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Else ie
Ma on Lluch, I.; Ma o ell Aigües, P.; Mullo , R.; Sánchez Galdón, AI.; Ma o ell Alsina, SS.
(2016). Op imiza ion o es and main enance o ageing componen s consis ing o mul iple
i ems and add essing e ec i eness. Reliabili y Enginee ing and Sys em Sa e y. 153:151-
158. doi:10.1016/j. ess.2016.04.015
Au ho ’s Accep ed Manusc ip
Op imiza ion o es and main enance o ageing
componen s consis ing o mul iple i ems and
add essing e ec i eness
I. Ma ón, P. Ma o ell, R. Mullo , A.I. Sánchez, S.
Ma o ell
PII: S0951-8320(16)30043-6
DOI: h p://dx.doi.o g/10.1016/j. ess.2016.04.015
Re e ence: RESS5548
To appea in: Reliabili y Enginee ing and Sys em Sa e y
Recei ed da e: 28 Oc obe 2015
Re ised da e: 5 Ap il 2016
Accep ed da e: 28 Ap il 2016
Ci e his a icle as: I. Ma ón, P. Ma o ell, R. Mullo , A.I. Sánchez and S.
Ma o ell, Op imiza ion o es and main enance o ageing componen s consis ing
o mul iple i ems and add essing e ec i eness, Reliabili y Enginee ing and
Sys em Sa e y, h p://dx.doi.o g/10.1016/j. ess.2016.04.015
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ABSTRACT:
The e a e many models in he li e a u e ha ha e been p oposed in he las decades aimed a assessing he
eliabili y, a ailabili y and main ainabili y (RAM) o sa e y equipmen , many o hem wi h a ocus on hei
use o assess he isk le el o a echnological sys em o o sea ch o app op ia e design and/o su eillance
and main enance policies in o de o assu e ha an op imum le el o RAM o sa e y sys ems is kep du ing all
he plan ope a ional li e. This pape p oposes a new app oach o RAM modelling ha accoun s o
equipmen ageing and main enance and es ing e ec i eness o equipmen consis ing o mul iple i ems in an
in eg a ed manne . This model is hen used o pe o m he simul aneous op imiza ion o es ing and
main enance o ageing equipmen consis ing o mul iple i ems. An example o applica ion is p o ided, which
conside s a simpli ied High P essu e Injec ion Sys em (HPIS) o a ypical Powe Wa e Reac o (PWR).
Basically, his sys em consis s o mo o d i en pumps (MDP) and mo o ope a ed al es (MOV), whe e bo h
ypes o componen s consis s o wo i ems each. These componen s p esen di e en ailu e and cause modes
and beha iou s, and hey also unde ake complex es and main enance ac i i ies depending on he i em
in ol ed. The esul s o he example o applica ion demons a e ha he op imiza ion algo i hm p o ide he
bes solu ions when he op imiza ion p oblem is o mula ed and sol ed conside ing ull lexibili y in he
implemen a ion o es ing and main enance ac i i ies aking pa o such an in eg a ed RAM model.
Keywo ds: Una ailabili y, cos s, mul i-objec i e op imiza ion, ageing, mul iple i ems, impe ec main enance,
es ing in e als, main enance in e als, NPP componen .
Op imiza ion o es and main enance o ageing componen s consis ing
o mul iple i ems and add essing e ec i eness
I. Ma ón1*, P. Ma o ell1, R. Mullo 3, A.I. Sánchez2 , S. Ma o ell1
1Depa men o Chemical and Nuclea Enginee ing. Uni e si a Poli ècnica de València, Valencia, Spain
2Depa men o S a is ics and Ope a ional Resea ch. Uni e si a Poli ècnica de València, Valencia, Spain
3Depa men o S a is ics and Ope a ional Resea ch. Uni e sidad de Alican e, Alican e, Spain
* Co esponding au ho : I. Ma ón ([email p o ec ed])
* Co esponding au ho : sma o [email protected] .es
* Co esponding au ho : sma o [email protected] .es
* Co esponding au ho : sma o [email protected] .es
a men o S a is ics and Ope a ional Resea ch. Uni e si a Poli ècnica de València, Valencia, Spain
NOTATION
0

Baseline ailu e a e when he i em is new
RP
Renewal pe iod

Linea ageing a e

Shape ac o

Cha ac e is ic ime

Main enance e ec i eness

Tes e iciency
 Cyclic o pe -demand ailu e p obabili y
D De ec ed ac ion o age-dependen s and-by ailu e a e
U Unde ec ed ac ion o age-dependen s and-by ailu e a e
UD Unde ec ed ac ion o age-dependen s and-by ailu e a e ha is hen de ec ed
UU Unde ec ed ac ion o age-dependen s and-by ailu e a e ha emains unde ec ed (sec ion 2.1.2)
TI Su eillance es in e al
RI
Func ional es in e al
L Li e o he i em
τ Down ime o es ing,
σ Down ime o p e en i e main enance,
M P e en i e main enance in e al
 Down ime o epai
 Down ime o eplacemen
uD Una ailabili y due o de ec ed ailu es
uUD Una ailabili y due o unde ec ed ailu es by su eillance es ing han a e hen de ec ed by unc ional es s
uUU Una ailabili y due o unde ec ed ailu es by bo h su eillance and unc ional es s
uT Una ailabili y due o es ing
uM Una ailabili y due o pe o ming p e en i e main enance
uC Una ailabili y due o pe o ming co ec i e main enance
uO Una ailabili y due o eplacemen o he i em
c
Cos con ibu ion as a consequence o pe o ming es ing
m
c
Cos con ibu ion as a consequence o pe o ming p e en i e main enance
c
c
Cos con ibu ion as consequence o pe o ming co ec i e main enance
o
c
Cos con ibu ion associa ed wi h eplacing
1 INTRODUCTION
Many models ha e been de eloped in he las decades o assess he eliabili y, a ailabili y and main ainabili y
(RAM) o sa e y equipmen . RAM models a e de eloped mainly o assess he isk le el o echnological
sys ems and/o wi h a ocus on hei use o sea ch o app op ia e design and/o su eillance and main enance
policies in o de o assu e ha an op imum le el o RAM o sa e y sys ems is kep du ing all he plan
ope a ional li e [1-3].
Complexi y o RAM modelling has e ol ed along his yea s in an a emp o cap u e he equipmen beha iou
in a mo e ealis ic way. Fo example, mos o RAM models ha we e in eg a ed in o s anda d P obabilis ic
Sa e y Assessmen (PSA), which is he mos used ool o sa e y and isk managemen in Nuclea Powe
Plan s (NPPs), do no add esses explici ly nei he he e ec o equipmen ageing no e ec i eness o
main enance and es ing p og ams, which could ha e a signi ican impac on he conclusions d awn om PSA
s udies and applica ions, pa icula ly when NPP a e ope a ed a an ad anced age o du ing long e m
ope a ion. The eason is ha equipmen ageing and main enance e ec i eness would mos likely esul in
la ge unce ain y o cu en componen un eliabili y and una ailabili y models ha suppo s anda d PSA
quan i ica ion, pa icula ly o aged equipmen . Fo una ely, hese e ec s a e limi ed o en implici ly by
adop ing a li ing PSA o a leas upda ing he s anda d PSA egula ly, which is manda o y by cu en
egula ion in many coun ies.
In ecen yea s mo e a en ion has been paid on modelling explici ly how equipmen ageing impac s RAM o
sa e y componen s and sys ems. Fo example, analy ical age-dependen una ailabili y models ha e been
de eloped adop ing linea ageing a es [1], which conside s he impac o es ing and main enance ac i i ies a
leas implici ly [2-5]. Nowadays, one can ind se e al p oposals in he li e a u e o in eg a e such a kind o
RAM modelling in o he so called Ageing PSA (APSA) [6-10].
These s udies p opose RAM o componen s should be modelled as a unc ion o he inhe en eliabili y o he
componen , i.e. componen ailu e a e imposed by design, he componen ageing, which deg ades he
inhe en eliabili y, and he e ec i eness o es and main enance ac i i ies, which imp o e he eliabili y
deg aded by ageing, i.e. he e is an a emp o e u n componen eliabili y back o i s inhe en alue
e en ually, bu no mally impossible, in case o pe ec main enance ac i i ies. In pa icula , Re . [6]
demons a es he impo ance o add essing explici ly he e ec i eness o main enance in managing equipmen
ageing and es e iciency in de ec ing hidden ailu es as his may impac he accu a e planning and
op imiza ion o es ing and main enance ac i i ies based on RAM c i e ia. This is e en mo e impo an when
he componen consis s o mul iple i ems, whe e e e y i em may unde ake speci ic main enance and es ing
ac i i ies o cope wi h di e en deg ada ion mechanisms and ailu e causes espec i ely a ec ing he mul i-
i ems componen .
On he o he hand, one can ind in he li e a u e an impo an numbe o wo ks de o ed o he op imiza ion o
es and main enance in e als o sa e y sys ems a NPPs , o example using Gene ic Algo i hms (GAs),

which ha ace ei he single-objec i e o mul i-objec i es adop ing RAM plus cos s as objec i es and/o
cons ain s unc ions [11-21, 25-30]. Some o hem conside he impac o componen ageing in he
op imiza ion o es and/o main enance in e als [16-21]. Only se e al o hem conside s bo h es and
main enance in e al op imiza ion simul aneously [12, 14, 18, 20].
This pape p oposes a new app oach o RAM modelling ha simul aneously accoun s o equipmen ageing
and main enance e ec i eness and es ing e iciency o equipmen consis ing o mul iple i ems. This model
is hen used o ace he p oblem o he mul i-objec i e and simul aneous op imiza ion o es ing and
main enance in e als o ageing equipmen consis ing o mul iple i ems. Resolu ion o such a p oblem b ing
a good chance o look o he bes balance be ween componen /sys em a ailabili y and cos o he esul ing
op imal es and main enance in e als o mul iple i ems componen s as i is shown in he example o
applica ion p o ided in his pape . The example o applica ion conside s a simpli ied High P essu e Injec ion
Sys em (HPIS) o a ypical P essu ized Wa e Reac o (PWR). Basically, his sys em consis s o en
componen s: h ee mo o d i en pumps (MDP) and se en mo o ope a ed al es (MOV). Bo h componen
ypes, MOV and MDP, consis o wo i ems: he mo o and pump in he case o he MDP and he ac ua o and
al e in he case o MOV, which a e ea ed sepa a ely. These componen s p esen di e en ailu e modes
and beha iou s, and also hey unde ake complex es and main enance ac i i ies, i.e. mul iple and di e en
asks, which depend on he pa icula i em in ol ed.
2 RAM+C MODELS
2.1 Model o a single i em
2.1.1 Age-dependen ailu e a e model inco po a ing impe ec main enance
As p oposed in [6], he in eg a ion o es ing and main enance e ec i eness was add essed in an imp o ed
APSA. Fo applica ion, speci ic ageing models o he ailu e a e need o be used in he equa ions o he
una ailabili y and cos models o ob ain speci ic nume ical esul s which can be used o analyze he in luence
o ageing, impe ec main enance and es ing.
So, he e ec o main enance on he age o he i em and on i s eliabili y is included based on a model o
impe ec main enance. Impe ec main enance models conside ha each main enance ac i i y educes he
age o he i em by some deg ee, depending on i s e ec i eness. Among he di e en models o impe ec
main enance ha can be ound in he li e a u e, his pape conside s he P opo ional Age Reduc ion (PAR)
model and he P opo ional Age Se back (PAS) model p oposed in Re s. [2, 3]. The selec ion o he mos
app op ia e model in each case depends on he i em ype, ailu e mechanism and so o main enance ac i i y.
In he PAR app oach, each main enance ac i i y is assumed o educe p opo ionally he i em age gained om
he p e ious main enance. Howe e , PAS model conside s ha he main enance ac i i y educes
p opo ionally, in a ac o o

, he age ha he i em has immedia ely be o e i en e s main enance. In hese
models, he e ec o main enance is in oduced by using an e ec i eness pa ame e 

 anging in he
in e al [0, 1]. I
0

, he p e ious models simply a e educed o an "As Bad as Old" model (no mally
co ec i e main enance), while i
1

a e educed o an "As Good as New" model (no mally o e haul
main enance). Fo p e en i e main enance,

 anges in in e al ]0, 1[.
In he li e a u e, one can ind di e en componen eliabili y models p oposed o add ess he e ec o
equipmen ageing, such as linea model, Exponen ial, Weibull, e c [1].
In his wo k, wo eliabili y models, Weilbull and Linea , and he impe ec main enance models p esen ed
abo e, PAS and PAR, a e conside ed o model he age-dependen ailu e a e. Weibull dis ibu ion is widely
used in eliabili y and li e da a analysis o ep esen equipmen ageing wi h ime due o i s e sa ili y [3].
Linea dis ibu ion is he simples way o de elop an age-dependen eliabili y model, which assumes ha he
ailu e a e has a linea beha iou wi h componen age depa ing o m an ini ial alue. This assump ion, when
applicable, simpli ies he modelling. In addi ion, one can ind in he li e a u e ageing ac o s p oposed o
se e al componen s in Nuclea Powe Plan s [1, 9].
Acco ding o [2, 3], conside ing a linea ageing model and impe ec main enance models can be ob ained an
a e aged s andby ailu e a e,
*

, o e he i em’s li e based on a double a e aging p ocess [3] which is gi en
by:




)2(
··
2
0
*
 M
PAS model (1)





 )1)·(1(1···
2
1
0
*
M
RP
M

PAR model (2)
whe e,
0

is he baseline ailu e a e when he i em is new,
M
is he main enance in e al,
RP
is he enewal
pe iod and

is he linea ageing a e.
Acco ding o [3], conside ing a Weibull ageing model and PAR o PAS model can be ob ained an a e aged
s andby ailu e a e,
*

, o e he i em’s li e based on a double a e aging p ocess [24] which is gi en by:
))1(1·(
)·(
1
0
*








M
PAS model (3)





)·2)·(1·(
)·())1·(2·(
0
*


 RP
MRPM
PAR model (4)
whe e,

and

a e he shape and scale ac o s, espec i ely. No e ha he Weibull dis ibu ion simpli ies o
he linea one o shape ac o equal o 2 and he scale ac o equal o√
⁄.
2.1.2 Age-dependen ailu e a e model add essing es e iciency
By es ing, componen ailu es can be de ec ed ha may ha e occu ed since he las es o he ime when he
componen was las known o be ope a ional. The main objec i e o su eillance es is o de ec hidden
ailu es so ha he componen can be es o ed o i s ope a ional s a e. Fo example, as p oposed in Re . [19], i
can be seen like a es ing co e age o ailu e mechanisms, whe e co e age is de ined as a sha e o de ec ed an
unde ec ed ailu es by es ing. Al e na i ely, Re . [10] de ines es e iciency like he p obabili y ha a gi en
ailu e is de ec ed by he es .
In bo h p e ious cases, es e iciency can be ep esen ed by a single pa ame e
η
. Re . [9] and [10] gi e
alues o
η
 o es e iciency o se e al componen ypes. As a esul , he conside a ion o a es e iciency
spli s he o al age-dependen ailu e a e in o wo age-dependen ailu e a e modes: de ec ed and unde ec ed.
UD* λλλ 
(5)
whe e he es e iciency anges in he in e al [0, 1]. In eqn. (5), he i s con ibu ion ep esen s he age-
dependen ailu e a e associa ed wi h de ec ed ailu es by es ing,
D
λ
, and he second pa ep esen s he
age-dependen ailu e a e associa ed wi h unde ec ed ailu es by es ing,
U
λ
, which can be de i ed using he
co esponding o mula ion o
*
λ
using eqn. (1) o eqn. (4).
*D ληλ 
(6)
*
1λη)(λU
(7)
On he o he hand, a la ge numbe o c i ical componen s o e akes unc ional es s mos ly pe o med
du ing e uelling o NPP, whe e he e uelling In e al (RI) anges be ween 12 and 24 mon hs, so ha
ypically RI could be se equal o 18 mon hs. The unc ional es o en in ol es es ing ull pe o mance o he
componen capaci y, so ha i pe o ms e y close o eal condi ions in case o eme gency. Then, he
e iciency o such a unc ional es should be e y close o one in de ec ing hidden ailu es. Simila ly o he
su eillance es s, in eliabili y e minology, he unc ional es in e als (o en adop ing he RI) a e called
BAO in e als since he componen age coming ou o he es is basically he same as he componen age
going in o he unc ional es , i.e. he componen is as old wi h ega d o i s age.
Thus, c i ical i ems o NPP sa e y may o e ake a leas wo es s: one su eillance es and ano he
unc ional es . Consequen ly, o add ess such a second o e uelling unc ional es , he unde ec ed age-
dependen ailu e a e, gi en by eqn. (7), should spli in o wo new con ibu ions: de ec ed and unde ec ed
a e he e uelling unc ional es , o yield
U
RI
UD ληλ 
(8)
U
RI
UU ληλ  )1(
(9)
whe e he es e iciency o he e uelling unc ional es R anges also in he in e al [0, 1], bu e y close
o one now. In addi ion, eqn. (8) ep esen s he age-depended ailu e a e con ibu ion associa ed wi h
de ec ed ailu es only a e he e uelling unc ional es , while eqn. (9) ep esen s he age-dependen ailu e
a e con ibu ion associa ed wi h ailu es ha emain unde ec ed e en a e he e uelling unc ional es .
The o mula ion p oposed in eqns. (5) o (9) can accommoda e a numbe o assump ions made in each
applica ion conside ed.
2.1.3 Una ailabili y models
The una ailabili y con ibu ions o a single i em no mally in s and-by a e di ided in o wo ca ego ies: a)
una ailabili y due o ailu es, i.e. un eliabili y e ec , and b) una ailabili y due o es ing and main enance
down imes, named he down ime e ec .
a) Un eliabili y con ibu ions
Adop ing he basis o he o mula ion o un eliabili y con ibu ions in Re . [6] conside ing he con ibu ions
in oduced in sec ions 2.1.1 and 2.1.2, he i em una ailabili y due o un eliabili y con ibu ions can be
e alua ed using he ollowing equa ions :
TIλuDD  2
1
(10)
RIλuUDUD  2
1
(11)
LλρuUUUU  2
1
(12)
whe e uD is he un eliabili y con ibu ion due o de ec ed ailu es by su eillance es ing, uUD is he
un eliabili y con ibu ion due o unde ec ed ailu es by su eillance es ing ha a e hen de ec ed by a second
unc ional es s and uUU is he un eliabili y con ibu ion due o unde ec ed ailu es by bo h su eillance and
unc ional es s . In addi ion, he ollowing no a ion has been used:
 = cyclic o pe -demand ailu e p obabili y,
D= de ec ed ac ion o age-dependen s and-by ailu e a e (sec ion 2.1.2),
UD = unde ec ed ac ion o age-dependen s and-by ailu e a e ha is hen de ec ed (sec ion 2.1.2),
UU = unde ec ed ac ion o age-dependen s and-by ailu e a e ha emains unde ec ed (sec ion 2.1.2),
TI = su eillance es in e al,
RI
= unc ional es in e al,
L = li e o he i em.
Table 4. Decision a iables: Tes and Main enance In e als.
Mul i-Objec i e op imiza ion unde cos and una ailabili y c i e ia has been pe o med using he non-
domina ed So ing Gene ic Algo i hm (NSGA-II) [32] oolbox in Ma lab using eqn. (25) as objec i e
unc ion. Rele an pa ame e s used in he op imiza ion p ocess a e showed in Table 5.
Table 5. NSGA-II pa ame e s
Six op imiza ion cases has been de eloped adop ing, in pa o as a whole, he se o decision a iables
p esen ed in Table 4. Lowe and uppe bounds ha e been adop ed o he decision a iables, which allows
sea ching o solu ions in he desi ed domain o easible ones. Thus, TIi (i = 1,3) mus ange in he in e al
[24, 80000] while Mj (j=1,4) mus ange in he in e al [720, 80000]. As said, he ini ial su eillance es and
main enance in e als a e TIi = 2184 and Mj = 4320 ( i=1,3 and j=1,4).
Table 6 shows he six op imiza ion p oblems ha ha e been o mula ed and sol ed. All cases adop s he same
objec i e unc ion consis ing o bo h una ailabili y and cos s o he HPIS, which a e calcula ed using
eliabili y and main enance da a showed in Tables 1 o 3, and he ini ial o op imized alues o he decision
a iables in Table 4 depending on he pa icula case. The NSGA-II algo i hm wi h he same pa ame e s
shown in Table 5 is used o all six cases.
Table 6. Cases s udied
Cases 1 o 3 adop es e iciency equal o one. This means una ailabili y o each componen ese s o he
esidual alue, no mally ze o, a e he su eillance es , i.e. he su eillance es is able o de ec wha e e
hidden ailu e o he componen and he e o e i is assumed he componen is a ailable a e he es p o ided
ha he componen is no ound ailed a he es . Cases 4 o 6 conside s a es e iciency o each MDP and
MOV equal o 0.6 and 0.4, espec i ely, which a e aken om NUREG 5587 [10]. In addi ion, Case 1 and 4
add ess su eillance es in e al (TI) op imiza ion only. Case 2 and 5 add ess op imiza ion o bo h
su eillance es in e als (TI) and main enance in e als (M). Case 3 and 6 add ess a e simila o he p e ious
one. Howe e , now main enance is g ouped ei he by elec ical o by mechanical main enance, conside ing
ha main enance o each g oup sha e he same pe iod. The e o e, now M1 is se equal o M3 and M2 is se
equal o M4.
Figu e 4 and Figu e 5 show he esul s o he op imiza ion p ocess. Figu e 4 shows he Pa e o F on s
co esponding o Cases 1 o 3. Figu e 5 shows he Pa e o F on s co esponding o Cases 4 o 6.

Figu e 4 shows ha be e esul s a e ob ained when he whole se o TI and M a e conside ed in he decision
making o he op imiza ion p oblem (Cases 2 and 3) as compa ed o he wo s esul s ound o he case whe e
only he se o TI is op imized (Cases 1). The alue o una ailabili y and cos ob ained a e signi ican ly lowe
in Cases 2 and 3. In addi ion, be e esul s a e ound unde Case 2 as compa ed o Case 3 in e ms o op imal
una ailabili y and cos o he HPIS. This means ha he bes esul s can be ound by including he whole se
o decision a iables and allowing lexibili y in he decision making. No e ha in Case 3 main enance
ac i i ies a e g ouped unde elec ical and mechanical ypes only and he e o e he decision space is educed.
Simila esul s can be ound in Figu e 5.
On he o he hand, by compa ing Figu es 4 and 5, one can ealize he impo ance o su eillance es
e iciency, since he una ailabili y o he HPIS is unde es ima ed in all cases ep esen ed in Figu e 4. In
addi ion, when a es e iciency lowe han one is conside ed, which is a mo e ealis ic assump ion based on
da a a ailable, he e is no so big di e ence be ween g ouping o no main enance ac i i ies in o elec ical and
mechanical ypes, see Cases 5 and 6 in Figu e 5 as compa ed o hei co esponding Cases 2 and 3 in Figu e 4.
Figu e 4. Pa e o F on ob ained o Cases 1 o 3
Figu e 5. Pa e o F on ob ained o Cases 4 o 6
7. CONCLUDING REMARKS
Many app oaches ha e been sugges ed in he pas o op imize he su eillance es and main enance in e als
o a sys em based on a ious analy ical una ailabili y and cos models. Mos o hese app oaches do no
conside simul aneously and explici ly he impac o equipmen ageing, main enance e ec i eness and
su eillance es ing e iciency, in pa icula o componen s consis ing o mul iple i ems.
This pape p oposes a new app oach o RAM modelling ha simul aneously accoun s o equipmen ageing
and main enance e ec i eness and es ing e iciency o equipmen consis ing o mul iple i ems. This model
is hen used o ace he p oblem o he mul i-objec i e and simul aneous op imiza ion o es ing and
main enance in e als o ageing equipmen consis ing o mul iple i ems.
The esul s ob ained in he applica ion case show subs an ial di e ences, mainly in he assessmen o he
HPIS sys em una ailabili y, when ageing and bo h main enance e ec i eness and es ing e iciency a e
conside ed explici ly. Thus, he example o applica ion shows ha main enance e ec i eness in managing
ageing and es e iciency in de ec ing hidden ailu es ha e a signi ican impac on he esul s ound, so ha ,
u u e esea ch should be di ec ed owa ds he es ima ion, o e en imp o emen , o main enance e ec i eness
and es e iciency and he assessmen o hei e ec on ailu e causes and ailu e modes a ec ing RAM o
sa e y equipmen , since hey impac he accu a e planning and op imiza ion o es ing and main enance
ac i i ies based on RAM c i e ia.
The esul s o he example o applica ion demons a e ha he op imiza ion algo i hm p o ide he bes
solu ions when he op imiza ion p oblem is o mula ed and sol ed conside ing ull lexibili y in he
implemen a ion o es ing and main enance ac i i ies aking pa o such an in eg a ed RAM model o
mul iple i ems componen s. Thus, he mul i-objec i e op imiza ion p oblem p o ide a Pa e o on o
solu ions co esponding wi h di e en alues o he decision a iables ( es and main enance). Each one o he
se o op imal (and di e en ) combina ion o es and main enance in e als co esponds o one ealiza ion o
he Pa e o on , which p o ides balance be ween sys em una ailabili y and o al cos . In NPP ope a ion,
decision make would selec he mos app op ia e combina ion o abo e op imized se ha co esponds o he
necessa y balance be ween una ailabili y and cos .
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ACKNOWLEDGMENTS
Au ho s a e g a e ul o he Spanish Minis y o Science and Inno a ion o he inancial suppo o his wo k
(Resea ch P ojec ENE2013-45540-R) and he doc o al ellow (BES-2011-043906) and (BES-2014-067602).
Figu e. 1. High P essu e Injec ion (HPIS) sys em
MOTOR DRIVEN PUMP (MDP)
MOTOR PUMP
FC1M, ...
MAINTENANCE ACTIVITIES
FC1P, ...
FAILURE
CAUSES
MM MP
FM1MDP, ...
TESTS
FAILURE
MODES
RI (RI)
TI ()
T1MDP T2MDP
MM () MP ()
Figu e 2. O e iew o basic in e ac ions o MDP
MOTOR OPERATED VALVE (MOV)
ACTUATOR VALVE
FC1A, ...
MAINTENANCE ACTIVITIES
FC1V, ...
FAILURE
CAUSES
MA MV
FM1MOV, ...
TESTS
FAILURE
MODES
RI (RI)
TI ()
T1MOV T2MOV
MM () MV ()
Figu e 3. O e iew o basic in e ac ions o MOV
PUMP A (PA)
PUMP B (PB)
PUMP C (PC)
VALVE 1
(V1)
VALVE 2
(V2)
VALVE 3 (V3)
VALVE 4
(V4)
VALVE 5 (V5)
VALVE 6
(V6)
VALVE 7
(V7)
FROM RWST
INJECTION
PATH A
INJECTION
PATH B
Figu e 4. Pa e o F on ob ained o Cases 1 o 3
Figu e 5. Pa e o F on ob ained o Cases 4 o 6
Table 1. Models and pa ame e s ob ained in he es ima ion p ocess
1,10E+05
1,15E+05
1,20E+05
1,25E+05
1,30E+05
1,35E+05
1,40E+05
1,45E+05
1,50E+05
1,55E+05
1,60E+05
0,000 0,001 0,001 0,002 0,002 0,003 0,003
Cos (x) (€)
Una ailabili y (x)
Case 1 Case 2 Case 3
0,00E+00
5,00E+05
1,00E+06
1,50E+06
2,00E+06
2,50E+06
3,00E+06
3,50E+06
4,00E+06
0 0,01 0,02 0,03 0,04 0,05 0,06
Cos (x) (€)
Una ailabili y (x)
Case 4 Case 5 Case 6

Mo o ope a ed al e (MOV)
Mo o d i en pump (MDP)
Val e
Ac ua o
Pump
Mo o
Uni s
ρ
1.81E-03
1.25E-05
5.18E-04
1.25E-05
[-]
λ0
6.80E-06
7.00E-06
2.30E-05
3.89E-06
[1/h]
IM model
PAR
PAS
PAR
PAS
--

0.76
0.84
0.77
0.29
--
Ageing Model
Linea
Weibull
Linea
Weibull
--

1.73E-09
--
2.37E-09
--
[h-2]

--
4.87
--
7.47
--

--
33347
--
15397
--
Table 2. Da a o es s and main enance o MDP and MOV
Mo o ope a ed al e (MOV)
Mo o d i en pump (MDP)
Val e
Ac ua o
Pump
Mo o
Uni s
σ
1
1
10
10
[h]
TI
2184
2184
2184
2184
[h]

{1, 0.6}
{1, 0.6}
{1,0.44}
{1,0.44}
--
RI
13140
13140
13140
13140
[h]
RI
1
1
1
1
--
τ
1
1
4
4
[h]

2,6
2,6
24
24
[h]
Γ
6
6
50
50
[h]
L
122640
122640
122640
122640
[h]
Table 3. Componen i em cos pa ame e s
Uni s
Val e
Ac ua o
Pump
Mo o
c
[€/yea ]
400
400
100
100
cc
[€/yea ]
25920
2880
2808
312
cm
[€/yea ]
7200
800
720
80
co
[€/yea ]
32400
3600
3240
360
Table 4. Decision a iables: Tes and Main enance In e als.
In e al
Componen
I em
Type o
Main enance/Tes
Main enance s a egy
M1
V1, V2,V3,V4,V5,V6,V7
Val e
Mechanical
M2
V1, V2,V3,V4,V5,V6,V7
Ac ua o
Elec ical
M3
PA, PB, PC
Pump
Mechanical
M4
PA, PB, PC
Mo o
Elec ical
Tes ing s a egy
TI1
V1, V2
--
Su eillance Tes
TI2
V3, V5, PA, PB, PC
--
Su eillance Tes
TI3
V4, V6, V7
--
Su eillanceTes
Table 5. NSGA-II pa ame e s
Pa ame e
Value
Gene a ions
1000
Popula ion Size
100
C osso e a e
2/7
C osso e ype
A i hme ic C osso e
Mu a ion a e
2/7
Mu a ion ype
Gaussian Mu a ion
S opping c i e ia
Maximum gene a ions numbe
Table 6. Cases s udied
Case #
Tes E ec i eness
{MDP, MOV)
Desc ip ion
Decision a iables
Case 1
{1,1}
TI op imiza ion
{TI1, TI2, TI3}
Case 2
{1,1}
TI and M op imiza ion
{TI1, TI2, TI3, M1, M2, M3, M4}
Case 3
{1,1}
TI and M op imiza ion
Main enance g ouped by ype o
main enance: elec ical o mechanical
{TI1, TI2, TI3, M1, M2, M3, M4}
being:
M1=M3
M2=M4
Case 4
{0.6, 0.4}
TI op imiza ion
{TI1, TI2, TI3}
Case 5
{0.6, 0.4}
TI and M op imiza ion
{TI, TI2, TI3, M1, M2, M3, M4}
Case 6
{0.6, 0.4}
TI and M op imiza ion
Main enance g ouped by ype o
main enance: elec ical o mechanical
{TI1, TI2, TI3, M1, M2, M3, M4}
being:
M1=M3
M2=M4
Highligh s
New app oach o RAM modelling
Equipmen ageing and main enance e ec i eness and es ing e iciency explici ly in
RAM models
Equipmen consis ing o mul iple i ems
Mul iple objec i e op imiza ion p oblem (MOP) unde una ailabili y and cos c i e ia
Simul aneous op imiza ion o es ing and main enance in e als