RELIABILITY AND SAFETY OF ELECTRONICS DEVICES VOLUME: 14 |NUMBER: 2 |2016 |JUNE
Fi e Risk in MTBF E alua ion o UPS Sys em
S e ano ELIA, Alessio SANTANTONIO
Depa men DIAEE – Elec ical Enginee ing Sec ion, Sapienza Uni e si y,
Piazzale Aldo Mo o 5, 00185 Rome, I aly
[email p o ec ed], alessio.san an onio@ou look.i
DOI: 10.15598/aeee. 14i2.1662
Abs ac . The eliabili y imp o emen o no-b eak e-
dundan elec ical sys ems is he i s aim o he p o-
posed s a egy. The ailu e o some UPS (Unin e up -
ible Powe Supply) sys em may lead o he i e occu -
ence. The mos used elec ical con igu a ions a e p e-
sen ed and discussed in he pape . The inno a ion o
he p oposed me hod consis s o aking in o accoun he
i e isk o imp o e he accu acy o wi ing con igu a-
ion and componen s’ ailu e a e. Tho ough esea ch
on MTBF (Mean Time Be ween Failu e) da a has been
pe o med o each wi ing componen and UPS. The
i e isk is aken in o accoun in oducing an equi a-
len i e block in he Reliabili y Block Diag am scheme;
i has an MTBF alue calcula ed o m yea ly s a is ics
o UPS i e e en s. The eliabili y o he mos used
UPS elec ical con igu a ions is e alua ed by means o
he RBD me hod. Di e en elec ical sys ems ha e been
in es iga ed and compa ed based on MTBF. The impo -
ance o i e compa men a ion be ween wo o mo e
UPS’ connec ed in pa allel is p o ed he e.
Keywo ds
Elec ical ins alla ion, ailu e a e, i e isk,
MTBF, no-b eak powe sys em, RBD, edun-
dan elec ical sys em, eliabili y, UPS.
1. In oduc ion
Ten yea s o main enance ac i i y in no-b eak elec i-
cal ins alla ions e eals a lo o design e o s and a lack
o eliabili y. Cu en ly, i is common o e alua e he
eliabili y only o he equipmen and o elec ical sys-
em’ componen s. Today, i can be no iced ha he e is
a de ec in eliabili y e alua ion o all p ojec choices.
Many eal i e case occu ences on UPS we e caused
by powe elec onic o ba e y ail. The p oduce s do
no conside i e haza d signi ican o he UPS de ice
and pe o m es s only in s anda d and good main e-
nance condi ions. The UPS machines a e e y ulne a-
ble and subjec ed o inadequa e main enance, o e ol -
ages, high empe a u e, wo king condi ions, and o he
elec ical sys em mal unc ions. Nowadays edundan
UPS’ a e no isola ed by a i e compa men . No-b eak
sys ems a e o en designed ollowing a w ong guideline.
The s anda d p ocedu e conside ed o eliabili y im-
p o emen consis s o a simple ins alla ion o wo UPS’,
which a e connec ed in pa allel. UPS powe elec onic,
Con ol Uni , manual and s a ic bypass, ba e ies and
o he sys em componen s a e usually ins alled in he
same oom. All de ices a e, he e o e, exposed o he
same i e isk. Wo king UPS uni may be in ol ed in
i e e en caused by he ailu e o ano he UPS uni in
he same oom, hus ende ing he sys em edundancy
ine ec i e. Mo eo e , an eme gency manual bypass
wi ed ou o he UPS oom is ne e ins alled. In hose
condi ions a i e e en en ails ce ainly he comple e
ailu e o he no-b eak sys em. A sho and con ained
i e is also su icien o gene a e smoke and isk o oxic
ai ; in his case nobody can access he UPS oom and
echnicians a e obliged o communica e immedia ely
wi h he di ec o o in o m him o he imminen ail-
u e and ecommend o s op all cu en ope a ions. A
lo o i e case s udies ha e been in es iga ed; he com-
ple e ailu e o he no b eak elec ical sys em was o en
due o he lack o i e compa men a ions be ween wo
UPS.
2. Reliabili y Model
The eliabili y e alua ion o each elec ical con igu a-
ion is based on he Reliabili y Block Diag am model
(RBD) [1], [2]. By means o his me hod, he MTBF o
UPS, Con ol Uni , ba e ies, swi ches, and o he com-
ponen s a e ep esen ed. Da a on UPS i e occu ence
equency we e ob ained du ing en yea s o consul an
ac i i y in he hospi als. In abou a hund ed o case
s udies he exis ence o wo UPS’ oom i e e en s is
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p o ed pe yea (2 % pe yea ). Two hypo heses a e
necessa y o e alua e he ailu e a e [3] by s a is ical
da a on i e isk. Fi s ly, he ailu e a e is cons an in
ime. Secondly, b eak componen s a e no epai able
bu quickly eplaceable (MT T R = 0). The a e age
i e ailu e a e is de ined as he a io be ween numbe
o i es and numbe o s udied e en s pe ime. I is
shown in Eq. (1):
λAV G =NF
NT OT ·T,(1)
whe e NFis he quan i y o i e e en s, NT OT is he
numbe o obse ed sys ems and Tis he obse a ion
ime. Subsequen ly he MT BF alue is calcula ed [4]
in Eq. (2):
MT BFF=1
λAV G
=NT OT ·T
NF
=100 ·8760
2=
= 438000 h.
(2)
Using he Eq. (2), he eliabili y calcula ion can be
based on di e en i e s a is ics. Mo eo e , calcula ion
can be de eloped implemen ing a pa ame ic analy-
sis a ying he alue o i e s a is ic. The eliabili y
e alua ion model is used based on hese hypo heses.
Fi s ly, UPS is only conside ed as a no b eak sys em
ha a oids ol age dips. Secondly, he con inuous en-
e gy sou ce is based only on powe supplie ’s g id o
eme gency diesel gene a o .
3. MTBF Da a
MTBF da a on s udied componen s ha e been de-
duced by an accu a e s a is ical su ey. Used da a
we e ob ained om: Gold Book [5], some pape s
[1], [6], [7], [8], [9] and many da ashee s. The UPS’
MTBF is e alua ed including he p esence o he on-
boa d au oma ic s a ic bypass and ba e ies. MTBF
alue o he Fi e Risk Fac o block is poin ed ou by
he main enance ac i i y expe ience, Eq. (2). The a -
e age alues o MTBF o all componen s a e poin ed
ou in Tab. 1.
Tab. 1: A e age MTBF o no-b eak sys em’s componen s.
Componen s Symbol Failu e a e
[ ailu e·h−1]MTBF [h]
Ba e y (lead acid) BAT 8.52086·10−71173590
Ci cui b eake CB 4.348·10−6229991
Comple e UPS module
(in e nal STS and
ba e ies included)
UPS 1.3779·10−572574
Con ol Uni CU 1.33333·10−6750000
Fi e Risk Fac o FRF 2.28311·10−6438000
In e e INV 0.00002 50000
Rec i ie REC 0.00002 50000
S a ic T ans e Swi ch STS 9.79499·10−6102093
Swi chgea Bus Ba SBB 1.08334·10−6923068
4. MTBF E alua ion o
Va ious No-B eak Elec ical
Sys ems
4.1. One UPS
The eliabili y o a base con igu a ion wi h only one
UPS is shown in his subsec ion.
UPS ROOM
UPS
SHORT-BREAK
BUSBAR
CB
CB
NO-BREAK
BUSBAR
LOW VOLTAGE SWITCHGEAR
Fig. 1: No-b eak sys em wi h one UPS.
The Reliabili y Block Diag am o he one UPS con-
igu a ion is shown in Fig. 2.
CB FRF UPS
SBB CB SBB
Fig. 2: RBD scheme o no-b eak sys em wi h one UPS.
The calcula ion shown in Eq. (3) e eals he o-
al MTBF o he sys em con igu a ion wi h only one
UPS.
MT BFT=
1
1
MT BFSBB
+1
MT BFCB
+1
MT BFF RF
+· · ·
1
· · ·
1
MT BFU P S
+1
MT BFCB
+1
MT BFSBB
=
= 37140 h= 4.2yea s.
(3)
4.2. Two UPS Wi hou Fi e
Compa men a ions
The con igu a ion wi h wo UPS‘ connec ed in pa allel
is conside ed he e. Each UPS has a a ed powe g ea e
han he load demand. Machines a e ins alled in he
same oom oge he wi h he ba e ies and wi hou any
i e compa men a ions. The espec i e con igu a ion
scheme is shown in Fig. 3. The RBD scheme o ha
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UPS1
UPS ROOM
UPS2
SHORT-BREAK
BUSBAR
CB CB
CB CB
NO-BREAK
BUSBAR
CU
LOW VOLTAGE SWITCHGEAR
Fig. 3: No-b eak sys em wi h wo UPS wi hou i e compa -
men a ions.
sys em is shown in Fig. 4, whe e i mus be highligh ed
ha he Fi e Risk Fac o o bo h UPS‘ in luences he
en i e sys em.
CU
CB
CB
UPS2
SBB
CB
CB
UPS1
SBBFRF1 FRF2
Fig. 4: RBD scheme o no-b eak sys em wi h wo UPS wi hou
i e compa men a ions.
The MTBF o ha con igu a ions is can be com-
pu ed wi h he use o Eq. (4), Eq. (5), Eq. (6) and
Eq. (7):
MT BFU P S =
=1
1
MT BFCB
+1
MT BFU P S
+1
MT BFCB
=
= 44494 h.
(4)
RUP S1U P S2=RUP S1+RU P S2−RU P S1·RU P S2,(5)
whe e R[8] is he eliabili y and i is de ined as
R=e
−
1
MT BF
· .
MT BFU P S1UP S2=Z∞
0
RUP S1U P S2·d =
= 66741 h.
(6)
MT BFT=
=1
1
MT BFSBB
+1
MT BFF RF 1
+1
MT BFF RF 2
+· · ·
1
· · ·
1
MT BFCU
+1
MT BFU P S1UP S2
+1
MT BFSBB
=
= 43385 h= 5 yea s.
(7)
Only one Con ol Uni is usually ins alled o an eme -
gency load swi ching be ween wo UPS‘, ha choice
makes he MTBF wo se.
4.3. Two UPS in Di e en Fi e
Compa men s
The eliabili y o wo i e compa men ed UPS‘ is s ud-
ied he e. In Fig. 5 and Fig. 6, he e a e shown he sys-
em con igu a ion and he RBD scheme espec i ely.
UPS1
UPS ROOM1
UPS2
UPS ROOM2
SHORT-BREAK
BUSBAR
CB CB
CB CB
NO-BREAK
BUSBAR
CU
LOW VOLTAGE SWITCHGEAR
Fig. 5: No-b eak sys em composed o wo UPS wi h i e com-
pa men a ions.
CU
CB
CB
FRF2 UPS2
SBB
CB
CB
FRF1 UPS1
SBB
Fig. 6: RBD scheme o no-b eak sys em wi h wo i e compa -
men ed UPS.
In his case, each Fi e Risk Fac o is ela ed exclu-
si ely o he espec i e UPS. Calcula ions o e alua e
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he o al MTBF a e ep esen ed in Eq. (8), Eq. (9),
Eq. (10) and Eq. (11):
MT BFU P S =1
1
MT BFCB
+1
MT BFF RF
+· · ·
1
· · ·
1
MT BFU P S
+1
MT BFCB
= 40391 h.
(8)
RUP S1U P S2=RUP S1+RU P S2−RU P S1·RU P S2.(9)
MT BFU P S1UP S2=Z∞
0
R12 ·d = 60587 h.(10)
MT BFT=1
1
MT BFSBB
+1
MT BFCU
+· · ·
1
· · ·
1
MT BFU P S1UP S2
+1
MT BFSBB
=
= 49987 h = 5.7 yea s.
(11)
4.4. Two UPS‘ and One STS wi h
Fi e Compa men a ions
Ano he sys em imp o emen consis s o ins alling a
sa e y ex e nal bypass o e wo UPS‘. All hese de-
ices mus be ins alled in di e en i e compa men ed
ooms. In he Fig. 7 and Fig. 8 he con igu a ion and
he RBD scheme a e shown espec i ely.
Acco ding o he p oposed sys em scheme, calcula-
ions o e alua e o al MTBF a e shown in Eq. (12),
Eq. (13), Eq. (14), Eq. (15), Eq. (16), Eq. (17), Eq. (18)
and Eq. (19).
MT BFU P S =1
1
MT BFCB
+1
MT BFF RF
+· · ·
1
· · ·
1
MT BFU P S
+1
MT BFCB
= 40391 h.
(12)
RUP S1U P S2=RUP S1+RU P S2−RU P S1·RU P S2.(13)
MT BFU P S1UP S2=Z∞
0
R12 ·d = 60587 h.(14)
MT BFU P S1UP S2CU =
=1
1
MT BFU P S1UP S2
+1
MT BFCU
= 56058 h.(15)
UPS1
UPS ROOM1
UPS2
UPS ROOM2
STS
STS ROOM
CB
SHORT-BREAK
BUSBAR
CB CB
CB CB CB
NO-BREAK
BUSBAR
CU
LOW VOLTAGE SWITCHGEAR
Fig. 7: No-b eak sys em made up o wo UPS and one STS wi h
i e compa men a ions.
CU
CB
CB
FRF2 UPS2
SBB
CB
CB
FRF1 UPS1
SBB
CB CB
STS
Fig. 8: RBD scheme o no-b eak sys em wi h i e compa -
men ed UPS and STS.
MT BFST S =
=1
1
MT BFCB
+1
MT BFST S
+1
MT BFCB
=
= 54080 h.
(16)
RUP S1U P S2CU ST S =RUP S1U P S2CU +
+RST S −RUP S1U P S1CU ·RST S .(17)
MT BFU P S1UP S2CUST S =
=Z∞
0
RUP S1U P S2CU ST S ·d = 82616 h.(18)
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MT BFT=
=1
1
MT BFSBB
+1
MT BFU P S1UP S2CUST S
+· · ·
1
· · ·
1
MT BFSBB
= 70070 h = 8 yea s.
(19)
The o al MTBF o compa men ed sys em is 8
yea s. Calcula ions ha e been also pe o med o he
case o absence o i e compa men a ions. Ins alling
wo UPS‘ and one STS in he same oom esul s in
MTBF o 6.4 yea s.
4.5. Th ee UPS‘ wi h Fi e
Compa men a ions
The sys em con igu a ion made o h ee UPS‘ ins alled
in di e en ooms is s udied he e. The con igu a ion
scheme is shown in Fig. 9.
UPS1
UPS ROOM1
UPS2
UPS ROOM2
UPS3
UPS ROOM3
CB
SHORT-BREAK
BUSBAR
CB CB
CB CB CB
NO-BREAK
BUSBAR
CU
LOW VOLTAGE SWITCHGEAR
Fig. 9: No-b eak sys em made o h ee i e compa men ed
UPS.
The espec i e RBD scheme is shown in Fig. 10.
The o al MTBF o he h ee UPS‘ con igu a ion
is compu ed using he Eq. (20), Eq. (21), Eq. (22),
CU CB
CB
CB
FRF2 UPS2
SBB
CB
CB
CBFRF3 UPS3
FRF1 UPS1
SBB
Fig. 10: RBD scheme o i e compa men ed h ee UPS con-
igu a ion.
Eq. (23), and Eq. (24).
MT BFU P S =
=1
1
MT BFCB
+1
MT BFF RF
+· · ·
1
· · ·
1
MT BFU P S
+1
MT BFCB
= 40391 h.
(20)
RUP S1U P S2=RUP S1+RU P S2−RU P S1·RU P S2.(21)
RUP S1U P S2UP S3=RU P S1U P S2+RU P S3−
−RUP S1U P S2·RUP S3.(22)
MT BFU P S1UP S2U P S3=
=Z∞
0
RUP S1U P S2UP S3·d = 76743 h.(23)
MT BFT=1
1
MT BFSBB
+1
MT BFCU
+· · ·
1
· · ·
1
MT BFU P S1UP S2U P S3
+1
MT BFSBB
=
= 60494 h = 6.9 yea s.
(24)
The o al MTBF o h ee compa men ed UPS‘ is
6.9 yea s. In case o absence o i e compa men s o
he same con igu a ion he eliabili y is s udied; and
MTBF o 5.1 yea s is ob ained o h ee UPS ins alled
in he same oom. Wi h espec o he con igu a ion
wi h wo UPS‘ and one STS, a li le dec ease o elia-
bili y is o be no iced. This is due o he be e MTBF
o he STS compa ed o he UPS. On he opposi e, his
h ee sys em UPS pe mi s all main enance ope a ions
du ing wo king ac i i ies.
5. Conclusions
Re ised s a is ical da a on MTBF componen s used
in no-b eak sys ems ha e been summa ized he e. A
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me hod o ake in o accoun he i e isk in a Reliabil-
i y Block Diag am model has been pe o med. The
eliabili y o se en di e en UPS con igu a ions has
been s udied by means o he RBD me hod. The o al
MTBF has been compu ed o each con igu a ion ak-
ing in o accoun he e ec o he de ices’ i e compa -
men a ion. The esul s o his compa a i e analysis a e
shown in Fig. 11.
Fig. 11: MTBF o di e en no-b eak powe sys ems by i e
compa men a ion.
These MTBF esul s can be also con e ed o yea ly
ailu e p obabili y alues by means o Eq. (25):
F P%=1
MT BF
·100.(25)
These esul s demons a e he impo ance o i e
compa men a ion o eliabili y imp o ing in edun-
dan UPS sys ems, especially o hospi als and sa e y
sys ems. The mo e sui able con igu a ion consis s o
wo UPS and one STS i e compa men ed, which
achie es he bes MTBF. Mo eo e , he h ee com-
pa men ed UPS‘ con igu a ion and pe mi s a comple e
main enance du ing sys em’s ope a ion.
Acknowledgmen
In his pa o he a icle he au ho s can exp ess hei
g a i ude o p ojec s om he esul s o which he a i-
cle has been w i en, o o people who ha e con ibu ed
o he esul s published in he a icle. I is no allowed
o inse any igu es o logos he e.
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Abou Au ho s
S e ano ELIA was bo n in Rome, I aly. He e-
cei ed his Deg ee in 1999 and he Ph.D. in 2003
in Elec ical Enginee ing om Sapienza Uni e -
si y o Rome. Now is employed as a P o esso a
he Elec ical Enginee ing Ins i u e o Sapienza
Uni e si y. His esea ch in e es s include powe
elec onics, elec ical sys ems, main enance, eliabili y,
sa e y, measu es, ene gy sa ing and enewable ene gy.
Alessio SANTANTONIO was bo n in Case a,
I aly. He is an Elec ical Enginee g adua ed a
Sapienza Uni e si y in 2014. Now is employed as labo-
a o y assis an a he Elec ical Enginee ing Ins i u e
o Sapienza Uni e si y. He collabo a es wi h some
elec icians’ companies on main enance p ocedu e o
elec ical powe sys ems. His esea ch in e es s include
powe sys ems, powe quali y, eliabili y, main enance.
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