedbyanANDgate.The
signal intensity at terminal in Fig.8 describes the
availabilityofcoolingsystem.
Fig.9
shows GO‐FLOW chart of propulsion
system.InFig.9,Operator1modeledbyanANDgate
with three signals which are the availability of F.O.
system, L.O. system and cooling system. Therefore,
theintensityofoutputsignalofOperator1describes
availabilityoftheauxiliarysysteminshippropulsion.
The
output signal becomes input to the subsequent
operators which model the M/E system and the
driveline system. Then the signal intensity at
Terminal in Fig.9 describes the availability of L.O.
system.
4 TIME‐DEPENDENTTECHNIQUE
A GO‐FLOW operator requires the probability for
successful/failedoperationasinput(e.g.Type21,26,
27inTable1).Inordertoconsideragingeffects,this
input parameter was derived from the time‐
dependent technique of [4] described in Section 4.1.
Section 4.2 shows the implementation of the time‐
dependent technique for GO‐FLOW. In the time‐
dependent technique, the unavailability of each
component depends
on its maintenance schedule.
Section 4.3 shows how the maintenance schedule is
managedinGO‐FLOW.
4.1 Time‐dependenttechniqueforagingcomponents
The technique used to model the time‐dependent
unavailability of aging components is based on the
extendedrenewalequation[4]
00
0
() () ( ,) ( ) ( , )
() ( ) ( , ) ( ,) ,
tt
tt
t
wt f t dtf t t dtwt gt t
f
tdtwtdtgttftt
(1)
where w(t)dt is probability that the component fails
within
(, )tt dt
,
()
f
t
is first failure density (FFD) for
the component at time t,
(,)
f
ttdt
is probability
component fails within
(, )tt dt
given that repair is
completed at
tt
, and
(,)
g
ttdt
is probability that
repair is completed within
(, )tt dt
given that
componentfailswithin
(, )tt dt
}.
Under the assumptions that, 1) surveillance/tests
are performed at times T units apart, 2) failures are
detectedonlyduringsurveillance/testsandcannotbe
detected at other times 3) surveillance/testing and
repairtimesarenegligiblecomparedtoT,and,4)the
component is restored to age 0 following
surveillance/testing (i.e.
through either minor
maintenancesuchas tighteninga valve orrepair), it
canbeshownthat,forasinglecomponent,thetime‐
dependentunavailabilityU(t)isgivenby[4],
()
1
00
( ) ( ,0) ( ) exp{ ( )} exp{ ( )}
( 1) ( 0,1, ),
nkT
t tkT
n
k
nT
U t dt f t U kT dt t dt t
nT t n T n
(2)
where
)t(
is the failure rate for the component at
timet.
In this study, the failure density of an aging
component is assumed to be given by the Weibull
distribution
00
1
0
0
1
otherwise,
exp{ ( )} if
(, )
() ()
exp{ [ ]}
1
bb
bb
tt tt
ftt
tt tt
b
b
(3)
where
is the threshold time at which aging starts,
0
is the pre‐aging constant failure rate,
b
is the
Weibullshapeparameterand
t
isthetimeatwhich
505
last repair is completed. The failure rate for this
failuredensityis
0
0
otherwise.
if
()
b
t
t
t
(4)
Then the time‐dependent unavailability is given
by[3]
1
() ( ) 0, ( ) [( ) ] ( ,)
( 1) ( 0,1, ),
n
k
Ut RnTq t UkTR n kTqkTt
nT t n T n
(5)
where
0
1
0
1
otherwise
exp( ) if
()
exp{ ( )}
1
b
b
ll
Rl
l
b
b
(6)
0
1
0
0
11
1
0
1 exp{ ( )} if ( )
(,) 1exp{ ( ) [ ]} if( ) ,
(1)
1 exp{ [ ]} otherwise.
(1)
b
b
b
bb
b
b
tnT nkT
qkTt t nT t kT n kT t kT
b
tkT nk T
b
(7)
IftheWeibullshapeparameterbissetas1,Eq.(7)
correspondstoalinearagingmodel.
Asindicatedearlier,Eq.(2)andsubsequentlyEq.
(5) is based on the assumption that surveillance is
performed at times T units apart.In order to
consider irregular surveillance, expanding Eq.(5)
we
have
() ( ) (0,)
() ( ) (,)
(2 ) ( 2 ) (2 , )
()()(,)
()(0)(,).
Ut RnT q t
UT RnT T qTt
UTRnT TqTt
UnTTRTqnTTt
UnT R qnTt
(8)
Under the assumption that each surveillance
periodissequentiallyassumedtobeT
j(j=1,2,3,…,n)
andT
0=0isforthecaseofn=0,Eq.(8)isbecomes
012
123 1
12 34 12
12 1 12 1
12 12
() ( ) (0,)
() ( ) (,)
()( )(,)
()()(,)
()(0)(,).
n
n
n
nn n
nn
Ut RT T T T q t
UT RT T T qT t
UT T RT T T qT T t
UTTTRTqTTTt
UT T T R qT T T t
(9)
Then
1
01111
1
11
() ( ) 0, { ( ) ( ) ( ,)}
( ) (0) ( , ) < ( 0,1, )
nnknk
jjjj
jkjjkj
nn
jjnn
jj
Ut R T q t U T R T q T t
UTRqTt TtT n
(10)
where
0
00
1
0
0
0
1
otherwise,
exp( ) if
()
()
exp{ [ ]}
1
nn
jj
jj
n
n
j
b
j
j
j
b
TT
RT
T
b
b
(11)
0
11
1
1
1
0
1
otherwise
exp( ) if
()
()
exp{ [ ]}
1
nn
jj
jk jk
n
n
j
b
jk
j
jk
b
TT
RT
T
b
b
(12)
and
1
1
0
1
11
0
0
1 1
1
0
1
,
if
if
1 exp{ ( )}
( , ) 1 exp{ ( ) [( ) ]}
(1)
1 exp{ [( ) ( )
(1)
k
j
j
kn
jj
jjk
n
j
j
knk
bb
jjj
b
jjkj
kn
bb
jj
b
jjk
t
t
T
TT
tT
qTt T t T
b
tT T
b
1
otherwise.]}
(13)
4.2 Time‐dependentprobabilityforGO‐FLOWoperators
Type 21 operator in Table 1 models a good/bad
component. This operator has one input signal and
oneoutputsignal line andrequires a probability for
successful operation. The output signal intensity is
givenby
() ()
og
Ri Si P
(14)
where S(i) is input signal at time point i, R
o(i) is
outputsignalattimepointi,P
gistheprobabilityfor
successfuloperation.Inordertoconsideragingeffect
of Type 21 operator, P
g is enabled for successful
operationby
1.0 ( )
g
PUt
(15)
whereU(t)isthetime‐dependentunavailabilitygiven
byEq.(10).
Type 26 operator in Table 1 models a normally
closed valve, which is opened by sub‐input signal.
This operator has one input signal, one sub‐input
signal,andoneoutputsignalline. Theoutputsignal
intensity
isgivenby
() () ()
() (') [1.0 ( ')] ()
o
g
Ri SiOi
Oi Oi Oi V i P
(16)
whereV(i)issub‐inputsignalattimepointi,i’istime
point immediately before the time point i, O(i) is
probability for valve in open state, P
g is the success
506
probability for opening valve operation. In order to
consideragingeffectofType26operator,P
gisgiven
byEq.(15).Forinitialtimepoint,O(1)isgivenby
(1)
P
OP
(18)
whereP
pisprobabilityforprematureoperation.
Type 27 operator in Table 1 models a normally
openvalve,whichisclosedbysub‐inputsignal.This
operator has one input signal, one sub‐input signal,
andoneoutputsignalline.Theoutputsignalintensity
isgivenby
() () ()
() (') [1.0 () ]
o
g
Ri Si Oi
Oi Oi V i P
(16)
where P
g is the success probability for closing valve
operation.InordertoconsideragingeffectofType27
operator,P
gisgivenbyEq.(15).
4.3 Maintenanceperiod
Time‐dependent unavailability of each component
depends on the maintenance schedule. In order to
implementandmanagethemaintenanceschedulein
GO‐FLOW,eachGO‐FLOWoperatorwasallocateda
unique3digitnumberandthemaintenanceschedule
foreachoperatorwaslinkedwith
this3digitnumber
(which we call the maintenance code) as will be
illustratedbelow.Then,eachoperator‘sunavailability
as given in Eq. (15) was calculated by the time‐
dependent technique using this maintenance
schedule.
GO-FLOW chart Maintenance schedule
Figure10. Example of GO‐FLOW chart and maintenance
schedule
Fig.10 shows example of GO‐FLOW chart which
modelsa two‐train heat removal system(Systems A
and B) and the maintenance schedule for each
operator. For example, Operator 3 in Fig.10 (Motor
PumpA)isassigned001asthemaintenancecodeand
itsmaintenancescheduleisdescribedinColumn001.
Incolumn001,timeswhenthemaintenanceofMotor
Pump A is executed is shown in months. This time
alsoindicatestheageofMotorPumpA.Thetablein
Fig.10 shows that the first maintenance of Motor
Pump A was executed at its age of six months, and
the
maintenanceafter that was executed at every 12
months. The maintenance schedule for Heat
ExchangerAwhichmaintenancecodeis003hassame
maintenancescheduleastheMotorPumpA.Onthe
other hand, Motor Pump B with maintenance code
002andHeatExchangerBwithmaintenancecode004
were maintained
every 12 months. Therefore, the
timingofmaintenanceforSystemsAandBhavegap
which described in Fig.11. Using this maintenance
schedulefunction,GO‐FLOWcouldconsiderthegap
ofthemaintenancetimingandchanging maintenance
period.
Figure11.ExampleoftimingofmaintenanceforsystemA
andB
5 CASESTUDY
In this section, three cases of GO‐FLOW simulation
for unavailability of ship’s propulsion system are
considered with aging effect and maintenance
modeled as described in Section 4. Case 1 has no
aging effects. In Case 2, the variation of the
unavailabilityofshippropulsionsystemunderaging
effects is simulated. Case 3 assumes that the ship is
soldatage20yearsandthemaintenanceperiodwas
changed.
5.1 Case1
To simulate the variation of unavailability before
agingeffects,theGO‐FLOWchartofshippropulsion
system described in Fig.9 was used. In this model,
Type
21 and Type 26 GO‐FLOW operators and
Eq.(10)‐(13)forT
j<τareneeded.Failurerateforeach
component was taken from Ship Reliability
InvestigationCommittee’s (SRIC)database[2]which
is compiled from the engine room failure reports of
265 merchant ships. The choice of the maintenance
periodisdescribedinSection5.1.1andresultsofthe
simulationaredescribedin
Section5.1.2.
5.1.1 Choiceofthemaintenanceperiod
In general, auxiliary components of engine room
are maintained by engineers during navigation. For
example,inthecaseofthe two‐trainsystem such as
describedinFig.3,SystemBcanbemaintainedwhen
System A is under operation. The component that
could
beonlymaintainedwhentheshipismooredat
thepierisM/E.Theshipisenteredinthedockoncea
year, and all components of engine room are
inspectedandmaintainedasrequired.Therefore,the
componentsofshippropulsionsystemweredivided
into three groups: Group 1includes components
which are maintained during navigation, Group 2
includes components which are maintained at the
port, and Group 3 includes components which are
maintained only at the dock. In this study, all
componentsofF.O.system,L.O.system,andcooling
system were classified as Group 1, and all
components of driveline system
and components of
M/E system except fittings and accessories were
classifiedintoGroup3.Thefittingsandaccessoriesof
507
M/EsystemwereclassifiedasGroup2.Maintenance
period for Group 3 (T3) was set to 1 year and
maintenance period for Group 2 (T2) was set to 1
monthwhichwasestimatedfromaveragenavigation
times. Maintenance period for Group 1 depends on
abilityoftheengineer.Itis
estimatedthatabilityofan
engineerinamajormarinetransportationcompanyis
highandabilityofanengineerinaminorcompanyis
lower. Therefore, maintenance period for Group 1
(T1)was chosenas T1=2weeksfor a major company
andT1=4weeksforaminorcompany.
5.1.2 Results
Usingtheapproachdescribedabove,thevariation
of unavailability of ship propulsion system was
calculated by GO‐FLOW. Figure10 shows the
unavailabilityofshippropulsionsystemasafunction
of time. From Fig.10, it can be seen that the
unavailability oscillates with a period of every 2
weeks and the average
unavailability increases
during the year. This oscillation is caused by the
maintenance of Group 1 components. The trend of
increasing unavailability is due to the unavailability
ofGroup3 componentswhich are maintainedevery
yearwhentheshipisinthedockasindicatedabove.
Thereforethepeakinthe
unavailabilityisjustbefore
the ship enters the dock. This unavailability just
beforethedock(UBD)is0.034asshowninFig.10.On
theotherhand,ifthemaintenanceperiodforGroup1
isssetto4weeks,UBDincreasesto0.061asshownin
Fig.11.
5.2 Unavailabilityunderagingeffect
As described in Section 5.1, to simulate the
unavailability of ship propulsion system, SRIC data
basewasusedforfailurerateofeachcomponent.To
calculate unavailability of ship propulsion system
under the aging effect, Eq(11), (12), and (13) require
the value of
which is the threshold time for the
start of aging effect and the value of b which is the
Weibullshapeparameterforagingcomponentmodel.
The choicer of these parameters is described in
Section5.2.1.Section5.2.2presentstheresults.
0 60 120 180 240 300 360
0.00
0.02
0.04
0.06
0.08
Unavailability
Time [day]
Figure10. Unavailability of the ship propulsion system
(T1=2weeks)
0 60 120 180 240 300 360
0.00
0.02
0.04
0.06
0.08
Unavailability
Time [day]
Figure11. Unavailability of ship propulsion system
(T1=4weeks)
5.2.1 Settingofagingparameter
In the insurance on the cargo of a ship, overage
additionalpremiumisappliediftheshipis15years
or older.. However, aging parameters are not
available for all components in the SRIC database.
Therefore,
for all components of the ship
propulsionsystemwassetas10yearsand15yearsto
account for the possible variation inτ.The aging
model was treated as linear (i.e. b =1) [5]. Also,
maintenance period for each component group was
setas
12T
weeks,
21T
month,and
31T
year.
5.2.2 Results
Figure12showsthevariationoftheunavailability
of the ship propulsion system until just before
entering dock. In this figure, the result of
10
years was drawn by solid line and the result of
15
yearswasdrawnbydottedline.Thevalueof
UBD before aging starts is assumed to be 0.03 (see
Section4.1.2).Attheageof35years,thevalueofUBD
for the case of
10
years is 0.078 and the value of
UBD for the case of
15
years was 0.060.
Naturally, the UBD of
10
year case for which
aging stars early is larger than the UBD of
15
years. Therefore,
was set to 10 years
conservativelyforthesimulationinSection5.3.
5.3 Unavailabilityunderchangingmaintenanceperiod
FromtheresultofSection5.1,itisseenthatthevalue
ofpre‐agingUBDfor4weekmaintenanceperiodfor
Group 1 is 0.061. On the other hand the result of
Section 5.2show that the value of UBD at 20 years
aftertheagingstartsis0.060.Fromthesetworesults,
it is clear that proper maintenance is important to
keeplowunavailabilityoftheshippropulsionsystem
inanagingship.However,itispossiblethatanaging
ship is
sold from a major marine transportation
companytominorcompany.In the minorcompany,
themaintenanceperiodforGroup1componentswas
assumedtobe4weeks(seeSection4.1)Thereforthe
maintenance period for Group 1 was changed from
2weeks to 4 weeks at the age of 20 years at
which
point the ship is assumed to sold to the minor
company.
508
0102030
0.00
0.02
0.04
0.06
0.08
Unavailability
Time [year]
:
=10 :
=15
Figure12. Unavailability of ship propulsion system at just
beforedock
Figure13 shows UBD of the ship propulsion
system when maintenance period T1 was changed
from2weeks(solidline)from4weeks(dottedline)at
20 years. The value of UBD increases rapidly as
expected from 0.054 to 0.085 at age 20 years and to
0.107atage35years.
6
DISCUSSION
Fromtheresults ofthecasestudiespresentedinthis
paper the value of pre‐aging UBD was found to be
0.034 (see Section 5.1.2) which implies that a
malfunction can occur in about 30 voyages
(1000/34=29.4).Inthisstudy,navigationtimeforone
voyage was assumed to be
1 month, however, the
number of voyages per year was estimated to be 8
ratherthan12,becausetheshipismooredattheport
attheendofineachvoyageandentersdockoncea
year.Therefore,themaximumnumberofnavigation
daysperyearwasestimatedtobe
250days.Basedon
thisreasoning,thatpre‐agingshiphasthepossibility
of a propulsion system malfunction once every four
years. Table 3 shows the resulting frequency of
malfunction as a function of age of a ship which is
sold from a major company to a minor company at
age 20 years. From the Table 3, it is seen that a 35
yearsoldshiphasthepossibilityofmalfunctiononce
inabout10voyagesvs.about30yearsforanewshp.
Thisresultshowthattheagingeffectsandimproper
maintenancecanpotentiallyincreasethefrequencyof
accidents
due to a malfunction of the propulsion
systembya factorof 3. Itshould be mentioned that
this results is based on the assumption that aging
effectsoftheallthecomponentoftheshippropulsion
systemstartatagetenyears.
Table3Frequencyofmalfunctionforagingship
_______________________________________________
Age Unavailability FrequencyofMeantimebetween
malfunction failures
[year][voyagetime][year]
_______________________________________________
0‐10 0.03429.43.7
200.05418.52.3
210.08511.81.5
350.1079.31.2
_______________________________________________
0102030
0.00
0.02
0.04
0.06
0.08
0.10
0.12
T1=2weeks
T1=4weeks (t>20year)
Unavailability
Time [year]
Figure13. UBD of ship propulsion system which
maintenance period T1 was changedfrom 2 weeks to 4
weeksatage20years.
7 CONCLUSION
This study examines the unavailability of ship
propulsion system under aging effects and
maintenance using an augmented GO‐FLOW
methodology to account for time‐dependent failure
rates. The results show that the aging effects and
improper maintenance can potentially increase the
frequency of accidents due to a malfunction of
the
propulsionsystembyafactorof3in35years.
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