ORIGINAL ARTICLE
Employing machine lea ning echniques in moni o ing au oco ela ed
p o iles
Ali Yeganeh
1
•A ne Johannssen
1
•Na aliya Chukh o a
2
•Saddam Akbe Abbasi
3,4,5
•
Fa had Pou panah
6
Recei ed: 31 Oc obe 2022 / Accep ed: 8 Ma ch 2023 / Published online: 29 Ap il 2023
The Au ho (s) 2023
Abs ac
In p o ile moni o ing, i is usually assumed ha he obse a ions be ween o wi hin each p o ile a e independen o each
o he . Howe e , his assump ion is o en iola ed in manu ac u ing p ac ice, and i is o u mos impo ance o ca e ully
conside au oco ela ion e ec s in he unde lying models o p o ile moni o ing. Fo his eason, a ious s a is ical con ol
cha s ha e been p oposed o moni o p o iles when be ween- o wi hin-da a is co ela ed in Phase II, in which he main
aim is o de elop con ol cha s wi h quicke de ec ion abili y. As a no el app oach, his s udy aims o employ machine
lea ning echniques as con ol cha s ins ead o s a is ical app oaches in moni o ing p o iles wi h be ween-p o ile au o-
co ela ions. Speci ically, new inpu ea u es based on con en ional s a is ical con ol cha s a is ics and no malized
es ima ed pa ame e s a e de ined ha a e capable o adequa ely accoun ing o he be ween-au oco ela ion e ec o
p o iles. In addi ion, six machine lea ning echniques a e ex ended and compa ed by means o Mon e Ca lo simula ions.
The simula ion esul s indica e ha machine lea ning echniques can ob ain mo e accu a e esul s compa ed wi h s a is ical
con ol cha s. Mo eo e , adap i e neu o- uzzy in e ence sys ems ou pe o m o he machine lea ning echniques and he
con en ional s a is ical con ol cha s.
Keywo ds Adap i e neu o- uzzy in e ence sys em A i icial neu al ne wo k Deep lea ning Long sho - e m memo y 
S a is ical p ocess moni o ing Suppo ec o eg ession
1 In oduc ion
S a is ical p ocess moni o ing (SPM) is usually employed
o indus ial p ocesses o omi assignable causes ha
de e io a e he p oduc ou come. SPM is he majo ield o
con olling p ocess a ia ions o e en ua e lowe cos s in
was e, sc ap, ewo k and claims, be e quali y, and mo e
insigh s in o he capabili y o he p ocess. Se en main
ools, en ailing sca e diag ams, Pa e o cha s, con ol
cha s, his og ams, cause-and-e ec diag ams, check shee s
and s a i ica ion, a e u ilized in SPM o implemen
inspec ion and moni o ing p ocedu es [1]. Among hem,
&A ne Johannssen
[email p o ec ed]
Ali Yeganeh
[email p o ec ed]
Na aliya Chukh o a
[email p o ec ed]
Saddam Akbe Abbasi
[email p o ec ed]
Fa had Pou panah
[email p o ec ed]
1
Facul y o Business Adminis a ion, Uni e si y o Hambu g,
20146 Hambu g, Ge many
2
Ha enCi y Uni e si y, 20457 Hambu g, Ge many
3
Depa men o Ma hema ics, S a is ics and Physics, Qa a
Uni e si y, Doha, Qa a
4
Depa men o Ma hema ics, S a is ics and Physics, College
o A s and Sciences, Qa a Uni e si y, 2713 Doha, Qa a
5
S a is ical Consul ing Uni , College o A s and Sciences,
Qa a Uni e si y, 2713 Doha, Qa a
6
Depa men o Elec ical and Compu e Enginee ing, Cen e
o Compu e Vision and Deep Lea ning, Uni e si y o
Windso , Windso , Canada
123
Neu al Compu ing and Applica ions (2023) 35:16321–16340
h ps://doi.o g/10.1007/s00521-023-08483-3(0123456789().,- olV)(0123456789().,- olV)
con ol cha s a e he mos success ul and e ec i e ools
o quali y con ol o manu ac u ing p ocesses [2–4].
To employ a con ol cha o p ocess moni o ing, wo
phases en ailing Phase I and II should be ini ially de ined.
In Phase I, i is ied o achie e p ope es ima ions o he
p ocess pa ame e s, whe eas Phase II moni o ing aims o
ind assignable causes in which he p ocess si ua ion
changes om In-Con ol (IC) o Ou -o -Con ol (OC) s a e
[5–9]. A e age Run Leng h (ARL) and S anda d De ia ion
o Run Leng h (SDRL) a e wo common pe o mance
indica o s in Phase II. The ARL is he a e age numbe o
samples o be ob ained by he p ede ined con ol cha be-
o e he cha igge s an OC signal. Thus, a con ol
cha wi h la ge (smalle ) alues o he ARL is o be
p e e ed when he unde lying p ocess is in IC (OC) s a e
[ he mo e common no a ion is ARL
0
(ARL
1
)] [10–12]. In
addi ion, he SDRL is de ined in a simila way as a sec-
onda y c i e ion in Phase II (i.e., SDRL
0
and SDRL
1
).
The e a e wo common app oaches o moni o a man-
u ac u ing p ocesses wi h he help o con ol cha s namely
moni o ing quali y cha ac e is ics and p o ile moni o ing
[13]. In his pape , we ocus on p o ile moni o ing. He e,
he quali y o a p ocess o p oduc is modelled ia a
unc ional ela ionship be ween a esponse (dependen )
a iable and one o mo e explana o y (independen ) a i-
able(s) [14]. The aim o p o ile moni o ing is o check he
s abili y o a p ede ined IC ela ionship (o p o ile) o e
ime, and i is essen ial o each a ue OC signal as soon as
possible when he IC model shi s o an unknown OC
p o ile [15].
Di e en IC models can be employed due o he na u e
o he unde lying p oblem, such as ci cula [16], linea
[5,17–22], logis ic [23–25], nonlinea [26], nonpa ame ic
[27,28], mul ichannel [29], polynomial [30] o quad a ic
[31]. Among hem, linea p o iles ha e ecei ed mo e
a en ion in he li e a u e [32,33]. The majo i y o p e ious
s udies in linea p o ile moni o ing is based on he inde-
pendency assump ion ega ding wi hin o be ween p o iles
in ela ion o he e o e ms. Howe e , his assump ion is
o en iola ed in manu ac u ing p ac ice ha is cha ac e -
ized by au oco ela ed p o iles and consequen ly, con en-
ional app oaches may lead o inaccu a e ou comes o his
ype o p o iles.
Au oco ela ed p o iles consis o wi hin- and be ween-
co ela ion models in he ela ed li e a u e [34–37]. In he
i s g oup, Soleimani, Noo ossana and Ami i [38] de el-
oped ou con ol cha s including T
2
and h ee well-known
Exponen ially Weigh ed Mo ing A e age (EWMA) cha s
conside ing he i s o de Au o eg essi e (AR) model, i.e.,
AR(1). The esul s showed he supe io i y o EWMA-based
app oaches o e T
2
. Au o eg essi e Mo ing A e age
(ARMA), Vec o ARMA (VARMA) e c. a e o he mo e
complex models ha ha e been de eloped in his ield
[39–43]. Due o he highe po en ial o applica ions o he
second g oup, his pape ocuses on be ween-p o ile au o-
co ela ion. To he bes o he au ho s’ knowledge, he
pionee ing wo k is Noo ossana, Ami i and Soleimani [44],
in which hey de eloped T
2
, EWMA o esiduals (EWMA/
R) and ans o med indi idual EWMA (EWMA-3) con ol
cha s o si ua ions whe e au oco ela ion e ec s exis
be ween p o iles. Simila o Soleimani, Noo ossana and
Ami i [38], hey concluded ha EWMA-based me hods
ou pe o m T
2
. Wang and Lai [45] agg ega ed he indi-
idual EWMA s a is ics o a Mul i a ia e EWMA
(MEWMA) con ol cha o p o iles wi h be ween-au o-
co ela ion, and i has been shown ha MEWMA ou pe -
o ms T
2
. Khedma i and Niaki [46] conside ed bo h linea
and polynomial p o iles; hey i s u ilized he U s a is ic
o emo ing he e ec o au oco ela ion and hen de el-
oped a T
2
-based con ol cha . The expe imen al esul s
showed ha his me hod pe o ms be e han con en ional
T
2
con ol cha s, bu compa isons wi h EWMA a e miss-
ing. Koosha and Ami i [47] p oposed a simila T
2
-based
con ol cha o moni o ing au oco ela ed logis ic p o iles.
Wang and Huang [48] modi ied he es ima ion p ocedu e
o he EWMA app oach, and he simula ion esul s
demons a ed ha his scheme has a as e de ec ion abili y
han ha o con en ional EWMA.
F om he li e a u e, i can be in e ed ha he p obabili y
o occu ing au oco ela ions in p ac ical applica ions is
e y high. The e o e, an ea ly de ec ion o OC condi ions is
mo e impo an han simula ion esul s, as a delay in
de ec ion may esul in he p oduc ion o noncon o mi ies
and addi ional cos s. Howe e , he con en ional con ol
cha s such as T
2
, EWMA/R and EWMA-3 a e no able o
pe o m well in line wi h his aim as hei pe o mance
de e io a e in he occu ence o au oco ela ion in com-
pa ison wi h simple si ua ions; o example, i can be
e e ed o he esul s o ARL
1
in Noo ossana, Ami i and
Soleimani [44] e sus Kim e al. [20].
Hence, p oposing a no el con ol cha wi h a angible
abili y in educ ion o he OC signaling ime in au oco -
ela ed p o iles is c ucial. To emedy his challenge, in
ecen yea s, se e al s udies inco po a ed machine lea ning
echniques in he SPM con ex in moni o ing oundness
[49], nonlinea [50–52], linea [53,54] and logis ic
16322 Neu al Compu ing and Applica ions (2023) 35:16321–16340
123
[25,55,56] p o iles. As a di e en app oach, Chen e al.
[57] employed a deep lea ning echnique, called s acked
denoising au oencode s, o moni o au oco ela ed p o iles.
Speci ically, his scheme ex ac s a numbe o ea u es
om he p ocess using au oencode s, and hen he ex ac ed
ea u es a e used o de elop con ol cha s based on T
2
and
EWMA. In o he wo ds, he main ask o hei app oach is
o selec p ope ea u es om he p ocess, whe eas he
di ec usage o machine lea ning echniques as a con ol
cha would be mo e p omising. As a as he au ho s
know, he e a e no u he a icles whe e machine lea ning
echniques a e employed in moni o ing au oco ela ed
p o iles.
The aim o his pape is o de elop a obus con ol
cha based on machine lea ning echniques o alle ia e he
abo e-men ioned challenges, i.e., educing he alues o
he ARL
1
and SDRL
1
o au oco ela ed linea p o iles ha
can esul in ea ly de ec ion o OC si ua ions in Phase II.
To achie e his, h ee combina ions o inpu ea u es based
on he e ec o he mean o esponses, he mean o e o s,
and T
2
s a is ic, each in he cu en and p e ious sample,
a e de ined o ed in o he machine lea ning echniques o
moni o ing p o iles wi h be ween-au oco ela ion o i s
o de , i.e., AR(1). Since each machine lea ning echnique
pe o ms di e en ly in ackling a ious p oblems, six
machine lea ning echniques anging om shallow o deep
s uc u es including adap i e neu o- uzzy in e ence sys em
(ANFIS), a i icial neu al ne wo k (ANN) wi h Back-
P opaga ion (BP) aining, Con olu ional Neu al Ne wo k
(CNN), long sho - e m memo y (LSTM) ne wo k, Radial
Basis Func ion (RBF) ne wo k and suppo ec o eg es-
sion (SVR), a e employed o ind he mos app op ia e one.
To sum up, he main con ibu ions o his pape a e as
ollows:
•Imp o ing he de ec ion abili y o Phase II con ol
cha s o moni o ing linea au oco ela ed p o iles wi h
he help o machine lea ning echniques,
•De ining di e en combina ions o inpu ea u es based
on he e ec o he mean o esponses, he mean o
e o s, and T
2
s a is ic, each in he cu en and p e ious
sample, o moni o ing he be ween-au oco ela ion
e ec o p o iles,
•E alua ing he pe o mance o he de ined inpu
ea u es and inding he bes combina ion using he
p oposed machine lea ning-based con ol cha , and
•Iden i ica ion o he mos app op ia e machine lea ning
echnique unde he mos sui able inpu combina ion o
his p oblem.
The es o his a icle is o ganized as ollows. In
Sec . 2, de ini ions o au oco ela ed linea p o iles a e
discussed. Sec ion 3p esen s he amewo k o he p o-
posed app oach. Resul s o simula ion s udies ega ding
pe o mance compa isons a e gi en and discussed in
Sec . 4. To show he e ec i eness o ou me hod, an
illus a i e example is gi en in Sec . 5. Finally, Sec . 6
gi es some conclusions and sugges s u u e esea ch
di ec ions.
2 P elimina ies
In his sec ion, i s , he gene al ela ions o linea p o iles
wi h be ween-au oco ela ion e o e ms a e p esen ed.
Then, h ee common con ol cha s, namely T
2
, EWMA/R
and EWMA-3, a e b ie ly in oduced. Finally, de ails abou
he O dina y Leas Squa es (OLS) es ima ion o he
pa ame e s a e discussed. These basics a e necessa y
agains he backd op ha (1) ou p oposed me hod employs
he T
2
s a is ic as inpu ea u e, and (2) hese con en ional
cha s a e used o compa ison pu poses in ou analyses.
2.1 The linea au oco ela ed p o ile in Phase II
A common linea p o ile, which is he simples bu he
mos undamen al ype o p o iles [19], is de ined as:
Yij ¼A0þA1Xiþeij;eij N0; 2

;
i¼1;2;...;n;j¼1;2;...;
ð1Þ
whe e X
i
ep esen he explana o y a iable in a linea
p o ile and he esponse a iable Y
ij
is he quali y cha ac-
e is ic unde s udy. The pa ame e s o he abo e IC model
(in e cep A
0
, slope A
1
and e o a iance
2
) a e es ima ed
om Phase I samples, and i is usually assumed ha sample
size nand independen a iable X
i
a e ixed in each p o ile.
When he e is an AR(1) s uc u e be ween he andom e o
e ms, (1) becomes:
Yij ¼A0þA1Xiþeij;eij ¼/eij1ðÞ
þaij;aij N0; 2

;
i¼1;2; :::; n;j¼1;2;...;
ð2Þ
whe e /is a cons an au oco ela ion coe icien , which is
assumed o be known in Phase II. To moni o he abo e IC
p o ile, we b ie ly p esen h ee common app oaches in he
ollowing subsec ions.
Neu al Compu ing and Applica ions (2023) 35:16321–16340 16323
123
2.2 The T
2
con ol cha o moni o ing
au oco ela ed p o iles in Phase II
By some calcula ions, i can be easily shown ha he
es ima ed esponses a e ob ained in he j
h
gene a ed sam-
ple o e ime as ollows [44]:
^
yij ¼/yij1ðÞ
þ1/ðÞðA0þA1XiÞ:ð3Þ
Thus, he empi ical esiduals can be w i en as:
eij ¼^
yij yij:ð4Þ
Noo ossana, Ami i and Soleimani [44] used a modi ied
o m o he T
2
s a is ics p oposed by Kang and Albin [14]
in a simple linea p o ile:
2
j¼ejX
1
e
e0
j;ej¼e1j;e2j;...;enj

;ð5Þ
whe e P
e
is he symme ic n9nma ix
2
I. Since he
cha s a is ic ð 2
j) is ensu ed o be la ge han ze o, i is
compa ed wi h a p ede ined Uppe Con ol Limi (UCL
T
)
o each an OC signal. No e ha he Lowe Con ol Limi
(LCL
T
) is equal o 0.
2.3 The EWMA/R con ol cha o moni o ing
au oco ela ed p o iles in Phase II
In he EWMA/R con ol cha , wo simul aneous s a is ics
moni o he gene a ed p o iles. The i s s a is ic is ela ed
o he mean o he esiduals and is de ined as ollows
[44,53]:
zj¼hejþð1hÞzðj1Þ;ej¼1
nX
n
i¼1
eij;ð6Þ
In (6), i holds z
0
= 0, and his he EWMA cons an ha
usually has a alue be ween 0.1 and 0.9 [20]. Following
p e ious wo ks [21,53,54,58], his se o 0.2 in his pape .
The second s a is ic o he EWMA/R cha is he ange
o he empi ical esiduals de ined by [37,48]:
j¼maxðeijÞminðeijÞ:ð7Þ
The EWMA/R decla es he p ocess as IC i bo h o he
ollowing condi ions a e me [14]:
L ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h
2hðÞn
s zj L ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h
2hðÞn
s;
d2Ld3
ðÞ j d2þLd3
ðÞ
ð8Þ
In (8), he alue o Lis assigned o each a p ede ined
ARL
0
, while d
2
and d
3
a e wo cons an s ha depend on he
sample size (see Mon gome y [1] o mo e de ails).
2.4 The EWMA-3 con ol cha o moni o ing
au oco ela ed p o iles in Phase II
To sol e he p oblem o dependency be ween he es ima-
o s in linea p o iles, Kim, Mahmoud and Woodall [20]
sugges ed o ha e ze o mean explana o y a iables, whe e
he leas squa es es ima o s o slope and in e cep a e
independen andom a iables. By his coding ( ans o -
ma ion), he EWMA-3 app oach has he IC model
Yij ¼B0þB1Xdi þeij;eij ¼/eij1ðÞ
þaij;eij N0; 2

;
i¼1;2;...;n;j¼1;2;...;
ð9Þ
whe e he coded explana o y a iables (Xdi ¼XiX) lead
o he ans o med IC in e cep B
0
=A
0
?A
1
X,A0and A1
a e de ined as in (1). No e ha he ans o med IC slope is
B
1
=A
1
in his app oach. The OLS es ima ion o he
pa ame e s ( b
B0j;b
B1j;b 2j) gene a es h ee sepa a e EWMA-
based e o s o in e cep (eIj), slope (eSj) and s anda d
de ia ion (eij), as ollows:
eIj ¼^
B0jþ;^
B0j1ðÞ
1;ðÞB0;
eSj ¼^
B1jþ;^
B1j1ðÞ
1;ðÞB1;
eij ¼yij ;yij1ðÞ
1;ðÞB0þB1Xdi;
MSEj¼1
nX
n
i¼1
e2
ij:
ð10Þ
Based on he OLS es ima ion, he Mean Squa e E o
(MSE) o he j h p o ile is conside ed as he es ima o o
he e o a iance ( o de ails see Kim e al. [20], Huwang
e al. [59] and Yeganeh and Shadman [54]), hus, h ee
cha s a is ics can be calcula ed as ollows:
EWMAIj ¼heIj þ1hðÞEWMAIj1ðÞ
;
EWMASj ¼heSj þ1hðÞEWMASj1ðÞ
;
EWMAEj ¼max hMSEj1

þ1hðÞEWMAEj1ðÞ
;0

:
ð11Þ
The con ol limi s o he h ee sepa a e con ol cha s a e
designed as:
16324 Neu al Compu ing and Applica ions (2023) 35:16321–16340
123
UCLI¼LCLI¼LI ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h
n2hðÞ
s
UCLS¼LCLS¼LS ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h
n2hðÞ
s
UCLE¼LEffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
hVa MSEj

2hðÞ
s
ð12Þ
I is wo h no ing ha LCLE¼0, and some sugges ions
ega ding Va ðMSEjÞcan be ound in Kim, Mahmoud and
Woodall [20], Noo ossana e al. [44] and Hosseini a d e al.
[53]. EWMA-3 igge s an OC signal when a leas one o
he s a is ics exceed he con ol limi s. The p oposed con-
s an s en ailing L
I
,L
S
and L
E
a e usually adjus ed o each a
desi ed alue o ARL
0
in such a way ha each o he
sepa a e cha s achie es an iden ical indi idual ARL
0
.
2.5 OLS es ima ion o he pa ame e s
Since he pa ame e s es ima ed ia OLS a e employed as
inpu s o he machine lea ning echniques, some de ails on
he OLS es ima o s a e gi en below [20,21,53]. While he
in e cep o he o iginal and he ans o med model is
es ima ed by b
A0j¼Yjb
A1jXand b
B0j¼Yj, espec i ely,
he slope pa ame e in bo h models is es ima ed ia
b
A1j¼b
B1j¼SXYj
SXX , whe e SXYj¼Pn
i¼1YijðXiXÞand SXY ¼
Pn
i¼1ðXiXÞ2(wi h Yj¼1
nPn
i¼1Yij and Xj¼1
nPn
i¼1Xij).
No e ha he de ini ion o MSE
j
based on (10) is equi alen
o he es ima o o he e o a iance.
3 The p oposed con ol cha o moni o ing
au oco ela ed p o iles
The basic idea in his pape is o use machine lea ning
echniques ins ead o s a is ical con ol cha s o moni-
o ing p o iles wi h be ween-au oco ela ion. Fo his pu -
pose, se e al ea u es a e ex ac ed om he p ocess o
embed in o he machine lea ning echniques. Using aining
pa e ns and he ob ained con ol limi s help o imp o e
decision-making abou he p ocess.
To employ a machine lea ning echnique as a con ol
cha , ou main s eps a e de ined in he ollowing. In he
i s s ep, he s uc u e o he inpu ea u es and ou pu s o a
machine lea ning echnique a e de e mined, and hen, a
aining da a se based on he inpu ea u es and ou pu s is
gene a ed by simula ing IC and OC p o iles in he second
s ep. The hi d s ep uses he gene a ed da a se o ain a
machine lea ning echnique, and inally, by he de ini ion
o a con ol limi , he machine lea ning echnique p o ides
in o ma ion abou he p ocess condi ion in he ou h s ep.
Figu e 1shows a s ep-by-s ep lowcha ega ding he
p oposed me hod in moni o ing au oco ela ed p o iles.
Mo eo e , de ails o hese s eps a e p esen ed in he ol-
lowing subsec ions.
3.1 De ining he s uc u e o inpu ea u es
and ou pu s
Ex ac ing p ope inpu ea u es is a key s ep in he
implemen a ion o machine lea ning echniques [60]. In he
li e a u e, a ious s a egies ha e been employed o
ex ac ing ea u es. Fo example, Chen e al. [57] and
Se gin and Yan [51] used au oencode s o ob ain Phase I
in o ma ion, which is no compa ible o his s udy. Hos-
seini a d e al. [53] and Yeganeh and Shadman [54] sug-
ges ed o ake he OLS es ima ions o he linea p o ile
pa ame e s as inpu ea u es. This inpu s uc u e pe o ms
well in p o iles wi hou au oco ela ion, bu i is no able o
p o ide eliable esul s when be ween-au oco ela ion o
he p o iles is p esen since he e ec o au oco ela ion is
no cap u ed by he dis ibu ion o he OLS es ima o s. So,
in addi ion o hese inpu s ( b
A0j,b
A1j,b j), u he app op ia e
inpu ea u es a e p oposed in he ollowing, which a e
sui able o accoun o be ween-au oco ela ion e ec s o
i s o de (i.e., AR(1) au oco ela ion). In pa icula , he
p oposed inpu s uc u e add esses he e ec o he mean o
esponses, he mean o e o s, and T
2
s a is ic each in he
cu en sample (j) and he p e ious sample (j-1). I should
be men ioned ha one o he main bene i s o machine
lea ning-based algo i hms is hei independency o he
basic assump ions abou he p ocess. So, when eplacing
p ope es ima ions ela ed o o he au oco ela ion models
De ine inpu ea u es
Gene a e aining da a se based on
he inpu ea u es
Selec a machine lea ning echnique
Gene a e IC p o iles wi h a ge as 0 Gene a e OC p o iles wi h a ge as 1
T ain he machine lea ning echnique
Se CV based on he ou pu o
machine lea ning and ARL0
Gene a e andom OC p o iles
Compu e p ope inpu s based on he
gene a ed p o iles
Impo he inpu s o he machine
lea ning echnique
Compu e ou pu and compa e i wi h
CV o decide on he p ocess
Fig. 1 The gene al s ep-by-s ep lowcha o he p oposed me hod
Neu al Compu ing and Applica ions (2023) 35:16321–16340 16325
123

such as MA, ARMA and ARIMA, he p oposed me hod
can be easily applied o o he p ocess condi ions.
In machine lea ning, he e a e se e al app oaches o
no malizing and scaling o he inpu s, one o which
in ol es he pa ame e dis ibu ion o be used. Fo
ins ance, Yeganeh and Shadman [54] scaled he pa ame e s
o simple linea p o iles, i.e., in e cep , slope and s anda d
de ia ion, wi h no mal and chi squa e dis ibu ion ( he
ela ions a e no epo ed o b e i y bu he in e es ed
eade is e e ed o Eqs. (4) o (9) in Yeganeh and Shad-
man [54]). Since he au oco ela ion was no conside ed in
Yeganeh and Shadman [54] o OLS es ima o s, we sug-
ges o u ilise he be ween-au oco ela ion e ec o he i s
o de by means o de ia ions be ween cu en (p e ious)
OLS es ima o s and hei espec i e IC alues, i.e., b
A0j
A0;b
A1jA1;b j 0ðb
A0ðj1ÞA0;b
A1ðj1ÞA1;b ðj1Þ
0Þ. Using his app oach, he means o cu en and p e ious
esponses (yj;yj1ðÞ
) a e au oma ically inco po a ed in he
inpu s uc u e as hey a e unc ions o he OLS es ima es
^
A0j¼yj^
A1jx;^
A0j1ðÞ
¼
yj1ðÞ
^
A1j1ðÞ
xÞ.
By conside ing he abo e inpu s, nume ous inpu com-
bina ions can be de ined in he p oposed me hod. Ha ing
in es iga ed se e al inpu ea u es, he ollowing h ee
inpu combina ions I, II and III wi h 8, 4 and 10 inpu s,
espec i ely, a e employed o each machine lea ning
echnique based on hei abili y o: (1) adequa ely add ess
he speci ic e ec s o be ween-au oco ela ion o ype
AR(1), and (2) inco po a e he de ia ions be ween OLS
es ima es and hei espec i e IC alues o e icien Phase
II moni o ing:
(I) b
A0ðj1ÞA0,b
A1ðj1ÞA1,b ðj1Þ 0,b
A0jA0,
b
A1jA1,b j 0,ej,eðj1Þ.
(II) b ðj1Þ 0,b j 0,
2
(j-1)
,
2
j
.
(III) b
A0ðj1ÞA0,b
A1j1ðÞ
A1,b ðj1Þ 0,b
A0jA0,
b
A1jA1,b j 0,ej,eðj1Þ,
2
(j-1)
,
2
j
.
These inpu combina ions a e mo i a ed by hei abili y
o conside e ec s ega ding au oco ela ion in a ious
ways. While inpu combina ion I add esses he aw AR(1)
s uc u e o he unde lying model, inpu combina ion II
aims o isola e he e ec s o he cu en and p e ious T
2
s a is ics ex ended by an addi ional conside a ion o he
cu en and p e ious e o a iances. Finally, inpu com-
bina ion III is he union o inpu combina ions I and II, and
he e o e, combines bo h main e ec s. In hese h ee inpu
combina ions, he ollowing no a ions a e u ilized:
•Es ima ed pa ame e s ia OLS in he p e ious sample
(b
A0ðj1Þ,b
A1ðj1Þ,b ðj1Þ).
•Es ima ed pa ame e s ia OLS in he cu en sample
(b
A0j,b
A1j,b j).
•Mean o e o e ms in he p e ious sample (eðj1Þ).
•Mean o e o e ms in he cu en sample (ej).
•T
2
s a is ic in he p e ious sample (
2
(j-1)
).
•T
2
s a is ic in he cu en sample (
2
j
).
No e ha he T
2
s a is ic is added as an inpu ea u e and
no u he s a is ics om o he con en ional con ol cha s
in o de o: (1) inc ease he wo se pe o mance o he T
2
con ol cha , and (2) a oid o e pa ame e iza ion and
complexi y wi h ega d o u he common compe i o s.
3.2 Gene a ion o he aining da a se
To cons uc he aining da a se , he IC and OC p o iles
a e gene a ed by means o simula ions. F om he simula ed
p o iles, he inpu s a e cons uc ed based on he p ede ined
h ee inpu s uc u es I, II and III in Sec . 3.1. Fo example,
he inpu s o he j h gene a ed p o ile consis o 10 ea u es
in inpu combina ion III as b
A0ðj1ÞA0,b
A1j1ðÞ
A1,
b ðj1Þ 0,b
A0jA0,b
A1jA1,b j 0,eðj1Þ,
ej; 2
ðj1Þand 2
j:Conside ing he sugges ions by Hosseini-
a d, Abdollahian and Zeephongsekul [53], equal numbe s
o IC and OC p o iles a e gene a ed in a way ha he a ge
alues o IC and OC p o iles a e se o 0 and 1,
espec i ely.
Hence, we conside he size o he aining da a se
(numbe o ows) as 6G. Fi s , 3GIC p o iles a e gene a ed
and hei inpu ea u es a e eco ded wi h a a ge alue
equal o 0. Then, 3GOC p o iles (Gp o iles wi h shi in
in e cep , Gp o iles wi h shi in slope, and Gp o iles wi h
shi in s anda d de ia ion) a e ob ained in he same way
wi h a a ge alue equal o 1. Finally, he aining da a se
has 6G ows and 9 (8 ?1), 5 (4 ?1) and 11 (10 ?1)
columns o inpu combina ions I, II and III, espec i ely
(no e ha he las column ep esen s he a ge alues). Fo
be e unde s anding, pseudo code 1 illus a es he p ocess
o da a se gene a ion o inpu combina ion III (an anal-
ogous p ocedu e also applies o inpu combina ions I and
II).
16326 Neu al Compu ing and Applica ions (2023) 35:16321–16340
123
3.3 T aining a machine lea ning echnique
A e ob aining a aining da a se , a machine lea ning
echnique can be ained on i s basis. In his pape , six
common machine lea ning echniques, i.e., ANFIS, ANN,
RBF, SVR, CNN and LSTM, wi h he abili y o gene a ing
con inuous ou pu s a e in es iga ed. Fo be e unde -
s anding, we p o ide a b ie desc ip ion abou he pa am-
e e s and adjus men s o each me hod in MATLAB
so wa e.
Neu al Compu ing and Applica ions (2023) 35:16321–16340 16327
123
•The ANFIS app oach u ilizes uzzy IF–THEN ules o
ain he pa ame e s wi h some basic algo i hms such as
sub ac i e clus e ing and g id po ioning, in which he
idea o ule gene a ion is di e en . The ‘gen is’
unc ion, which is a well-known single-ou pu Sugeno
uzzy in e ence sys em, is used o ob ain a g id pa i ion
o he aining p ocedu e.
•The ANN s uc u e, especially a Mul i-Laye Pe cep-
on (MLP), wi h g adien -based op imiza ion is
employed he e. An impo an issue in ANNs is ela ed
o he adjus men o he numbe o hidden laye s and
he neu ons. The unc ion ‘ eed o wa dne ’ u ilises a
ully connec ed ne wo k a chi ec u e using he BP
Le enbe g–Ma qua d aining algo i hm (‘ ainlm’
op ion). In his s udy, a single hidden laye wi h 10
neu ons is sugges ed o aining.
•RBF conside s di e en aining app oaches based on
he idea o clus e ing. I has only one hidden laye in a
way ha he neu ons wi h a dis inc sp ead ( adius) a e
added o i s s uc u e un il he p e-speci ied e o o
maximum numbe o neu ons is ob ained. Because he
aining p ocedu e is comple ed by he aim o aining
e o educ ion, he p obabili y o o e i ing would be
gene ally high in his app oach. The unc ion ‘new b’
wi h sp ead ( adius) 1, e o a e 0.05 and maximum
neu on size 100 is selec ed o aining pu poses.
•As addi ional machine lea ning echniques, SVM and
SVR ob ain he pa ame e s based on gene a ing a
hype plane in he p oblem space in o de o minimize
he gaps be ween he p edic ed and ob ained alues
conside ing a ke nel unc ion o mapping he inpu s o
he p oblem space. As we aim o each a con inuous
ou pu ( eg ession p oblem) in his s udy, he SVR
unc ion ‘ i s m’ wi h he gaussian ke nel unc ion is
used o aining (mo e de ails abou he classi ica ion
and eg ession na u e o machine lea ning-based con ol
cha s can be ound in Yeganeh and Shadman [54]).
The pa ame e epsilon, which de e mines he dis ance
be ween he eal and he es ima ed planes in he space,
is an impo an pa ame e o he SVR echnique. As he
common ange o epsilon is [0.3–0.5] [61], he alue 0.3
is selec ed in his pape .
•The deep leaning echnique CNN is u ilized o in es-
iga e i s de ec ion abili y in he SPM ield. Gene ally, a
CNN laye mo es some il e s along he inpu e ically
and ho izon ally and compu es he do p oduc o he
weigh s and he inpu , and hen adds a bias e m o
each some no el ea u es om he p ocess. CNNs ha e
se e al pa ame e s such as padding and il e size. As
he inpu s o his pape a e in ec o o m, he laye s a e
c ea ed wi h ‘con olu ion1dLaye ’ unc ion wi h il e
size 5.
•As a u he deep lea ning echnique, LSTM is ained
o e alua e i s pe o mance. Due o he conside a ion o
ime dependencies wi h he aim o ime uni s, LSTM
can iden i y he ime se ies ela ed pa e ns in an
e ec i e way. The mos impo an pa ame e o LSTM
is he numbe o hidden neu ons in each uni ha is
nea ly like he numbe o hidden laye s in common
ANNs. Two LSTM laye s a e de ined by he
‘ls mLaye ’ unc ion wi h 40 hidden neu ons in a way
ha he Adam op imize is u ilised o ob ain he bes
weigh s.
3.4 Decision on he p ocess condi ion
Conside ing he de ini ion o a ge alues, Hosseini a d
e al. [53] se he LCL o hei p oposed me hod o 0 and
deno ed he UCL as Cu ing Value (CV). The CV is
adjus ed by simula ions o each he desi ed alue o ARL
0
.
A e adjus men o he CV, he ou pu o he conside ed
machine lea ning echnique, e.g., ANN, is compa ed wi h
he CV o make a decision on he p ocess [43]. I he ou pu
o he ANN in he j h sample (O
j
) is la ge han he CV, his
indica es an OC condi ion (see Fig. 1 in Hosseini a d e al.
[53] o mo e de ails).
By employing his app oach in ou p oposed amewo k,
we can iden i y he p ocess condi ion when compa ing he
ou pu O
j
o a machine lea ning echnique wi h he
espec i e CV. Fo be e unde s anding, pseudo code 2
illus a es he p ocedu e o eaching an OC signal in one
i e a ion o simula ions when inpu combina ion III is used.
To compu e he ARL and SDRL by means o Mon e Ca lo
simula ions, his p ocedu e is i e a ed 10,000 imes.
16328 Neu al Compu ing and Applica ions (2023) 35:16321–16340
123
4 Simula ion s udy
To show he e ec i eness o ou p oposed me hod, a
comp ehensi e simula ion s udy is conduc ed in his sec-
ion. To compa e he six machine lea ning echniques
ANFIS, ANNBP, CNN, LSTM, RBF and SVR, he CV o
each me hod is se o each ARL
0
equal o 200, as i is he
mos common alue in p o ile moni o ing. The nex aim is
o ind he bes inpu among he h ee combina ions I, II
and III. As such, h ee inpu combina ions unde di e en
pa ame e se ings a e used as inpu s o he machine
lea ning echniques. Due o he page limi , we only p esen
he esul s o h ee inpu combina ions o he shi in
in e cep in Table 1unde /= 0.1 and o he esul s can be
gi en o he in e es ed eade s upon eques . As can be
seen, nea ly all machine lea ning echniques p oduced he
bes (i.e., lowes ) alues in e ms o ARL
1
o inpu com-
bina ion III. This is due o he ac ha inpu combina ion
III is able o combine bo h main e ec s o inpu combi-
na ions I and II, namely:
(1) app op ia ely add essing he aw AR(1) s uc u e o
he unde lying model, and.
(2) he e ec s o he cu en and p e ious T
2
s a is ics as
well as o cu en and p e ious e o a iances.
In o he wo ds, only conside ing (2), i.e., using inpu
combina ion II, is no enough o each p ope esul s. On
he o he hand, concen a ing on (1), i.e., using inpu
combina ion I, enables o ob ain be e pe o mance on
a e age han wi h (2). The combina ion o (1) and (2) ia
inpu combina ion III clea ly s eng hens he e ec o (1)
and leads o supe io esul s.
Simila esul s a e ob ained o he es o pa ame e
se ings; hus, we only p esen he esul s o inpu combi-
na ion III o he es o he expe imen s. In addi ion, due o
he i s -p io i y impo ance o de ec ing small shi s in he
unde lying p ocess, he ocus is mainly on smalle shi s in
he simula ion s udies. As o la ge shi s, he e a e gen-
e ally he same pa e ns as o smalle shi s.
Fo compa isons o single shi s in in e cep , slope and
s anda d de ia ion, he IC model is aken om Noo ossana
e al. [44] and Wang and Huang [48], whe e A
0
=3,A
1
=2
and
2
= 1. In addi ion, he explana o y a iables ha e he
alues 2, 4, 6, 8 (n= 4), and 0.1, 0.5, 0.9 a e conside ed as
ixed alues o /. Fo compa isons o simul aneous shi s,
he IC model is ex ac ed om Wang and Lai [45].
In Sec . 4.1, he pe o mance o a ious machine
lea ning echniques is compa ed and he me hod wi h he
bes pe o mance is selec ed. In Sec . 4.2, he selec ed
machine lea ning echnique and con en ional s a is ical
con ol cha s in Phase II p o ile moni o ing a e compa ed.
Finally, Sec . 4.3 epo s he pe o mance o he bes
app oach o simul aneous shi s in p o ile pa ame e s.
4.1 Compa ing di e en machine lea ning
echniques based on inpu combina ion III
In his subsec ion, h ee indi idual shi s a e conside ed o
each pa ame e o compa e he pe o mance o each ech-
nique in a way ha he shi ed pa ame e s a e A
0
?k ,
A
1
?g and c . The alues o ARL
1
associa ed wi h
di e en machine lea ning echniques a e gi en in Table 2.
To ha e a ai compa ison, he alues o he SDRL
1
a e
addi ionally p o ided in Table 3 o each o he conside ed
shi s. The bold alues ep esen he app oach wi h he bes
pe o mance.
Neu al Compu ing and Applica ions (2023) 35:16321–16340 16329
123
compe i o s en ailing T
2
, EWMA/R and EWMA-3 a e
selec ed ollowing Noo ossana e al. [44]. Table 7shows
he esul s o ARL
1
o ANFIS and he compe i o s. No e
ha he se ups a e he same as in he p e ious subsec ion,
and he esul s o ANFIS and RBF a e ex ac ed om
Table 2.
As can be seen, ANFIS pe o ms conside ably be e
han he o he me hods o shi s ega ding in e cep and
slope. The e is a la ge di e ence especially o smalle
shi s; o example, ARL
1
is 3.096 o ANFIS gi en
k= 0.4, while ARL
1
is 99.7, 21.9 and 19.7 o he con-
en ional compe i o s T
2
, EWMA/R and EWMA-3,
espec i ely. Howe e , EWMA-3 and RBF ob ain he bes
esul s o shi s in he s anda d de ia ion. In addi ion, he
s a is ical me hods ou pe o m ANFIS ega ding shi s in
he s anda d de ia ion.
4.3 Compa ing he bes machine lea ning
echnique wi h con en ional s a is ical
app oaches conside ing simul aneous shi s
In indus ial p ocesses, simul aneous shi s may occu , so a
con ol cha should also be able o de ec such ype o
shi s. Wang and Lai [45] conduc ed se e al simula ions
abou simul aneous shi s wi h he IC model p oposed by
Noo ossana, Ami i and Soleimani [44]. In he ollowing,
we compa e ANFIS wi h wo epo ed schemes in Wang
and Lai [45], i.e., T
2
and MEWMA. MEWMA is an
ad anced e sion o EWMA con ol cha s ha in eg a es
he e ec o p e ious samples in one s a is ic, and some
esea che s epo ed ha he pe o mance o his app oach
in p o ile moni o ing is e y well [17,21,59]. Table 8
shows he esul s in e ms o ARL
1
o simul aneous shi s
in in e cep and slope. No e ha we es ic he compa ison
o loca ion pa ame e s and do no conside u he simul-
aneous shi s, which include shi s in he s anda d de ia-
ion, due o he supe io pe o mance o ANFIS ega ding
shi s in in e cep and slope. This is also in line wi h he
app oach p oposed in Wang and Lai [45].
Acco ding o Table 8, ANFIS ou pe o ms bo h o he
me hods. The de ia ions in e ms o ARL
1
a e angible; o
example, he alues o ARL
1
a e 135.73, 180.42 and
196.15 (1.91, 34.22 and 49.64) o ANFIS, MEWMA and
T
2
, espec i ely, o he smalles (la ges ) shi k= 0.2 and
g= 0.025 (k= 1 and g= 0.125). While he e is no dis inc
end o he absolu e de ia ions be ween he alues o
ARL
1
o ANFIS and each o bo h compe i o s o
inc easing shi sizes, he e is gene ally an inc easing
beha iou o he co esponding ela i e de ia ions, i.e.,
ARLMEWMA
1ARLANFIS
1
ARLANFIS
1
and ARLT2
1ARLANFIS
1
ARLANFIS
1
ega ding small shi s (see Table 8). Tha is, he la ge he
shi s in slope and/o in in e cep , he la ge he ela i e
de ia ions.
As o la ge shi s in slope and/o in e cep (k[1 and
g[0.125, no abula ed due o lowe ele ance), he al-
ues o ARL
1
ega ding ANFIS dec ease o a small ex en ,
while he alues o ARL
1
ega ding MEWMA and T
2
become close o he espec i e ARL
1
alues o ANFIS,
i.e., we obse e a dec easing beha io o he co espond-
ing ela i e de ia ions ega ding la ge shi s. To sum up,
ANFIS clea ly ou pe o ms bo h me hods in de ec ing
simul aneous shi s and i s de ec ion abili y is especially
be e o lowe shi sizes.
S a is ical con ol cha s usually equi e he ul ilmen o
some p incipal assump ions o each he bes pe o mance,
while he occu ence o complica ed pa e ns in he man-
u ac u ing p ocess may lead o he in alidi y o some o he
p esumed assump ions and hus o de e io a ions in hei
pe o mance. In con as , machine lea ning echniques
encoun e less challenges p o ided ha inpu combina ions
and aining p ocedu e a e de ined p ope ly. I could be
concluded om he abo e esul s ha he machine lea n-
ing-based echniques, and especially ANFIS, pe o m be -
e han con en ional s a is ical me hods when moni o ing
au oco ela ed p o iles; howe e , some compu a ional
e o may be equi ed when implemen ing hese app oa-
ches. Due o he exis ence o online da a collec ion sys ems
in eal applica ions, big da a s o age and de elopmen o
high echnology compu e s, his challenge is becoming
easie in a way ha machine lea ning-based sys ems can
au oma ically analyze p ocess da a o iden i y OC si ua-
ions. To his end, he de ini ion o p ope inpu ea u es,
da ase de elopmen , ele an aining adjus men and
accep able alse ala m a es a e essen ial asks. These s eps
a e usually pe o med as o -line modelling phase while he
ope a ion (online) phase e e s o he implemen a ion o he
ained model on he online da a o de ec he p ocess
Table 9 The IC (black) and OC ( ed) gene a ed esponses in he
illus a i e example
jy
ij
172.253 73.264 72.967 75.188
272.345 73.845 73.610 74.569
372.333 73.363 72.709 74.548
472.193 73.147 73.649 73.942
573.157 74.618 73.373 74.962
673.239 74.219 73.498 75.270
772.352 74.249 73.949 74.897
16336 Neu al Compu ing and Applica ions (2023) 35:16321–16340
123

condi ion [57,60]. By his p ocedu e, he p oposed
machine lea ning-based app oach in his pape can imp o e
he moni o ing o indus ial p ocesses in e ms o OC
de ec ion abili y.
5 Illus a i e example
In his sec ion, an illus a i e example o a chemical p o-
cess is conduc ed o demons a e a eal applica ion. In ac ,
his example could be conside ed as a calib a ion sys em in
he chemical indus y. Some imes, i is necessa y o con ol
a chemical p ocess a om he labo a o y wi h emo e
schemes in which some gas senso s a e used as he con-
olle . These senso s a e used o moni o such a chemical
p ocess o e ime. Al hough i is a bene icial app oach, i
needs new calib a ion by changing he senso s’ adjus men s
as he a iabili y o gas senso s may a ec he pe o mance
o he unde lying calib a ion model [67]. These changes
may be caused by di e en chemical ma e ials, p ocess
condi ions, and equipmen mo emen s so hei calib a ion
should be checked o e ime. The app oach o p o ile
moni o ing can be applied o add ess calib a ion issues and
o online moni o ing o he p ocess.
Fo hese easons, some s udies such as Mahmood e al.
[68] and Nadi e al. [36] sugges ed o apply p o ile moni-
o ing. Me al oxide (MOX) as a conduc ome ic ype o gas
senso s is one o he bes op ions due o i s sensi i i y,
ope a ional ease, cos e iciency, apid esponse, and he
capabili y o spo ing a high numbe o ola iles. The
au ho s supposed MOX as a senso and moni o ed a
unc ional ela ionship be ween he esis ance (R) o he
senso (i.e., MOX) as he dependen a iable and he
concen a ions o ca bon monoxide in he senso as he
independen a iable.
To moni o his unc ional o mula, hey eco ded he
esul s o senso esis ance and di e en concen a ion
le els o e ime. Based on he eco ded da a, he
explana o y a iables a e ixed a 25, 100, 125, and
150 ppm. To each a be e pe o mance, i is sugges ed o
change he p ocess si ua ion wi h some addi i es. These
subs ances a e blended o a special p ocess o accele a e he
p ocessing abili y o he polyme s, imp o e he cha ac e -
is ics such as du abili y, s i ness, and enhance he se ice
li e. A wide ange o addi i es such as gas, eed, an i-wea ,
ood, uel, an ioxidan , plas ic addi i es ha e been ex en-
ded ye . Indeed, gas addi i es a e usually added o he gas
senso p ocesses o adjus he low o gas du ing he
expe imen [67]. Howe e , p e ious wo ks showed ha he
ela ion be ween esis ance and ca bon concen a ion migh
change in he case o addi i e ma e ials. To add ess hese
issues, Nadi e al. [36] in es iga ed si ua ions ela ed o he
be o e and a e o adding he addi i e ma e ial in a way
ha one addi i e ma e ial was added o he p ocess a e
ime 3278; so, he IC model was ex ac ed om he i s
3278 p o iles. Conside ing hese p o iles, Nadi e al. [36]
conside ed a simple linea IC model wi h he au oco ela-
ion e ec as ollows:
Yij ¼71:741 þ0:0176Xiþeij;
eij ¼0:565eij1ðÞ
þaij;aij N0;0:142ðÞ;
i¼1;2;3;4;j¼1;2;...
ð13Þ
To show he applicabili y o he p oposed me hod in
moni o ing he abo e IC model, Nadi e al. [36] u ilized
simula ions o OC da a gene a ion (ins ead o using he
da a a e he 3278 h p o ile). Following hem, we i s
gene a ed i e IC p o iles and hen con inued wi h he OC
p o ile gene a ion conside ing a shi in he in e cep un il
eaching an OC signal. The magni ude o he OC shi was
conside ed as 0.15 (o 0.5 ). Table 9shows he esponse
a iables o he gene a ed p o iles ( he black and ed alues
a e IC and OC p o iles, espec i ely).
To speci y he de ec ion abili y o ANFIS o his da a
se , i is ained based on he IC model in Eq. (13) and inpu
combina ion III. Conside ing ARL
0
= 200, he CV is se o
0.615. A e adjus men o he CV, he gene a ed da a in
Table 9is impo ed o ANFIS and he ou pu o each inpu
is compu ed. Table 10 epo s he inpu and ou pu alues
Table 10 Inpu and ou pu
alues o he i s se en
gene a ed p o iles applying
ANFIS wi h inpu combina ion
III (/= 0.565)
jInpu s Oj
10 0 0 0 -0.2 0.001 0.433 4.406 0 -0.08 0.477
2-0.2 0.0012 0.4332 4.406 0.219 -0.001 -0.26 0.963 -0.08 0.14 0.358
30.22 -0.0013 -0.2557 0.963 0.124 -0.004 0.213 3.209 0.14 -0.31 0.230
40.12 -0.004 0.213 3.209 0.076 -0.003 -0.37 1.404 -0.31 -0.12 0.318
50.08 -0.003 -0.3709 1.404 1.194 -0.007 0.304 9.352 -0.12 0.68 -0.357
61.19 -0.007 0.3045 9.352 1.08 -0.005 0.196 1.575 0.68 0.26 0.157
71.08 -0.005 0.196 1.575 0.21 0.002 -0.22 0.971 0.26 0.05 0.849
Neu al Compu ing and Applica ions (2023) 35:16321–16340 16337
123
o he i s se en gene a ed p o iles. Hence, ANFIS only
needs wo OC samples o igge a signal. The signal in he
7 h sample appea s because he inal s a is ic exceeds he
CV ( ed ho izon al line in Fig. 2), so ANFIS can igge an
OC signal (O
7
= 0.849 [0.615 = CV).
6 Conclusions
In p o ile moni o ing, he e o e m o en does no ollow a
simple s uc u e and is a ec ed by au oco ela ions. Fo
his eason, a no el moni o ing scheme o linea au o-
co ela ed p o iles wi h be ween-au oco ela ion o i s
o de in Phase II o p ocess moni o ing has been p oposed
in his pape . Unlike mos o he exis ing me hods ha use
common s a is ical con ol cha s, his pape employed
a ious machine lea ning echniques, such as ANFIS,
ANNBP, CNN, LSTM, RBF and SVR as a con ol cha .
To his aim, ou main s eps we e de ined. In he i s s ep,
he s uc u e o he inpu ea u es and ou pu s o a machine
lea ning echnique we e de e mined, and hen, a aining
da a se based on he inpu ea u es and ou pu s was gen-
e a ed by simula ing IC and OC p o iles in he second s ep.
The hi d s ep u ilized he gene a ed da a se o ain a
machine lea ning echnique, and inally, by he de ini ion
o a con ol limi , he machine lea ning echnique p o ided
in o ma ion abou he p ocess condi ion in he ou h s ep.
The s udy conduc ed pu sued h ee main objec i es. Due
o he high impo ance o inpu ea u es in machine
lea ning, some inpu ea u es, which a e app op ia e o
accoun o be ween-au oco ela ion e ec s o i s o de ,
we e de ined and compa ed o achie e he mos app op ia e
inpu combina ion. The esul s indica ed ha inpu com-
bina ion III, which is de ined as he union o inpu com-
bina ions I and II and combines bo h main e ec s o hese
inpu combina ions, is he mos app op ia e one. Fo he
second aim, di e en machine lea ning echniques we e
compa ed o iden i y he mos adequa e one. Expe imen al
s udies showed ha ANNBP, CNN, LSTM and SVR we e
mos ly no able o each a sa is ac o y de ec ion abili y in
compa ison wi h ANFIS and RBF. Among ANFIS and
RBF, ANFIS was p e e able wi h espec o shi s in
in e cep and slope, while RBF had he bes pe o mance
ega ding shi s in he s anda d de ia ion. This supe io i y
was ob ious o low and mode a e au oco ela ion coe i-
cien s (i.e., /= 0.1 and 0.5), while i was no possible o
iden i y a consis en ly bes me hod o a la ge alue (/
= 0.9). To add ess his issue, we addi ionally implemen ed
an o e all pe o mance measu e, called RMI. Following
RMI, we ound ha ANFIS u ns ou o be he me hod wi h
he bes o e all a e age pe o mance o /= 0.9. The hi d
aim o his s udy was o compa e machine lea ning-based
echniques wi h s a is ical con ol cha s. This compa ison
led o he esul ha he de ec ion abili y o ANFIS ou -
pe o med all he compe i o s ega ding shi s in in e cep
and slope. Howe e , he de ec ion abili y o ANFIS
ega ding shi s in he s anda d de ia ion was in e io
compa ed o he selec ed s a is ical con ol cha s. In his
ega d, he EWMA-3 con ol cha pe o med be e , and
he bes machine lea ning echnique o his pu pose was
RBF (wi h a pe o mance ha is ha dly wo se han ha o
EWMA-3). Hence, machine lea ning-based con ol cha -
s, and ANFIS in he i s place, a e sugges ed o be u ilized
in p o iles ha a e cha ac e ized by be ween-sample AR(1)
au oco ela ion o conside ably imp o e he de ec ion
abili y o he con ol cha .
Employing he p oposed no el inpu ea u es wi h o he
machine lea ning echniques and o he p o ile ypes such as
nonlinea o Gene alized Linea Models (GLMs) in he
p esence o au oco ela ions could be a p omising a enue
o po en ial u u e esea ch. Also, implemen ing he p o-
posed me hod in p o iles ha a e cha ac e ized by wi hin
0.477
0.358
0.230
0.318
-0.357
0.157
0.849
-0.500
-0.300
-0.100
0.100
0.300
0.500
0.700
0.900
1234567
Oj
Sample Numbe
Fig. 2 The inal cha s a is ics
o he i s se en andom
gene a ed p o iles in he
illus a i e example (/= 0.565)
16338 Neu al Compu ing and Applica ions (2023) 35:16321–16340
123
sample au oco ela ion o in p o iles wi h o he au oco e-
la ion pa e ns, such as ARMA o VARMA a e u he
sugges ions o po en ial u u e di ec ions.
Acknowledgemen s The au ho s would like o hank ou anonymous
e iewe s o hei aluable eedback and sugges ions, which we e
impo an and help ul o signi ican ly imp o e he pape .
Funding Open Access unding enabled and o ganized by P ojek
DEAL.
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