O ganiza ion, Technology and Managemen in Cons uc ion 2021; 13: 2521-2538
Resea ch Pape Open Access
Da ja Kubečko á1,*, S anisla Smugala2
De e mina ion o cons uc ion p ocess du a ion
based on labo p oduc i i y es ima ion: A case s udy
DOI 10.2478/o mcj-2021-0031
Recei ed: Ma ch 21, 2021; Accep ed: Sep embe 30, 2021
Abs ac : Moni o ing labo p oduc i i y and how o
dec ease cons uc ion cos s a e he key issues in he plan-
ning p ocess o a cons uc ion p ojec . The CONTEC au o-
ma ed sys em combined wi h s a is ical me hods assis s
in p edic ing he amoun o ime equi ed o comple e
cons uc ion wo ks acco ding o he speci ied numbe
o deployed wo k c ews, echnological p ocesses, and
labo equi ed o ce ain p oduc ion in pe son-hou s.
This s udy applies s a is ical analyses and p obabili y
heo ies o plas e ing wo k, which ep esen s a labo -in-
ensi e cons uc ion p ocess. The goal o he esea ch is
o de e mine he p obabili y o comple ion o he con-
s uc ion p ocess based on moni o ing he mean alue
o pe o mance. By applica ion o s a is ical analyses a
dec ease in he pe o mance s anda d has been p o ed
compa ed wi h he planned alues gi en in he CONTEC
da abase. The dec ease in pe o mance, which was also
caused by he numbe o days wi h un a o able clima ic
condi ions and demons a ed by pe o ming in e al
es ima es based on he collec ion o s a is ical da a, was
la e con i med by a ela i e equency es . The meas-
u es aken we e in e ms o es ablishing he equi ed
numbe o pe sonnel capaci ies o complying wi h he
cons uc ion schedule.
Keywo ds: mean alue, s anda d de ia ion, p oduc i i y,
sample ela i e equency, p obabili y heo y, hypo hesis
es
1 In oduc ion
The p edic ion o wo k p oduc i i y is one o he key aspec s
in he planning p ocess o cons uc ion wo k. Many con-
s uc ion p ojec s oday a e planned and managed using
compu e echnology. An in eg al pa o his p ojec man-
agemen is applica ion o he s a is ical p obabilis ic me hod
wi h sophis ica ed so wa e suppo . The con olling p ocess
o wo k p oduc i i y using s a is ical me hods, combined
wi h applica ion o he cons uc ion so wa e ools, enables
o achie e no only a dec ease in he wage cos s bu also a
educ ion o o e head and p oduc ion cos s connec ed o he
ul illmen o sho ening he p ocess o building du a ion.
In he pas , a numbe o esea che s ha e s udied he p o-
duc i i y o indi idual ypes o cons uc ion wo k using con-
s uc ion so wa e, and s ochas ic me hods combined wi h
he use o cons uc ion so wa e and simula ion echnique.
1.1 Rela ed wo k om li e a u e
His o ically, one o he i s wo ks dealing wi h his
p oblem was by Nelson (1990), who c ea ed a model
ha ep esen s a new es ing me hod o assessmen s.
The educ ion o he di e ence be ween he planned
and ac ual wo k p oduc i i y is he subjec o he s udy
published by Thomas e al. (2002). F equen ly discussed
p oblems desc ibed by Gulezian and Samelian (2003) is a
di e en ia ion among labo p oduc i i y de iances. Elab-
o a ion o he s anda d pe o mance da es ha ha e been
ca ied ou by B iec e al. (2012) and Goue e al. (2011) is
necessa y o he p edic ion o du a ion o he cons uc-
ion p ocess. The es ima ion and comple ion (EAC) index
me hod equen ly used in he Wes is p esen ed by De
Ma co e al. (2009) and Na bae and De Ma co (2011). The
s a is ical me hod o he ela i e impo ance index and
mean sco e p esen ed by Salunkhe (2018), Salunkhe and
Pa il (2013), and Asiedu e al. (2017) was used o de e -
mining he c i ical cons uc ion delay ac o s. The Posi i e
*Co esponding au ho : Da ja Kubečko á, VŠB-Technical Uni e si y
o Os a a, Facul y o Ci il Enginee ing Depa men o Cons uc ion
L. Podeš ě 1875, 708 00 Os a a-Po uba, Czech Republic,
E-mail: da ja.kubecko a@ sb.cz
S anisla Smugala, Depa men o Cons uc ion, Facul y o Ci il
Enginee ing, VŠB – Technical Uni e si y Os a a, Lud íka Podéš ě
1875/17, 708 33 Os a a – Po uba, Czech Republic
Open Access. © 2021 Kubečko á and Smugala, published by Sciendo.   This wo k is
licensed unde he C ea i e Commons A ibu ion NonComme cial-NoDe i a i es 4.0 License.
2522  Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion
impac o Enginee ing So wa e on Cons uc ion P ojec
Managemen in Bah ain was p esen ed by Aqlan (2014).
P ojec managemen in cons uc ion using p ima e a and
MS p ojec is he subjec o s udy p esen ed by Saini e
al. (2017) and Sub amani and Ka hick (2018). The con-
s uc ion so wa e p oposed by Ja ský e al. (2000, 2019)
is applied o cons uc ion p ojec managemen a build-
ing si es in Cen al Eu ope. Simila o he wo ks o B iec e
al. (2012) and Goue e al. (2011), s anda d pe o mance
da es enabling he p edic ion o p ojec du a ion ha e
been ca ied ou . The abo e-men ioned wo ks a e based
on he use o cons uc ion so wa e.
The ollowing li e a u e is ocused on desc ib-
ing models ep esen ing a combina ion o s a is ical
me hods and he use o cons uc ion so wa e. Ve mo
and Kansal (2020) iden i ied delays in cons uc ion
p ojec s. The measu es o educe he delays ha e been
sugges ed by means o a ious obse a ions. The s udy
published by Geo ge e al. (2015) p oposed o cons uc
he dis ibu ion unc ion o he s a is ical me ic space/
s a is ical semi-me ic space (SMS/SSMS) in a na u al
way o quan i y he eliabili y o he o ecas . S ochas ic
p ojec scheduling simula ion (SPSS), p oposed by Lee e
al. (2005), was de eloped o measu e he p obabili y o
p ojec comple ion in a ce ain ime. This me hod is one
o he ollowing ways o how o p edic he cons uc ion
ime pe iod. Nassa e al. (2005) p esen ed he analysis o
explo e use o he Weibull me hod in s ochas ic assess-
men s o a cons uc ion p ojec de elopmen using he
cos pe o mance index (CPI) and schedule pe o mance
index (SPI) da a iles. Lowe e al. (2006) p oposed he
linea eg ession models o p edic he cons uc ion cos
o buildings, based on 286 se s o collec ed da a. El-Kholy
(2015) p esen ed wo models in he s udy p edic ing cos
o e un pe cen age in cons uc ion p ojec s based on he
p inciple o eg ession analysis. A pa simonious mul iple
linea eg ession (MLR) model o p edic ing he pe cen -
age o cos o e uns based on pa ame e s known be o e
as he con ac awa d phase was p esen ed oge he wi h
he one- ac o ANOVA es by Sinesilassie e al. (2016).
Sh es ha e al. (2013) p oposed he in es iga ion o la ge
p ojec s ha ha e a signi ican ly highe cos and sched-
ule o e uns han smalle ones. Acco ding o a me hod
p esen ed by D uke e al. (2009), a combina ion o he
EAC index me hod and s a is ical analysis elimina es he
p oblem by delaying he signal ha indica es he cos
being exceeded. Applica ion o he EAC index me hod can
cause an omission o some impo an in o ma ion ela ed
o he olume o he conduc ed wo k, acco ding o he
s udy published by Leu and Lin (2008). The esul o his
esea ch wo k is an imp o emen in he adi ional ea ned
alue managemen (EVM) me hod, and he me hodology,
connec ed o CPI and SPI, which shows ce ain limi a-
ions in de ining he gi en c i ical pa h, wo k quali y, and
isk impac . The pe o mance o EVM me hod was also
imp o ed by Lipke (2002) by implemen a ion o he s a-
is ical p ocess con ol (SPC). Many wo ks emphasize he
impo ance o in eg a ion o he SPC and EVM, because
o he la e ’s sensi i i y o disco e ing abno mal signals,
ha is, big di e ences be ween he planned and eal
alues (Wang e al. 2006). Ano he imp o emen in he
EVM me hod in e ms o he p edic ion abili y o abno -
mal de iance applying ma hema ical s a is ics was made
by Lipke e al. (2009) by de elopmen o ano he sys em.
The p oposed ea n alue (EV) me hod by Vanhoucke and
Vande oo de (2007) imp o es he o ecas abili y o he
o al p ojec du a ion compa ed wi h EVM.
A new o ecas ing me hod is de eloped based on he
Kalman il e and he ea ned schedule me hod o Kim and
Reinschmid (2010), emo ing poo accu acy o he EVM
in p edic ing p ojec du a ions. The con ol analysis com-
ple ed by U gilés e al. (2019) compa es he e iciency o
he EVM echnique and i s Ea ned Schedule ex ension,
as means o o ecas ing cos s and deadlines. S cu e
(SS-cu e) as an al e na i e me hod in ela ion o he
de e mining S cu e is applied o he con ol cons uc ion
p ocess, acco ding o s udy p esen ed by Ba aza e al.
(2004). Applica ion o he SS-cu e enables o de e mine
he cos o e in he equi ed ime. San C is óbal (2017) p o-
posed a sys em S-cu e en elope made up o wo cu es,
which can be used as an ea ly wa ning sys em i he ac ual
cons uc ion p ocess does no co espond wi h he ime
schedule. The p obabili y model de eloped by Khanzadi
and Shahbazi (2018) compa es he deg ee o p obabili y
o he p edic ed and, subsequen ly, implemen ed pe o -
mances in he case o p ojec s implemen ed in he pas
and simila p ojec s ha a e a p esen ime in he plan-
ning p ocess. Building he ime-pe iod o u u e p ojec s
is p edic ed on he basis o he p obabili y calcula ion
ca ied ou in he al eady implemen ed p ojec s. The
p inciple o Khanzadi’s me hod is compa able wi h he
me hod p esen ed by Kubečko á and Smugala (2020). The
di e ence consis s in p edic ion o he p ocess du a ion,
which is based on he e alua ion o eal implemen ed pe -
o mances a he cons uc ion si e acco ding o Smugala’s
solu ion. The impac o ainy days on labo p oduc i i y
a he cons uc ion si e o highway pa emen ope a ion
is analyzed by Choi and Ryu (2015). Rad and Kim (2018)
explo ed he po en ial ac o s ha ing an impac on he
cons uc ion p ocess. Ano he me hod p oposed by Khan-
zadi e al. (2017) models wo k p oduc i i y wi h he help o
a dynamic app oach.
Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion    2523
Simula ion echniques a e desc ibed by Mizell and
Malone (2007) as so-called in e media e cons uc ion
managemen de elopmen s age be ween he applica ion
o he classic me hod using cons uc ion so wa e and a
combina ion o he s a is ical me hods and cons uc ion
so wa e. Ba be (2005) claims ha he EAC index calcu-
la ion does no conside he consequences o he gi en
u u e o de isk. This sho coming was emo ed by
Hillson e al. (2004) and El-Maa y e al. (2017), who imple-
men ed isk managemen wi hin he ame o he classic
EVM calcula ion. In e nally gene a ed isks in he con-
s uc ion p ocess a e explo ed by Zawis o ski e al. (2010),
as ac o s ha ha e an impac on he cons uc ion p ocess.
Schedule o e un and cos escala ion pe cen ages o
highway p ojec s a e modeled by Minasowicz e al. (2011)
using he uzzy app oach. Simila uzzy op imiza ion o
cons uc ion p ojec ne wo k was p esen ed by Kuma
and Faheem (2008). A uzzy Mamdani in e ence me hod
was p oposed by Plybankiewicz (2018). The model iden i-
ies no only cos o e un, bu also de ailed cons uc ion
wo ks necessa y o comple ion o a cons uc ion p ojec .
Simula ion applica ions a e he subjec o s udies p o-
posed by Han e al. (2014), which a e based on he eal
da a eco ded a he gi en cons uc ion si e ha we e
used o he cons uc ion p ocess modeling. This sys em
is based on an analogous p inciple as he model p esen ed
by Kubečko á and Smugala (2020), which was used in he
Czech Republic. Compa ed wi h Han’s s udy he me hod
p oposed by Smugala explo ed ano he ype o building
and e alua ed mo e cons uc ion p ocesses making up
he whole s uc u e. Fu he jou nal a icles, ocused on
he o ecas o cons uc ion p ocess o high- ise build-
ing cons uc ion wi h he epea ed wo k p ocesses, we e
published by Ko and Han (2015). The e alua ion o mean
alue o pe o mance o he gi en cons uc ion p ocess is
done by applica ion o Bayesian analysis.
E alua ion o plas e ing c ew pe o mance is he
subjec o he s udy published by Ge ek e al. (2016).
Da a we e collec ed om 40 c ews o a ying cha ac e is-
ics, and hei echnical e iciency sco es we e compu ed
using he banke , cha nes, and coope (BCC) model,
which is based on a iable e u ns- o-scale (VRS). The
simila p oblem, ha is, in es iga ion o labo p oduc-
i i y da a o wall plas e ing wo k ac i i y is discussed
by Idiake and Ikeme una (2014). Da a used o he s udy
we e ob ained using he daily me hod o da a collec ion,
which was applied o he e alua ion o cons uc ion
p ocess p oduc i i y. App oxima ely 800 obse a ions
we e made o he wall plas e ing ac i i y. Simple eg es-
sion and co ela ion analyses we e applied o de e mine
he ela ionships among he esea ch a iables. Abdullah
e al. (2019) in es iga ed he pe o mance da a o gips
plas e ing wo ks acco ding o ou buildings o di e -
en cons uc ion. The o e all 11 impo an ac o s o 30
p ac ical eco ds on ield si es we e p ac ically obse ed.
Labo e s’ e iciency (LE) was measu ed and di ided in o
h ee ca ego ies, high, medium, and low, o wo speci ic
heigh s, which we e 0–2 m and 2–3 m high walls. Labo
p oduc i i y o wall plas e ing ac i i y was also explo ed
by Odesola e al. (2015) using Wo k S udy. The de e mina-
ion o building c a smen p oduc i i y in wall plas e ing
ac i i y is documen ed in his s udy and he p oduc i i y
no m is es ablished o accu a e es ima ion o manpowe
equi emen s o ealiza ion o he p ojec s. The ANOVA
es and desc ip i e s a is ics we e used o analyzing he
collec ed pe o mance da a. Ano he s udy by Olomo-
laiye and Ogunlana (1989) achie ed su p isingly di e en
esul s. The esul s p o ed no o be such a signi ican
di e ence in cons uc ion labo p oduc i i y in e ms o
wall plas e ing p ocess ac oss he e i o y. The labo p o-
duc i i y alue o ex e io b ick wall conc e e plas e ing
was in es iga ed by Monkaew and Nawale spunya (2015).
The indings show ha he labo p oduc i i y a e in con-
c e e plas e ing o ex e io b ick wall was a an a e age
o 1.13m2/p/h, which is compa able o hose achie ed in
o he building si es acco ding o p e ious publica ions.
This a e includes ac o s o delays du ing ma e ial p epa-
a ion, su ace epai ing, and any acciden s.
1.2 Objec i es and asks
The s udy sugges s a sys em ha is de e mined o he man-
agemen o cons uc ion p ocesses. A compu e ized sys em
o he cons uc ion planning CONTEC combined wi h a s a-
is ical me hod p o ides he possibili y on he basis o he
mean alue and s anda d de ia ion o de e mine he p ob-
abili y o cons uc ion p ocess comple ion. The main ask
is o e i y he alidi y o hese pe o mance mean alues
by collec ing eal pe o mance da a a building si es based
on which he en i e cons uc ion p ocess can be p edic ed.
By c ea ing and upda ing he pe o mance da a, he p ob-
abili ies o he cou se o cons uc ion p ocesses in simila
u u e cons uc ion wo ks may be es ima ed. The wo k
p oduc i i y is in luenced by many ac o s. A d op in he
pe o mance is expec ed due o occu ence o un a o able
wea he condi ions in he ime pe iod Decembe 2020–
Ma ch 2021. The hypo hesis es o ela i e equency is
ca ied ou o de e mine i he educ ion pe cen age o ul-
illmen o he ange mean alue is s a is ically signi ican ,
whe eas ze o hypo hesis H0 ep esen s a alue no educed
due o wo k in e up ions; al e na i e hypo hesis HA is a
2524  Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion
alue co esponding o he pe o mance educ ion caused
by ad e se clima ic condi ions.
2 S a is ical me hods used
2.1 Es ima ing mean alue μ
In case o calcula ion o he mean alue es ima e μ, we
s a om he assump ion o a no mal dis ibu ion, no
knowing he s anda d de ia ion σ, ha is, de ia ion o
he pe o mance o indi idual wo ke s pe wo k shi , in
he case o cons uc ion p ocesses, whe e i is possible o
eco d he pe o mance o ≥30 wo ke s o a pe iod o 1day,
so ha he condi ion o he p ocedu e acco ding o Lin-
dembe g–Lé y and he Moi o–Laplace heo em is me .
Using he Kolmogo o –Smi no es (see Sec ion 2.7) he
assump ion o whe he he popula ion is subjec o a no -
malized no mal dis ibu ion will be e i ied. The ollowing
ela ions (1)–(3) a e used o ind he app op ia e in e al
es ima e (whe e: σ=s; see B iš and Li schmanno á (2004))
− − −−


⋅ +⋅− < < =−

1 1 ,1 1
22
,
1
nn
P
ss
xz xz
nn
αα
µα (1)
5
1
i
ix
x
n
=
=∑ (2)
()
2
22 1
1
n
i
i
xx
s ss
n
=−
= ⋅=
−
∑ (3)
whe e P is he in e al wi h a 95% p obabili y;
x
is he sample
a e age; s is he pe o mance s anda d de ia ion; s2 is he
sample dispe sion; n is he numbe o wo ke s; 1 ,
2
z
−α is he
selec ed quan ile o he s anda dized; 1 − α is he con idence
o in e al p edic ion; and α is he signi icance le el.
2.2 Rela i e equency π
Fo cons uc ion con ac o s, he pe cen age da a is
impo an , such as he p obabili y o mee ing he ange o
he mean alue μ pu suan o Sec ion 2.1. A ime in e al
o 1mon h was chosen, du ing which he pe o mance o
employees was measu ed and he pe cen age ul illmen
o he ange o he mean alue μ was e alua ed. The cal-
cula ion is based on he assump ion ha he condi ion o
he Moi e–Laplace heo em is me . To ind he 95% con i-
dence in e al o ela i e equency, we use he ollowing
ela ionship (4) (B iš and Li schmanno á 2004):
()()
1 1
22
. 1
. 1
1
Ppp pp
pz pz
nn
−−




= −α
−−
− ⋅< <+ ⋅
αα
π
(4)
whe e p is he sample ela i e equency and π is he ela-
i e equency.
2.3 S anda d de ia ion con idence in e al
The lowes alue o wo ke pe o mance is explo ed by
de e mina ion o he 95% es ima e o he le -hand side
con idence in e al o he ange and s anda d de ia ion
o he a e age o he achie ed pe o mance s anda d. The
de e mina ion o he le -hand side con idence in e al,
ha is, he lowes de ia ion o he pe o mance achie ed,
is calcula ed acco ding o Eq. (5) (B iš and Li schmanno á
2004) as
22
1 , 1
1
( 1)
n
Pns
x−−

<

−
⋅
α
σ (5)
whe e P1 is he le -sided in e al wi h a 95% p obabili y.
2.4 Poisson p ocess
To assess he p obabili y o occu ence o days wi h
un a o able clima ic condi ions du ing he pe o mance
o hese wo ks, he Poisson p ocess was used, which
desc ibes he occu ence o andom e en s in some ixed
ime in e al. Then he p obabili y unc ion o he occu -
ence o aul s is calcula ed using he ollowing ma he-
ma ical ela ionship (6) (B iš and Li schmanno á 2004):
−
= ≤ < =λ
( ) .
( ) , 0 EX
!
k
e
PX k k
k
λ
λ (6)
whe e EX is he mean alue; λ is he mean numbe o
e en s; and is he ime e en .
2.5 Tes hypo hesis on ela i e equency
The cons uc ion p ocess o a esiden ial complex in
P ague 13 Klemen o a S ee is in e up ed due o un a-
o able wea he condi ions. We hypo hesized a dec ease
in he ela i e equency o compliance wi h he pe o -
mance s anda d assessed by a subsequen ne signi icance
Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion    2525
es . The de e mina ion o he hypo hesis consis s o he
ollowing s eps (see B iš and Li schmanno á (2004)).
2.5.1 Fo mula ion o null and al e na i e hypo hesis
Ze o hypo hesis H0 ep esen s a alue no educed due o
wo k in e up ions while al e na i e hypo hesis HA alue
co esponding o pe o mance educ ion is caused by
ad e se clima ic condi ions. I is assumed ha he s a e
whe e mean alue μ < μ0.
2.5.2 Selec ion o es s a is ics
We p oceed acco ding o he ollowing ela ionship (7):
2
( ) (0.1)
(1 )
p
TX P n N
−
== ⋅ →
−
π
ππ (7)
whe e T(X) is he al e na i e o he s a is ical cha ac e is ic.
2.5.3 Calcula ion o he moni o ed alue o he es
s a is ics xOBS
p- alue is calcula ing using Eq. (7); la e i is decided
whe he H0 is ejec ed o adop ed.
2.6 Tes o mean alue hypo hesis
Es ablishing he mean alue hypo hesis consis s o he
ollowing p ocess s eps.
2.6.1 Fo mula ion o ze o and al e na i e hypo hesis
The equilib ium s a e H0 co esponds o he alue o he
s anda d hou acco ding o he CONTEC da abase; mean-
while HA ep esen s eal achie ed pe o mance which is
lowe . We he e o e assume a s a e whe e mean alue μ<μ0.
2.6.2 Selec ion o es s a is ics
When de e mining he choice o es s a is ics, we assume
ha we do no know he s anda d de ia ion, jus as when
calcula ing he s anda d de ia ion es ima e (see Sec ion
2.3 Eq. (8)) as
1 1
x
()
nn
Tµ
n
s
XT −−
−⋅→== (8)
whe e Tn−1 is he andom a iable wi h n deg ees o leeway;
s is he s anda d de ia ion and he sample a e age; μ is
he mean alue; and n is he numbe o deg ees o leeway
(numbe o wo ke s).
2.6.3 Calcula ion o obse ed alues o es s a is ics xOBS
Fo he calcula ion, ela ionship (8) is used, based on
which he p- alue is de e mined and e ec i e decision is
made ega ding he accep ance o ejec ion o H0 (see B iš
and Li schmanno á (2004)).
2.7 In e al es ima ion o he di e ence
be ween he mean alues o wo
popula ions
The esiden ial complex in P ague 13 Wes Ci y is made
up o wo buildings, J12 and J34. Due o he mu ual in e -
connec ion o he buildings, i is necessa y o pe o m a
s a is ical compa ison o pe o mance by pe o ming he
basic cha ac e is ics, such as es ima es o mean alues.
In his case, jus as in Sec ion 2.1, we assume ha he pop-
ula ion has a no mal dis ibu ion wi h unknown s and-
a d de ia ions. The andom a iable T2 wi h S uden ’s
di ision wi h (n1+n2−2) and deg ee o la i ude
12
2nn
+−
has
he o m o Eqs (9) and (10) (see B iš and Li schmanno á
(2004))
()
12
12
1 2 12
1 , 2
122
1 , 2
12
2
()
11
.
11
. 1
pnn
pnn
Px x s
nn
s
nn
− +−
− +−

−− + ⋅



+⋅ α
<−
<
 =−

α
α
µµ
(9)
()()
1 2 12
2
12
2 2 2 2
1 2
12
– , whe e
11
.
( 1 1) ( 2 1)
2
p
p
x x µµ
T
snn
n sn s
snn
−−
=

+


− +−
+−
=
(10)
2.8 Kolmogo o –Smi no ’s es
The heo e ical dis ibu ion (no mal dis ibu ion) o he
gi en popula ion in he case o indi idual es s is assumed
(see p e ious Sec ions 2.1–2.7). Good compliance es s a e
needed o e i y ha his es ima e is co ec . The Kolmogo-
o –Smi no es is applied o es he ag eemen be ween

2526  Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion
he sample and heo e ical dis ibu ion. I is used o e i y
he hypo hesis ha he selec ion gi en comes om a dis-
ibu ion wi h a con inuous dis ibu ion unc ion F(x),
whe eas he unc ion mus be ully speci ied (see B iš and
Li schmanno á (2004)).
2.8.1 Selec ion o ze o al e na i e hypo hesis
0
0
() ()
() ()
:
:
Fx F x
Fx F x
=
≠
0
A
H
H
whe e F(x) is he dis ibu ion unc ion o sepa a ion, om
which he andom selec ion de i es, ep esen ing a heo-
e ical dis ibu ion unc ion.
2.8.2 Selec ion o es s a is ics T(X) including ze o
dis ibu ion
The es s a is ic Dn is de ined as he maximum de ia ion
o heo e ical and empi ical dis ibu ion unc ion (see Eqs
(11) and (12)). The selec i e empi ical dis ibu ion unc ion
Fn(x) is gi en as
0, 1()
n
F x
i
n
===
( )
** *
0 12
sup| ( a() ,) ()| ,,mx
nn n
TX D F x F x D D D−== =  (11)

−
=−

−
=

*
00
1
w: ()he e max , ,
1, 2, 3
)
,,
(
ii
ii
D F Fx
nn
i
x
n
(12)
0
(µ
) x
F x
s
−
= (13)
3 Da a measu emen , goal se ing,
e alua ion
The du a ion o he plas e ing wo k p ocess depends on
he mean alue o he pe o mance and i s de ia ion. The
aim o he esea ch is o de e mine he uppe and lowe
limi s o pe o mance wi h 95% eliabili y on he basis o
he collec ion o a ce ain numbe o da a.
By e alua ion o hese andom a emp s in he o m o
e e yday wo ke pe o mance, a p obabili y es ima e was
achie ed ega ding he comple ion o he gi en p ocess. By
implemen ing he lowe and uppe pe o mance alues,
we ob ain an op imis ic and pessimis ic pe o mance
a ian wi h he sho es and longes du a ion o he plas-
e ing p ocess. The gi en s a is ical e alua ions a e pe -
o med a he beginning o he cons uc ion p ocesses so
ha i is possible o implemen pe sonnel measu es o
ensu e he o iginally planned cons uc ion deadlines. A
ypical loo is shown in Figu e 1.
3.1 P oduc i i y o plas e ing wo ks
The subjec o he assessmen is 15-mm- hick lime–
gypsum plas e coa ings, which a e made on he su aces
o he mason y o he pe ime e cladding and in e nal
pa i ions on he 1s loo –7 h loo , whose pe o mance
s anda d, wi h ega d o s anda dized mean alue μ,
is based on he CONTEC da abase (see Ja ský (2000),
0.73m2/h), which ep esen s an ou pu o 10.95m2/shi .
Conc e e su aces o ceiling s uc u es and walls a e
ea ed wi h a 5-mm- hick coa ing, he pe o mance s and-
a d o which is 42.1m2/shi /wo k (0.19Nh/m2) Since he
mu ual a io o he a eas ea ed wi h a owel o hickness
o 5mm o he a ea plas e ed wi h lime plas e is abou 1:3,
he a e age s anda d hou is 0.59Nh/m2 and he wo ke ’s
ou pu pe shi 13.6m2/shi /wo ke . A o al o 32 employ-
ees will be deployed o ca y ou his p ocess, wi h ou
plas e ing pla oons wi h a o al numbe o 16 employees
deployed a each o he SO J34 and SO J12 acili ies. The
minimum wo k queue is wo ypical loo s, whe e eigh
plas e e s will wo k in each o hem (see Table 1). The
las wo k queue ep esen ing he 7 h loo is occupied by
eigh wo ke s and he es is deployed in he unde g ound
loo s o comple e esidual plas e ing wo k.
3.1.1 Es ima e o he ange o he pe o mance mean
alue μ including s anda d de ia ion s
To achie e ≥30 andom ials, he pe o mance o 16
wo ke s will be eco ded in wo consecu i e shi s, gi ing
32 pieces o da a on daily pe o mance. As in he case o
mason y s uc u es, he plas e ing wo ks o he SO J34 and
SO J12 buildings a e ca ied ou simul aneously, he e o e
di e en wo king capaci ies mus be used he e, assuming
di e en anges o mean alues μ.
A) Building J34
In Table 2, 32 andom ials a e eco ded in he o m o
wo ke pe o mances in wo consecu i e wo k cycles. We
ha e a ailable ≥30 andom ials, so we can s a om he
no malized no mal dis ibu ion and he Moi e–Laplace
heo em (see B iš and Li schmanno á (2004)).
Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion    2527
• Kolmogo o –Smi no es
The heo e ical in e p e a ion gi en in Sec ions 2.1–2.7 is
based on he assump ion ha he esul s o andomized
ials gi en acco ding o Table 2 a e subjec o no mal
dis ibu ion. The p oo conce ning es ima ion is ha
gi en he subjec ’s no mal dis ibu ion is decisi e o how
o choose he way o he espec i e calcula ion. Wi h he
help o good compliance es s, as i was men ioned, he
assump ion ega ding dis ibu ion o he popula ion is o
be e i ied. The applica ion o he Kolmogo o –Smi no
es will p o e his assump ion o enable calcula ion
acco ding o in e p e a ion acco ding o Sec ions 2.1–2.7,
whose p inciple is based on hypo hesis (see B iš and
Li schmanno á (2004)).
3.1.1.1. Selec ion o ze o and al e na i e hypo hesis
0
: () ()Fx F x=
0
H
whe e F0(x) is he dis ibu ion unc ion o no mal dis ibu-
ion wi h he pa ame e s μ = 11.5; s = 0.83 is based on he
assump ion ha he da a a e de i ed om N (11.5; 0.832).
Tab. 1: Plas e ing wo ks – Dis ibu ion o numbe o plas e e s in
wo k queue no.1
Floo No. o
plas e e s
O e all pe o mance
plan m2/sm
O e all pe o mance
plan m2/mon h
1 8 87.6 1,752
2 8 87.6 1,752
3 – – –
4 – – –
5 – – –
6 – – –
7 – – –
ς 16 175.2 3,504
Fig. 1: Type o abo e-g ound loo o building J1–J2.
2528  Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion
0
): () (Fx F x≠
A
H
whe e F0(x) is he dis ibu ion unc ion o no mal dis i-
bu ion wi h he μ = 11.5; s = 0.83 based on he assump ion
ha he da a a e no de i ed om N (11.5; 0.832).
3.1.1.2. Selec ion o he es s a is ic T(X) including ze o
dis ibu ion
Tes s a is ic Dn is de ined as he maximum de ia ion o
he heo e ical and empi ical dis ibu ion unc ion.
When calcula ing he alues o dis ibu ion unc-
ions and hei de ia ions gi en in Table 2, ma hema ical
ela ions (11)–(13) (Sec ion 2.7) will be used (see B iš and
Li schmanno á (2004)).
)1(
µ 11.5 10
1.807
0.83
see label no 1 [16] 1 0.964 0.036
x
x
Fs
−−
== =
→− =
(14)
)2(
µ 11.5 10 1.807
0.83
see label no 1 [16] 1 0.964 0.036
x
x
Fs
−−
== =
→− =
)9(
µ 11.5 – 11
0.602
0.83
see label no 1 [16] 1 0.726 0.274
x
x
Fs
−
== =
→− =
)10(
µ 11.5 – 12 0.602
0.83
see label no 1 [16] 0.726
x
x
Fs
−
= = =−
→=
)11(
µ 11.5 12 0.602
0.83
see label no 1 [16] 0.726
x
x
Fs
−−
= = =−
→=
)12(
µ 11.5 12 0.602
0.83
see label no 1 [16] 0.726
x
x
Fs
−−
= = =−
→=
)13(
µ 11.5 12 0.602
0.83
see label no 1 [16] 0.726
x
x
Fs
−−
= = =−
→=
)14(
µ 11.5 12 0.602
0.83
see label no 1 [16] 0.726
x
x
Fs
−−
= = =−
→=
)15(
µ 11.5 13 1.807
0.83
see label no 1 [16] 0.964
x
x
Fs
−−
= = =−
→=
)16(
µ 11.5 13 1.807
0.83
see label no 1 [16] 0.964
x
x
Fs
−−
= = =−
→=
0 / /
1
2
15
)
6
(
1
sup|
0.063 0.036 0.027
0.125 0.036 0.089
0.875 0.938 0.026
1 0.964 0.036
( ) () ()|
n n p o i n i n F x
T xXD F F D
D
x
D
D
D
=−
== − =
==−=
== − =
= = − =−
= =− =
(15)
1
2
15
16
1
( ) ()
0.036 0 0.036
0.036 0.063 0.027
0.964 0.875 0.089
0.964 0.938 0.026
n
i
TX D Fx n
D
D
D
D
−
== −
= = −=
==−=−
== − =
== − =
*
00
1 1, 2, max ( ) 3, ,, ( )
ii
ii
D F F x p o i n
n
x
n

−
−=

−
=


(16)
{ }
{ }
{ }
{ }
*
9
*
16
max 0.036 ; 0.036 0.036
max 0.036 ; 0.036 0.036
0.289; 0.226 0.289
0.036; 0.026 0.036
max
max
D
D
==
==
−
=
=
−=
=
3.1.1.3. Calcula ion o p- alue
{ }
0 00
00
0
0
() () ( ); ( )
( ) (0.289)
(0.28
2
: - alue 2. min 1
0.90,see label no 4 (se
9
e Li schmanno á )
0.1 1
- alu
2
e 0.
9) ( 015)
(0.28 )
OBS OBS
OBS
Fx Fx p Fx Fx
Fx F
F
F
p
≠= −
=
<
<−
>
A
H
Tab. 2: Plas e ing wo ks SO J 34
Wo ke no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Pe o mance/shi 12 11 10 12 11 13 12 11 10 12 11 10 13 10 12 11
Wo ke no. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Pe o mance/shi 12 11 11 12 11 13 12 11 12 12 11 12 13 12 10 12
Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion    2529
I ollows ha he p- alue is >0.2, ha is, we do no ejec
he ze o hypo hesis, ha is, da a in he o m o c ew
pe o mances a e subjec ed o no mal dis ibu ion. The
calcula ion o selec ion cha ac e is ics will ake place
in acco dance wi h ha gi en in Sec ion 2.1. In case he
no mal dis ibu ion is no con i med by u ilizing he
abo e men ioned es , i would no be possible o p oceed
acco ding o he heo e ical p ocess s a ed in Sec ions
2.1–2.7. The calcula ion p ocess co esponds o he conclu-
sion o he es conce ning he speci ic dis ibu ion (see
Li schmanno á (2015)).
• Sample cha ac e is ics:
()
12
1
Sample a e age:
12 11 10 12 11 13 13 12 10 12
11.5
32
i
ix
xn
=
=
+++++ +++
==
∑

2
Sample s anda d de ia ion: 0.69 0.8ss
== =
()
2
21
22 22
Sample ange: 1
(1.6 1.61) (1.5 1.61) . (1.5 1.61) (1.7 1.61)
32
0.69
n
i
ixx
sn
=−
−
−+−+…+−+−
=
=
=∑
1 – 1
22
– . µ . 1P
ss
x z xz
nn
−

< < + = −α


αα
0.83 0.83
11.5 1.96 11.5 1.96 1
32 32
Pα

=
+

− ⋅ <µ< ⋅ −
11.21 11.79<µ<
• Reliabili y o in e al es ima e: 1−α = 0.95, ha is,
he le el o signi icance α = 1−0.95 = 0.05,
2
α
= 0. 025,
1−α/2 = 0.975, z0.975, = 1.96 (see Table 2). Selec ed quan-
iles o he s anda dized no mal dis ibu ion (see
Li schmanno á (2015)).
|AD A) E alua ion
The in e al es ima e o he ange o he mean alue wi h
95% con idence anges om 11.21m2 o 11.79m2, while
he cen e o his ange ep esen s he alue o 11.5m2.
In ela ion o he s anda dized CONTEC da abase, his
alue is 15% lowe , which equi es a ein o cemen o
wo wo ke s, p o ided ha he con ac ual HMG is com-
plied wi h.
B) Building J12
To secu e he plas e ing wo k on his building, 16 wo ke s
we e deployed in wo consecu i e wo k cycles. These a e
di e en wo k c ews, so i can be assumed ha di e en
anges o mean alues, μ, will be ob ained. E en in his
case, we can s a wi h espec o he numbe o eco ded
powe s ≥30 om he s anda dized no mal dis ibu ion and
he p inciple o Moi e–Laplace heo em. Based on he
calcula ion o he wo-sided in e al wi h 95% con idence,
i was p o ed by calcula ion ha he es ima e o he ange
o he mean alue anges om 10.91m2 o 11.52m2, while
he mean o he ange ela i e o he CONTEC da abase is
17.5% lowe . To elimina e his dec ease in pe o mance, i
is p oposed o s eng hen he capaci y by h ee plas e e s.
3.1.2 Es ima e o in e al o eliabili y o s anda d
de ia ion
In his sec ion, he calcula ion o he le -hand side in e -
al es ima e wi h 95% eliabili y o he sca e ing and
s anda d de ia ion o he plas e ing p ocess will be pe -
o med, ha is, he smalles possible a ea o plas e pe -
o med by one wo ke pe shi . Le -hand de ia ions will
be calcula ed due o he deploymen o di e en wo k
c ews on SO J34 and SO J12 o each building sepa a ely.
A) Building J34 – Le -hand in e al o eliabili y o
s anda d de ia ion
Ou s a ing poin ollows om he esul s o he calcula-
ion o he ange o mean alue o pe o mance o plas e -
ing wo ks (see Sec ion 2.1. A). The ma hema ical ela ion-
ship (5) (see Sec ion 2.3) will be used o he calcula ion,
whe eas s2 = 0.0061, n = 32:
2
1
32 1. 0.0061 1
19.3
P

−<σ = −α


(5)
2
10.00(98 1)P<σ = −α
)0.099 ( 1
<σ = −α
• Reliabili y o in e al es ima e: 1−α = 0.95, ha is, he
le el o signi icance α = 1−0.95 = 0.05, = 0.95, z0.95, 31=
19.3 (see Table 3). Selec ed quan iles χ2 o dis ibu ion
wi h ν deg ee o la i ude (see Li schmanno á (2015)).
AD A) E alua ion
We can s a e wi h 95% eliabili y ha he maximum le -
hand side s anda d de ia ion o he sample a e age is
1.053m2. Inco po a ing his da a in o he cons uc ion so -
wa e CONTEC, we ge he longes pe iod o plas e wo k,
2536  Kubečko á and Smugala, De e mina ion o cons uc ion p ocess du a ion based on labo p oduc i i y es ima ion
Based on hese s a is ical analyses, i is hen possible
o de e mine in su icien ime he measu es necessa y o
mee cons uc ion deadlines, which is he main ad an age
compa ed wi h he adi ional way o managing p ojec s
using only he cons uc ion so wa e based on he ime
s anda d ha is no me a his si e. The esul s o he p o-
duc i i y pe o mance analysis p o ed he dec ease in pe -
o mance, which mean an inc ease in pe sonnel capaci y,
which was done a he beginning o he pe o mance o
he p ocess in o de o mee he ini ially planned deadline.
Subsequen es o hypo hesis o ela i e equency ejec -
ing ze o hypo hesis H0 e alua ed he pe o mance dec ease
due o wo k in e up ions caused by un a o able clima ic
condi ions in he pe iod o Decembe 2020–Ma ch 2021 as
s a is ically signi ican , which mean u he s eng hen-
ing o plas e ing capaci ies by wo wo ke s eaching he
inal numbe o 20 plas e s a SO J34 and 21 plas e s a SO
J12. The dec ease in p oduc i i y pe o mance is a global
p oblem due o he lack o quali ied wo ke s.
This pape o e s ano he op ion on how o inc ease
labo p oduc i i y případě in he case o epea ed o
long-las ing cons uc ion p ocesses. Based on he expe-
iences he inc ease in he indi idual cons uc ion pe -
o mance can be achie ed by he epea ed moni o ing,
e alua ion o s a is ical da a o indi idual wo ke s’ pe -
o mance, and use o s a is ical me hods combined wi h
an applica ion o cons uc ion so wa e. The subjec o
u he esea ch is an expansion o s udied p ocesses a
he a ious ypes o cons uc ion. The c ea ion o a da a
ile and i s con inuous upda e allows mo e p ecise p edic-
ion o he ime cou se a he bidding s age. The heo e -
ical p obabilis ic me hods suppo ed by he cons uc ion
so wa e migh con ibu e o he quali y imp o emen o
cons uc ion managemen .
Acknowledgemen s
This con ibu ion was inanced by own inancial sou ces
coope a ing wi h cons uc ion company Ride a l.c. con-
s uc ing he abo e-men ioned p ojec , whe e s a is ical
me hods in combina ion wi h cons uc ion so wa e ha e
been applied om he Ins i u ional inancial esou ces o
he Minis y o Educa ion, You h and Spo s o he Czech
Republic o he yea 2021.
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