The Jou nal o Na iga ion (2021), 74:4 931–943
doi:10.1017/S0373463321000291
RESEARCH ARTICLE
De e mining he likelihood o inciden s caused by human
e o du ing dynamic posi ioning d illing ope a ions
Zaloa Sanchez-Va ela,1,2*Da id Boullosa-Falces,2Juan L. La abe-Ba ena,2and
Miguel A. Gomez-Solaeche2
1Facul y o Ma i ime S udies, Uni e si y o Spli , Spli , C oa ia.
2Facul y o Enginee ing in Bilbao, Uni e si y o he Basque Coun y (UPV/EHU), Bilbao, Spain.
*Co esponding au ho . E-mail: zsanchez @p s .h
Recei ed: 5 Decembe 2020; Accep ed: 4 Ma ch 2021; Fi s published online: 23 Ma ch 2021
Keywo ds: dynamic posi ioning (DP), offsho e, isk minimisa ion, human ac o
Abs ac
The p obabili y o a human-caused inciden occu ing du ing dynamic posi ioning (DP) d illing ope a ions is
de e mined in his pape using bina y logis ic eg ession models buil wi h da a on 42 inciden s ha ook place
du ing he pe iod 2011–2015. Fo each case, a ange o a iables cha ac e ising he configu a ion o he DP sys em,
wea he condi ions and wa e dep h a e aken in o accoun . These a iables a e aken in o accoun o de elop a
logis ic eg ession model ha shows he likelihood o an inciden being caused by human e o . The esul s ob ained
show ha human-based inciden s a e significan ly mo e likely o occu when he e is a lowe usage o h us e s.
These esul s a e use ul o ocusing ou a en ion on a iables ha may be associa ed wi h inciden s a ibu able o
human e o , as well as o se ing ope a ional limi s ha could help o p e en hese inciden s and imp o e sa e y
du ing hese ope a ions.
1. In oduc ion
A dynamic posi ioning (DP) sys em allows a d illing uni o main ain posi ion and heading, while a he
same ime making su e he angle o he ise ( he line connec ing he pla o m wi h he d illing bi ) is as
close as possible o ze o. Despi e he high sa e y s anda ds o he offsho e d illing indus y, on occasions
he e ha e been acciden s wi h se e e consequences. Images o he explosions on he Deepwa e Ho izon
in he Gul o Mexico and Pipe Alpha in he No h Sea emain in he collec i e memo y (Singh e al.,
2010; Theophilus e al., 2017). These a e examples o acciden s ha occu ed due o loss o posi ion
du ing d illing ope a ions. In es iga ions in o a ali ies and/o o he acciden s a e published by he U.S.
Bu eau o Sa e y and En i onmen al En o cemen (2019); howe e , less se ious inciden s a e a ely he
subjec o such an in es iga ion and ins ead a e esol ed wi hin he company (Theophilus e al., 2017).
Indeed, lis s o inciden s a e conside ed highly confiden ial and a e a ely made public o accessible
o esea che s. None heless, i is known ha in he oil and gas indus y in gene al (Ka iuki and Löwe,
2007; Manca and B ambilla, 2012), and he offsho e d illing sec o in pa icula (Hogenboom e al.,
2020), inciden s due o di ec and indi ec human ac o ailings a e no a e.
I is impo an , in sa e y e ms, o iden i y he po en ial haza ds associa ed wi h gi en ope a ions, and
de e mine he p obabili y o inciden s occu ing and hei possible ou comes and consequences. This
app oach is commonly known as quan i a i e isk assessmen (QRA) (K is iansen, 2005). Al hough QRA
was ini ially applied o nuclea acili ies (Le ine and Rasmussen, 1984), i has since been ex ensi ely
applied in o he indus ies, including he oil and gas indus y, whe e he esul s ha e been e y sa is ac o y
©The Royal Ins i u e o Na iga ion 2021. This is an Open Access a icle, dis ibu ed unde he e ms o he C ea i e Commons A ibu ion
licence (h p://c ea i ecommons.o g/licenses/by/4.0/), which pe mi s un es ic ed e-use, dis ibu ion, and ep oduc ion in any medium, p o ided
he o iginal wo k is p ope ly ci ed.
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932 Zaloa Sanchez-Va ela e al.
(Kalan a nia e al., 2010). No ably, inadequa e isk managemen was ound o be a con ibu o y cause
in 27·1% o all ypes o ma i ime acciden s (Acejo e al., 2018).
O e he yea s, he idea o QRA has been imp o ed by he de elopmen o a ious me hodologies.
Some examples o hese a e haza d and ope abili y s udies (HAZOPs), ailu e mode and effec analysis,
aul ee analysis and e en ee analysis (Khan and Abbasi, 1998). Ano he me hod which has been
ex ensi ely used o isk analysis o DP inciden s is he Bayesian ne wo k, a g aphical model ha
ep esen s he dependency be ween a iables, using nodes and di ec ed links, making i possible o show
condi ional p obabili ies o a se o a iables (Ancione e al., 2020). This echnique is widely applied in
DP inciden analysis; howe e , he pa ame e s used o quan i ying he associa ed isk gene ally depend
on he bes judgemen o he pe son pe o ming he analysis (Mk chyan e al., 2015).
Thanks o he high le el o he p o ec i e measu es aken o p e en ca as ophic consequences, he
equency o acciden s in he oil and gas indus y can be conside ed low, and hence, hough da a on
acciden s a e published, he e is a limi ed olume o acciden da a a ailable o analysis. Tha is why
inciden s and nea -misses began o be used o upda ing isk analysis and managemen (Bie and Mosleh,
1990; Bie and Yi, 1995). S udies using his app oach ha e been epo ed by Khakzad e al. (2014);
Yang e al. (2015), and mo e ecen ly, A naldo Valdes e al.(2018), Rebello e al. (2019) and Shengli
and Yong u (2019).
P ecu so da a o an inciden is all he da a ha may influence a pa icula inciden . When such a
da abase is analysed, a specific pa e n may be seen ha could be used o p edic an inciden . This is he
p inciple unde lying he eg ession modelling echnique used in his pape . Se e al publica ions ha e
appea ed in ecen yea s documen ing he use o eg ession modelling o p edic ing and p e en ing
inciden s in he anspo a ion field. Fo example, in e es ial anspo a ion, logis ic eg ession mod-
elling was applied in he de ec ion o affic inciden s (Aga wal e al., 2016) and hei du a ion (Li e al.,
2015). In he ai anspo a ion sec o , always closely connec ed o he ma i ime indus y in e ms o
sa e y, his s a is ical app oach has been used o he p edic ion o human-e o inciden s (McFadden,
1997; E ja ac e al., 2018).
None heless, o he bes o ou knowledge, e y ew publica ions can be ound in he li e a u e con-
ce ning he use o logis ic eg ession modelling o he p edic ion o inciden s in he ma i ime indus y.
The ew excep ions include an a icle in which Hogenboom e al. (2020) used logis ic eg essions o
explain he influence o human e o on ma i ime inciden s; while Boullosa-Falces e al. (2017) applied
his me hod as pa o a a iable selec ion p ocess be o e hen cons uc ing a p edic ion model. Fu -
he , Weng e al. (2018) used mul inomial logis ic eg ession o in es iga e he likelihood o occu ence
o human e o s, and he eby ob ain a model based on me eo ological condi ions o p edic ing majo
acciden s in shipping. Fiskin e al. (2020) used logis ic eg ession o analyse he a iables con ibu ing
o ugboa acciden s.
1.1. Elemen s o DP du ing d illing ope a ions
D illing ope a ions ake place o e a wellhead. The p ima y unc ion o he DP sys em, known as he
ise angle o ise - ollow mode, is o main ain he posi ion o he d illing essel such ha he ise /s ack
angle, con aining he d ill s ing, is close o ze o, compensa ing o cu en s o idal flow as necessa y
(Mao e al., 2019). This angle is ha measu ed be ween he ise (on he op) and he wellhead o lowe
ma ine ise package (B ay, 2018). The ise diffe ence angle is moni o ed h ough senso s loca ed
a ound he lowe ma ine ise package by he dynamic posi ioning ope a o (DPO). The DPO is a
ce ified office o he wa ch who has comple ed a aining and ce ifica ion p og amme o be able o
hold his posi ion on boa d (The Nau ical Ins i u e, 2017). A wa ch ci cle sys em is c ea ed o enable
he DPO o moni o he mo emen s o he essel. When he ig is mo ing, a ious le els o ala m a e
se o ensu e he sa e y o he ope a ions a all imes (Mao e al., 2019).
The main isk in any DP ope a ion is he loss o posi ion, o excu sion, du ing ope a ions. The DPO
should, he e o e, eac apidly o co ec o mi iga e he consequences o any such loss (Hogenboom
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The Jou nal o Na iga ion 933
e al., 2020). The se e i y o hese acciden s is g ea e in ad e se wea he condi ions. (E ol e al., 2018).
The sys em o main aining he posi ion o he d illing ise consis s o a closed-loop con ol unc ion
ha ecei es in o ma ion om senso s ha measu e wind, cu en s, heading and posi ion. I sends a
command o he p opulsion uni s o coun e ac he o ces ha , acco ding o he in o ma ion a ailable,
end o ake he essel ou o posi ion. The desi ed posi ion is inpu by he DPO who supe ises he
ope a ion h ough a human–machine in e ace, also known as he DP console. The cen al elemen is
he con olle , composed o compu e s o p ocesso s, which es ablishes wo-way communica ion wi h
all o he DP elemen s ia he essel ne wo k.
To acqui e in o ma ion on he posi ion o he ig, posi ion e e ence sys ems (PRS) a e used. Al hough
on mos essels hese a e usually e e ed o as global posi ioning sys ems (GPS), in DP d illing
ope a ions he e a e se e al PRS which p o ide addi ional accu acy (B ay e al., 2015). Mos commonly,
d illing igs selec dual diffe en ial global na iga ion sa elli e sys ems (DGNSS) and hyd oacous ic
posi ion e e ence (HPR) sys ems, usually o he long-baseline ype. Tau wi es a e only used in shallow
wa e s, his ype o de ice no being a ailable o deep wa e s (B ay, 2018).
The mo ion o he essel is moni o ed wi h se e al senso s. Specifically, yawing is moni o ed wi h
he help o one o mo e gy ocompasses ha send in o ma ion abou he heading, while mo ion e e ence
uni s (MRUs) p o ide in o ma ion abou su ge and sway. Wind and cu en s a e also moni o ed o
di ec ion and speed, and his in o ma ion is sen o he con olle . The e a e wind senso s in a ious
posi ions onboa d he ig, in o de o a oid e o s due o windshields, u bulence nea s uc u es e c. Wi h
all his in o ma ion, he con olle is able o p edic he mo emen o he essel, and send app op ia e
commands o he p opelle s and h us e s (pi ch, e olu ions pe minu e, azimu h, udde angle) o
coun e ac associa ed o ces and main ain he ig in he desi ed posi ion. A i al pa o he DP sys em is
he powe supply. Diesel al e na o s, swi chboa ds, cabling, p opulsion mo o s and powe managemen
o m pa o he powe sys em equi ed o DP ope a ions (Sø ensen, 2011).
1.2. DP d illing acciden s
As DP echnology de eloped, i allowed he oil and gas indus y o explo e o hyd oca bons in deepe
wa e s (Rokse h e al., 2017). This p og ess b ough wi h i a numbe o challenges which in ol ed
he in oduc ion o new ope a ional guidance and he co esponding isk managemen . DP d illing
inciden s ha e been he subjec o a ious lines o academic esea ch. Chen e al. (2008) published a
pape analysing he sa e y o DP ope a ions based on a ba ie model. These au ho s iden ified a ange o
p oblems ha may a ise in each wa ch ci cle excu sion and es ablished ha only a DPO could a oid an
inciden by e u ning he uni o he posi ion wi hin he yellow wa ch ci cle, unde lining he impo ance
o his figu e. P ocedu es o de e mining he ajec o y o he essel when an excu sion akes place
we e s udied by Bhalla and Cao (2005); hei esul s can be used o imp o e d illing ope a ions by
es ima ing he disconnec ion imes. Sanchez-Va ela e al. (2021) p oposed a model o p edic ing loss
o posi ion o DP d illing ope a ions, whe e gene a o s and me eo ological condi ions we e he main
ac o s influencing excu sions.
1.3. The human elemen
Any ma i ime sys em is based on people (End ina e al., 2019). The le el o au oma ion s ill depends
on he figu e o he sys em ope a o , namely, a pe son. Any ope a ional ailu e has a s ong componen
o human e o (Abaei e al., 2019). When a DP sys em ails o keep he posi ion, he DPO mus ake
o e and egain con ol o e he deg aded s a us o he sys em. Fo his, p ocedu es a e in place and
ollowing hem allows sa e eco e y om an unexpec ed inciden . None heless, ope a o s’ skills and
seamanship may be key o adap ing p ocedu es, op imising hem o acili a e he e u n o a no mal
si ua ion (O e ga d e al., 2015). In his con ex , an addi ional challenge is he lack o ained and
expe ienced s aff o ca y ou DP ope a ions (Rahman e al., 2019).
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934 Zaloa Sanchez-Va ela e al.
A e y in e es ing app oach o analysing human ac o s in DP inciden s using a Bayesian ne wo k
was p oposed by Chae (2015), and building on his wo k, he same esea ch g oup applied a o mal
sa e y assessmen o hese ac o s, he na u e o he human e o being de e mined and some mi iga ing
measu es p oposed (Chae, 2017). Fu he , O e ga d e al. (2015) esea ched he human elemen du ing
DP inciden s conside ing diffe en le els o si ua ional awa eness. On he o he hand, Dong e al. (2017)
concluded ha mos acciden s du ing offsho e loading ope a ions a e caused by a combina ion o human
e o and echnical and o ganisa ional ailu es based on an app oach using an e en -and-cause diag am,
change analysis (desc ibing how he e en s de ia ed om common p ac ice) and ba ie analysis.
F om all he abo e, he impo ance o human e o s in DP ope a ions has been es ablished. This
pape p esen s a new app oach ha analyses a ange o wea he and sys em configu a ion a iables ha
migh be associa ed wi h human ac o s in ol ed in inciden s. Specifically, a ma hema ical model ha
can p edic he human na u e o an inciden is defined. Based on his model, ope a ional limi s can be
p oposed o imp o e he pe o mance and sa e y o he ope a ions.
The inciden s ocused on in his pape a e he DP ailu es ha happen du ing ma ine seabed d illing
ope a ions. The main objec i e o his pape is o find a ma hema ical exp ession ha desc ibes he
p obabili y o an inciden du ing DP d illing ope a ions ha ing been caused by human e o . Iden i ying
which a iables a e associa ed wi h an inciden being caused by human e o and in wha way may help
pinpoin he iskies si ua ions and he eby make i possible o ake s eps o imp o e he sa e y o d illing
ope a ions. F om he esul s ob ained, i would be possible o p opose ope a ional limi s o imp o e he
sa e y o d illing ope a ions.
2. Ma e ial and me hods
The esea ch eam ga he ed da a on inciden s om he In e na ional Ma i ime Con ac o s Associa ion
(IMCA) s a ion keeping e en epo s om 2011 o 2015. The inciden s ha ook place while he e we e
d illing ope a ions in p og ess we e selec ed, 50 cases in o al. The da a in he e en ee we e ca e ully
ex ac ed and a da abase was de eloped, including he a iables shown in Table 1. Once he da abase
had been c ea ed, some missing alues we e obse ed o some o he a iables. The co esponding
eigh cases we e elimina ed o make he sample uni o m, and his did no significan ly influence he
mean o median alues calcula ed o he sample. Thus, he sample analysed consis s o 42 cases.
This da abase was uploaded o he IBM SPSS S a is ics o Windows, e sion 23·0, so wa e. Desc ip-
i e s a is ics a e calcula ed o each a iable be o e de eloping bina y logis ic eg ession models.
Logis ic eg ession does no equi e da a on he independen a iables o be no mally dis ibu ed (Swee
and G ace-Ma in, 1999). Figu e 1 is a desc ip i e diag am showing he a iables aken in o accoun
o he eg ession modelling and hei ole du ing d illing ope a ions.
2.1. Bina y logis ic eg ession model
A bina y logis ic eg ession echnique is used o build a model ha ela es a ca ego ical dependen
a iable and one o mo e independen a iables, in such a way ha he condi ional p obabili y o an
e en occu ing is calcula ed (Kim e al., 2015). In his case, he dependen a iable is human cause, and i
will ake a alue o 0 i he e is no human cause and 1 i he e is a human cause. The es o he a iables
a e conside ed o be independen a iables. Excep o wa e dep h, pe cen age o h us e s online,
pe cen age o gene a o s online, wind o ce, cu en speed and wa e heigh , which a e all quan i a i e,
he independen a iables a e ca ego ical. Gi en his, he p og am manipula es hei alues in e nally,
in a way ha p oduces as many a iables as he e a e ca ego ies minus one. Fo example, he e a e fi e
ca ego ies o wind senso s, and he p og am p oduces ou a iables: wind senso s (i), i=1, 2, 3, 4.
Conside ing he alues o each case in he independen a iables, he p og am calcula es he p oba-
bili y o a human cause o each o hem. This p obabili y a ies be ween 0 and 1; he close o 0, he
lowe he p obabili y o a human cause, and he close o 1, he highe he p obabili y o a human cause.
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The Jou nal o Na iga ion 935
Table 1. Va iables included in he analysis o DP d illing inciden s, ex ac ed om e en ees o each
DP inciden epo ed.
Va iable Desc ip ion
Yea Yea in which he inciden occu ed
Wa e dep h (m) Dep h o wa e a which he d illing ope a ions ook
place
Pe cen age o h us e s online Numbe o h us e s online di ided by he o al
numbe o h us e s online and on s andby
Pe cen age o gene a o s online Numbe o gene a o s online, di ided by he o al
numbe o gene a o s online and on s andby
DGNSS Numbe o DGNSS sys ems ha a e selec ed in he
DP sys em
HPRs Numbe o hyd oacous ic sys ems ha a e selec ed in
heDPsys em
Tau wi es Numbe o au wi es in use du ing he ope a ions
Ine ia sys ems Numbe o ine ia sys ems in use du ing he d illing
ope a ions
Gy os Numbe o gy os in use du ing he d illing ope a ions
MRUs Numbe o MRUs in use du ing he d illing ope a ions
Wind senso s Numbe o wind senso s in use du ing he d illing
ope a ions
Wind o ce (in kno s) Fo ce o he wind blowing when he inciden happened
Cu en speed (in kno s) Speed o he cu en when he inciden happened
Wa e heigh (m) Heigh o he wa es when he inciden happened
Visibili y Visibili y when he inciden happened ca ego ised as
ollows: poo , <2 nm; mode a e, 2–5 nm; and good,
>5 nm (Me Office, 2020)
Main cause The leading cause, as defined in he classifica ion
p esen ed by he IMCA
Seconda y cause The seconda y cause, i p esen , as defined in he
classifica ion p esen ed by he IMCA
Excu sion Whe he o no an excu sion ook place
Human cause When ei he he main o seconda y causes ha e a
human o igin, hen 1 is en e ed; o he wise, 0 is
inse ed indica ing no human cause
Pe iod The fi s pe iod is om 2011 o 2013 and he second
om 2013 o 2015
In his way, each case is assigned a p obabili y P. This is impo an in o de o in e p e he coefficien s
in he eg ession.
The a iables a e selec ed by he chosen me hod: o wa d Wald. This me hod is based on adding o
emo ing a iables om he model by using wo s a is ics: he sco e o Rao and he Wald s a is ic. The
sco e o Rao allows compa ison o each independen a iable Xj wi h he null hypo hesis: Ho =𝛽j=0;
ha is, he pa ame e associa ed o he a iable in he model is null. The a iable ha p esen s he
minimum associa ed P- alue, always less han 0·05, o he s a is ic will be selec ed o en e he model.
Also o he Wald s a is ic he null hypo hesis can be compa ed Ho: 𝛽j=0, bu in his case i is o he
independen alues ha a e al eady selec ed and ha e en e ed he model. A a iable wi h a P- alue
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936 Zaloa Sanchez-Va ela e al.
Figu e 1. Va iables conside ed in he logis ic eg ession modelling classified acco ding o hei ole
du ing DP d illing ope a ions.
associa ed o he Wald s a is ic g ea e han 0·1 will be elimina ed, as his is by de aul he op ion o he
p og am (POUT(.10)).
The e will be se e al s eps in which independen a iables will be en e ed and elimina ed, acco ding
o he c i e ia exposed abo e. A s ep 0, only he cons an is in oduced o he model. Fo his cons an ,
i is impo an o measu e B, he es ima ed s anda d e o in he es ima ion, he Wald s a is ic and i s
deg ees o eedom and associa ed P- alue. When his P- alue is less han 0·1, he cons an is conside ed
o be significan .
A s ep 0, all he independen a iables a e ou o he model. One a iable has o be selec ed o en e
he model in s ep 1. The a iable wi h he smalles P- alue associa ed o he sco e which is less han
0·05 will be selec ed. I should be no ed ha he a iables c ea ed om a ca ego ical a iable should
be conside ed as a whole. In he case o wo o mo e a iables ha ing he same P- alue, he Rao sco e
should hen be conside ed, choosing he a iable wi h he bigge sco e o en e he model in s ep 1.
Fo he a iables in he equa ion, which a e al eady in he model, we should s udy he Wald s a is ic,
gi en by:
Wald =(𝐵/𝑆.𝐸.)2(1)
I i s P- alue is g ea e han 0·1 (ou pu alue, POUT), he co esponding a iable would be elimina ed
(as a whole in he case o he ca ego ical a iables). I is always elimina ed be o e he new a iable is
selec ed.
The sys em will examine he need o add o dele e a a iable un il no u he imp o emen s can be
made.
2.2. Ma hema ic model
The equa ion o he model is gi en by
𝑍=𝐵1𝑋1+...+𝐵𝑘𝑋𝑘+𝐵0(2)
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The Jou nal o Na iga ion 937
whe e Zis he linea p edic o unc ion o de e mine he excu sion o he inciden , X1,. . . , X𝑘 ep esen
each independen a iable, kbeing he numbe o independen a iables, and B0,B1, ...,B𝑘a e he
eg ession coefficien s ha mus be es ima ed.
T ans o ming Equa ion (1), we can ob ain he unc ion ha gi es he likelihood o an inciden ha ing
been caused by human e o :
𝑃=1/(1+𝑒−𝑍)(3)
In his way, he p obabili y o each case can be ob ained. A p obabili y alue o less han 0·5
indica es ha he model p edic s his case no o ha e been caused by human e o and a alue o mo e
han 0·5 indica es ha i p edic s he case o ha e been caused by human e o (while cases ob aining a
p obabili y alue o 0·5 a e unclassifiable and hence elimina ed).
To de e mine whe he he p edic ion o he model is accu a e, i needs o be alida ed. The alida ion
is based on obse ing he ac ual cause o a case inciden and compa ing i wi h he p edic ion om
he p oposed model. I he p edic ed and ac ual cause ma ch, hen i is said ha he model has good
p edic i e powe . Fu he mo e, conside ing he dynamic na u e o he inciden s, he model should be
alida ed in wo diffe en pe iods. The model should no only include he same independen a iables
wi h no significan changes in hei coefficien s bu also main ain he a e o p edic ion i i is o be
conside ed alid o use. The model is hen alida ed by compa ing he accu acy in wo diffe en pe iods.
Due o he size o he sample, he diffe en pe iods o e lap.
2.3. Goodness o i
The likelihood o an inciden ha ing been caused by human e o o no has been es ima ed, bu his does
no necessa ily ma ch he eal cause; ha is, acco ding o he model, he case may ha e a significan ly
g ea e p obabili y o belonging o he fi s g oup (no human cause) and ye belong o he second g oup
(human cause). Assessing goodness o fi in ol es checking how p obable he esul s ob ained o he
es ima ed model a e. This is based on compa ing he numbe o cases ha belong o he second g oup
(human cause) wi h he numbe expec ed i he model we e o be alid. This expec ed numbe is he
o al numbe o cases in he sample mul iplied by he es ima ed p obabili y o belonging o he second
g oup. When he pe cen age o he co ec ly classified cases is high, i is expec ed o p o ide good
esul s when p edic ing whe he o no an inciden has a human cause.
The diffe ence be ween he obse ed p obabili y (Pobse ed) and he es ima ed p obabili y
(Pes ima ed), he e o , is gi en by E𝑖:
𝐸𝑖=𝑃obse ed𝑖−𝑃es ima ed𝑖(4)
whe e E𝑖can ake alues in he ange (−1, 1). E𝑖will ake a alue o ze o i human e o is bo h he
es ima ed and he obse ed cause. S udying he dispe sion o he e o s o he model, he goodness o
fi can be e alua ed.
3. Resul s
All 42 cases we e included in he analysis. The e we e nine inciden s wi h a human cause, 21% o he
o al. The es had o he causes, such as en i onmen al condi ions, h us e /p opulsion ailu e o powe
ailu e. The s a is ical desc ip ion o he independen a iables is shown in Table 2.
As a fi s s ep, he a iables a e in oduced in he model one by one o check hei significance in
he model desc ibing he possibili y o an inciden being caused by a human e o . When a a iable is
conside ed indi idually in he model, we can obse e i s influence in he model wi hou in e e ence
om o he ac o s. The significance o he a iable is hus highes when i is conside ed indi idually.
This s ep is conside ed use ul as he a iables wi hou any significance can be elimina ed a his s age,
and in his way he p ocess o c ea ing he model can be simplified. Excep o he pe cen age o h us e s,
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938 Zaloa Sanchez-Va ela e al.
Table 2. S a is ical desc ip ion o he independen a iables included in he s udy.
Va iables Mean S anda d E o
Wa e dep h (m) 1409·238 112·0642
Pe cen age o h us e s (%) 92·55 2·341
Pe cen age o gene a o s (%) 64·5125 3·47436
DGNSS (no. o uni s) 2·33 0·121
HPR (no. o uni s) 1·40 0·103
Tau wi e (no. o uni s) 0·12 0·061
Ine ia sys em (no. o uni s) 0·05 0·033
Gy os (no. o uni s) 3·00 0·034
MRU (no. o uni s) 2·90 0·046
Wind senso s (no. o uni s) 2·83 0·102
Wind o ce (kno s) 16·005 1·8750
Cu en speed (kno s) 1·895 0·2266
Wa e heigh (m) 1·879 0·2976
Visibili y (ca ego y) 2·619 0·961
Table 3. Main s a is ics ob ained o he a iable pe cen age o h us e s when applying Fo wa d Wald
o bina y eg ession modelling.
Va iable B S.E. Wald Deg ees o eedom Sig. Exp(B)
Pe cen age o h us e s −0·094 0·029 10·289 1 0·001 0·910
Cons an 7·053 2·612 7·289 1 0·007 1156·017
he o he a iables did no mee he c i e ia o inclusion in he equa ion o de e mining he likelihood
o an inciden ha ing been caused by human e o . The able showing he main s a is ics o he a iable
included in he model a e shown in Table 3. Gi en his ou come, only he pe cen age o h us e s is
aken in o accoun in he model.
The ollowing exp ession defines he model:
𝑍=7·053 −0·094 ·Pe cen age o h us e s (5)
3.1. Model alida ion
I is obse ed ha he p oposed model co ec ly classifies 31 inciden s as no ha ing been caused by
human e o (94%), and six inciden s as ha ing been caused by human e o (67%). O e all, he numbe
o co ec ly p edic ed inciden s is 37 ou o 42, yielding an accu acy o 88%. This can be conside ed a
e y good p edic ion.
In he fi s pe iod, 2011 o 2013, he model p oposed when eg ession modelling is applied o he
educed sample is:
𝑍=7·543 −0·104 ·Pe cen age o h us e s (6)
When his model is es ed in he selec ed sample o he fi s pe iod, composed o 17 inciden s,
16 we e co ec ly classified (94% accu acy). The model co ec ly classified all 15 inciden s wi hou a
human cause (100%), and one ou o wo inciden s wi h a human cause (50%).
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The Jou nal o Na iga ion 939
Figu e 2. Dis ibu ion o he e o s ound du ing he alida ion o he model, whe e 0 shows no e o ,
1 indica es an inciden ha was inco ec ly classified as caused by human e o , and −1 indica es an
inciden inco ec ly classified as no human cause.
In he second pe iod, 2013 o 2015, he same echnique is applied o he 34-case inciden sample,
ob aining he p oposed model:
𝑍=7·144 −0·097 Pe cen age o h us e s (7)
This model is able o classi y 30 inciden s (88%) co ec ly, co ec ly classi ying 25 ou o 27 inciden s
wi hou a human cause (93% accu acy), and ou ou o se en inciden s wi h a human cause (57%). This
a e o co ec ly classified human-caused inciden s is highe when he model o he comple e sample
[Equa ion (4)] is applied o he sample o he second pe iod, fi e ou o se en inciden s being co ec ly
classified (71%).
Finally, he e o dispe sion is analysed, showing he as majo i y o e o s lie on he ho izon al axis
(e o o ze o), as shown in Figu e 2. This dis ibu ion indica es ha he model is mos ly no p oducing
e o s.
3.2. Model applica ion
Ha ing alida ed he model, i can be conside ed o make e y good p edic ions when applied du ing
no mal ope a ions. In o de o explo e he p ac ical applica ion o he model, he odds o he diffe en
pe cen age o h us e s online (in s eps o 10) we e calcula ed, as shown in Table 4. The likelihood
o an inciden ha ing been caused by human e o dec eases as he pe cen age o h us e s inc eases.
Specifically, when mo e han 70% o h us e s a e online, he odds show ha he likelihood o a human-
caused inciden is low, while o h us e pe cen ages below 50%, he odds show ha he e is a 90%
likelihood o a human cause unde lying an inciden , as shown in Figu e 3.
4. Discussion
The esea ch p esen ed in his pape aimed o de elop a model ha would calcula e he likelihood o an
inciden ha ing been caused by human e o while DP d illing ope a ions a e in p og ess. The esul s
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