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A Model for Determining the Dependability of Continuous Subsystems in Coal Mines Using the Fuzzy Logic Approach

Authors:
Nikola Stanic at Mining and Metallurgy Institute Bor
Nikola Stanic
Miljan Gomilanović at Mining and Metallurgy Institute Bor
Miljan Gomilanović
Petar Markovic at University of Belgrade - Faculty of Mining and Geology
Petar Markovic
  • University of Belgrade - Faculty of Mining and Geology
Daniel Krzanovic at Mining and Metallurgy Institute Bor
Daniel Krzanovic
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Abstract

This study presents a unique model for assessing the dependability of continuous parts of combined systems in open-pit mining through the application of fuzzy logic. Continuous sub-systems as part of the combined system of coal exploitation in surface mines have the basic function of ensuring safe operation, high capacity with high reliability and low costs. These subsystems are usually part of the thermal power plant's coal supply system and ensure stable fuel supply. The model integrates various independent partial indicators of dependability into an expert system specifically designed for evaluating these systems. It deconstructs the complex parameter of system dependability into distinct partial indicators: reliability, maintainability, and logistical support. These indicators are then integrated using fuzzy composition (max-min composition). Historical data from 2018 to 2023 is utilized alongside the fuzzy model to provide a retrospective analysis of system dependability, serving to validate the model's effectiveness. What sets this model apart from conventional approaches is its consideration of practical dependability indicators, thereby obviating the need for extensive long-term monitoring and data collection to portray the system's status accurately over time. This model serves as a valuable tool for assisting decision-makers in open-pit mining operations, facilitating planning, exploitation control, and the selection of maintenance strategies to ensure consistent production and cost reduction. Designed for quick assessment, the model relies on expert judgments and assessments to determine system dependability efficiently.
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Article Not peer-reviewed version
A Model for Determining the
Dependability of Continuous
Subsystems in Coal Mines Using the
Fuzzy Logic Approach
Nikola Stanic * , Miljan Gomilanovic , Petar Markovic , Daniel Kr
ž
anovi
ć
, Aleksandar Doderovic ,
Sasa Stepanovic
Posted Date: 24 July 2024
doi: 10.20944/preprints202407.1952.v1
Keywords: fuzzy logic; max-min composition; continuous part of combined system (CCS); open pit; mining;
dependability
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Article
AModelforDeterminingtheDependabilityof
ContinuousSubsystemsinCoalMinesUsingthe
FuzzyLogicApproach
NikolaStanic1*,MiljanGomilanovic1,PetarMarkovic2,DanielKrzanovic1,
AleksandarDoderovic1andSasaStepanovic1
1MiningandMetallurgyInstituteBor
2FacultyofMiningandGeology,UniversityofBelgrade
*Correspondence:Author:NikolaStanic;E‐mail:nikola.stanic@irmbor.co.rs
Abstract:Thisstudypresentsauniquemodelforassessingthedependabilityofcontinuouspartsof
combinedsystemsinopen‐pitminingthroughtheapplicationoffuzzylogic.Continuoussub‐
systemsaspartofthecombinedsystemofcoalexploitationinsurfacemineshavethebasicfunction
ofensuringsafeoperation,highcapacitywithhighreliabilityandlowcosts.Thesesubsystemsare
usuallypartofthethermalpowerplantʹscoalsupplysystemandensurestablefuelsupply.The
modelintegratesvariousindependentpartialindicatorsofdependabilityintoanexpertsystem
specificallydesignedforevaluatingthesesystems.Itdeconstructsthecomplexparameterofsystem
dependabilityintodistinctpartialindicators:reliability,maintainability,andlogisticalsupport.
Theseindicatorsarethenintegratedusingfuzzycomposition(max‐mincomposition).Historical
datafrom2018to2023isutilizedalongsidethefuzzymodeltoprovidearetrospectiveanalysisof
systemdependability,servingtovalidatethemodelʹseffectiveness.Whatsetsthismodelapartfrom
conventionalapproachesisitsconsiderationofpracticaldependabilityindicators,therebyobviating
theneedforextensivelong‐termmonitoringanddatacollectiontoportraythesystemʹsstatus
accuratelyovertime.Thismodelservesasavaluabletoolforassistingdecision‐makersinopen‐pit
miningoperations,facilitatingplanning,exploitationcontrol,andtheselectionofmaintenance
strategiestoensureconsistentproductionandcostreduction.Designedforquickassessment,the
modelreliesonexpertjudgmentsandassessmentstodeterminesystemdependabilityefficiently.
Keywords:fuzzylogic;max‐mincomposition;continuouspartofcombinedsystem(CCS);openpit;
mining;dependability
1.Introduction
Miningoperations,crucialtonumerouseconomiesworldwide,areundergoingatransformative
phase,markedbyheightenedenvironmentalconcerns,technologicaladvancements,andagrowing
emphasisonoperationalefficiency[1,2].Theseoperationsincludeawiderangeofactivities,from
excavationandmaterialextractiontotransportationandprocessing.Withinthecomplexstructureof
miningactivities,transportsystemsareoneofthekeycomponents,enablingthesmoothmovement
ofmaterialsacrosslargeminingsites[3].
Materialtransportationisacriticalaspectofminingoperations,significantlyinfluencingcosts,
efficiency,safety,andenvironmentalimpact[4,5].Consideringthatloadingandtransportationcosts
amountto60%ofthetotaloperatingcosts,itisessentialthatthesesystemsareefficientandreliable
[6].Theenvironmentalfootprintoftraditionaldiesel‐poweredtransportmethodsnecessitates
researchintosustainablealternativeslikeelectricandautonomousvehicles[7,8].Moreover,safety
andriskmanagementareparamount,withadvancedtechnologiessuchasautomationandreal‐time
monitoringofferingnewopportunitiesforoptimizingtransportroutesandenhancingdecision‐
making[9].Giventhecomplexandvariableconditionsofminingenvironments,tailoredsolutions
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from any ideas, methods, instructions, or products referred to in the content.
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© 2024 by the author(s). Distributed under a Creative Commons CC BY license.
2
areessential,makingcontinuousresearchinthisareacrucialforachievinggreatersustainability,
operationalexcellence,andeconomicviabilityintheminingindustry.
Variousmethodsandmodelsareusedforthepurposesofthisresearchinthefieldofmining,
whichprovidethepossibilityofdealingwiththecomplexandchangingconditionsofthemining
environment.Oneofthemostwidelyappliedmathematicalapproachesisthetheoryoffuzzysets,
whichissuitablefortheanalysisofprocessesinwhichuncertainty,ambiguity,subjectivity,and
indeterminacyprevail[10].
Theapplicationofthismethodenablestheaforementionedproblemtobesuccessfullyanalyzed,
andtheanalysisresultsreflectthepreviousexpertexperiencesandresultsofexperimental
measurementsinagoodway.Toassessthesuccessofusingthismethod,priorknowledgeofthe
behavioroftheanalyzedsystemsandprocessesisnecessary.Bycomparingtheexperienceand
experimentaldatawiththeanalysisresultsofthefuzzylogicmethod,itsverificationiscarriedout.
Belowisanoverviewofworkswiththeapplicationoffuzzylogicinminingandsimilartopics.
Thelargestnumberofworksisrelatedtothefieldofmechanizationinmining,wherefuzzylogic
wasusedtoevaluatetheperformanceofminingequipmentunderdifferentoperatingconditions.
Theapproachtakesintoaccountmultiplecriteriasuchasreliability,efficiencyandmaintenancecosts
[10–14].Thismathematicalapproachhasalsofoundapplicationinvariouspartsoftheproduction
processinsurfaceandundergroundmines,whereprocessessuchasloading,transportation,drilling
andblastingareadequatelyoptimized[15–19].Thescientificliteraturealsohighlightsthepervasive
natureofriskinminingoperations[20–24],emphasizingtheneedforrobustriskmanagement
strategiestomitigatetheimpactofpotentialfailures,whereriskassessmentmethodologiessuchas
failuremodeandeffectsanalysis(FMEA)andriskprioritynumber(RPN)calculationsareusedvery
effectivelyincombinationwithfuzzylogic[25].Fuzzylogiccanalsobeappliedtoanalyze
environmentaldatacollectedfromminingsitestoassesstheimpactofminingactivitiesonairand
waterquality,soilstability,andbiodiversity.Thisinformationcanhelpindevelopingstrategiesto
minimizeenvironmentaldegradationandcomplywithregulatoryrequirements[26–28].
Whenitcomestotransportsystems,theevolutionofminingpracticeshaswitnessedachange
thathasentailedtheadoptionofcontinuoushaulagesystems,markingadeparturefrom
conventionaldiscontinuousmethods.Whiletraditionaltransportationsystemsthatrelyontrucks
andloadersstillpredominateincertaincontexts,theadventofcontinuoussystemsusheredinanew
eraofefficiencyandproductivity.Continuousconveyorsystems,characterizedbycrushers,
conveyorbelts,andintegratedautomationtechnologies,offercountlessadvantagesover
discontinuoustechnologies[29].
Giventheevolvingchallengesofenvironmentalsustainability,safetyandcostoptimization,the
roleofcontinuoustransportsystemsisgainingincreasingimportanceinminingoperations.These
systems,characterizedbytheirabilitytooperate24/7withoutinterruption,offerapathtowards
sustainableandresponsibleminingpractices.Byminimizingenergyconsumption,reducingcarbon
emissionsandincreasingworkersafety,continuoustransportsystemssupporttransformative
changesintheminingindustry[30].
ThecontinuouspartofthecombinedsystemisusedatthecoalopenpitGacko,RepublicSrpska.
Thispaperpresentsamodelthatpredictsthedependabilityofthecontinuouspartofthecombined
system(CCSsystem)attheopenpitGackoapplyingthefuzzytheory.Moreprecisely,thispaper
dealswiththedevelopmentofamodelforpredictingthedependabilityofthecontinuouspartofthe
combinedsystemattheopenpitusingthemax‐mincomposition.Thebasicideaofthispaperisan
expertassessmentofpartialindicatorsthataffectthedependabilityandtheirsynergyinorderto
determinethedependabilityoftheCCSsystemswiththehelpoffuzzymodels.Inadditiontothe
fuzzymodel,ahistoricaloverview(period2018‐2023)ofdatarelatedtothedependabilityofthese
systemsisgiven.Thesehistoricaldataservedtoverifythefuzzymodel.
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2.ContinuousPartsoftheCombinedSystem
TheCCSsystem(crusher‐beltconveyors‐landfill)consistsoftwosemi‐mobileprimary
crushersSB1315andSB1515,beltconveyorsTU‐3,TU‐2,TU‐1,andPTU.Coalbroughtbytruckto
theSB1515crusherisdirectlyshakenontothesamerake,andthatbroughttotheSB1315crusheris
depositedatthelandfillanddosedtotherakeusingaloader,whereaftercrushingandpulverization
bytheconveyorsystem,itishandedovertopowerplant.Figure1showsaviewoftheopenpit
Gacko.Figure2showsthepositionoftheCCSsystemattheopenpitGacko.
Figure1.Gackoopenpit(photographedbytheauthorofthearticle:N.S.).
Figure2.ViewoftheCCSsystem(SourceGoogleEarth).
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Figure3.PartsofCCSsystemattheopenpitGacko(privatearchive).
3.Dependability
Dependabilityisacommontermusedtodescribetheavailabilityandfactorsaffectingit:
reliability,maintainability,andlevelofmaintainability[31,32].Thetermavailabilityiscommonly
usedasameasureofoperationalsafety[31,33].Theavailabilityisexpressedinquantitative
indicators,andassuchrepresentsameasureofoperationalsafetyandthusameasureofqualityin
use[34].Theperformanceofavailabilityhasadecisiveeffectonoperationalsafetyandqualityinuse
duetothewell‐knownfactthatthemachineshouldfirstofallbeavailableforwork,inordertorealize
theotherperformancesaswell[31,34].
Dependabilityisacomplexfunctionthatdependsonthefollowingperformances[35]:
performancesofreliability
performancesofmaintainability
performancesoflogisticsupportformaintenance
Operationalsafety:ʺAcollectivetermusedtodescribetheavailabilityperformanceandfactors
thatdeterminetheseperformances:reliabilityperformances,maintainabilityperformances,and
logisticssupportperformancesʺ[35]
ThedependabilityoftechnicalsystemsisconceptuallystipulatedbyISO‐IECstandards[36,37].
4.MaterialsandMethods
4.1.DevelopmentFuzzyModel
Thefirststepwhencreatingafuzzymodelisthedefinitionoflinguisticvariablesthatreferto
thepartialindicatorsofdependability,namely:
Reliabilityrepresentstheprobability,atacertainlevelofconfidence,thatthesystem(machine)
willsuccessfullyperformthefunctionforwhichitisintended,withoutfailureandwithinthe
specifiedperformancelimits,takingintoaccounttheprevioustimeofsystemuse,duringthe
specifieddurationofatask.Whenitisusedintheprescribedmannerandforthepurposeforwhich
itisintended,underthespecifiedloadlevels.[11]
Maintainabilityasasetofstructuralcharacteristicsthataffectthetimetoeliminatefailuresor
thetimeofperformingothermaintenanceprocedures,isaninternalpropertyoftheobserved
technicalsystem,thereforeitiscalledstructuralmaintainability.Thefollowingparametersaffectthe
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maintainability:t‐technology,e‐toolsandequipment,u‐ unification,d‐diagnostics,m‐
manipulativeness,s‐standardization[11,38].
Forthetechnicalsystemtosuccessfullyperformthesettasks,itisnecessarytoprovidelogistical
supportandnumerousconditions.Thelogisticsupportcombinesthemanagementprocesswith
appropriatetechnicalmeasurestodefinethenecessarysupportandcreateconditionsforthe
realizationofthegivenfunctionofthetechnicalsystemgoal.
LogisticalsupportperformancesaccordingtotheISO‐IECStandardaredefinedas:ʺTheability
ofmaintenancesystem,i.e.theorganizationthatperformsmaintenance,toprovideundergiven
conditionstherequiredmaintenanceofthetechnicalsysteminaccordancewiththemaintenance
policy[35,36]theStandardsoftheIEC300seriesdealwiththeconceptoflogisticsupportfor
maintenance[37].
D‐Dependability
R‐Reliability M‐Maintainability F‐Logisticalsupport
t‐Technological
e‐Toolsandequipment
u‐Unific ation
d‐Diagnostic
m‐Manipulativness
s‐Standardization
Figure5.Presentationofpartialindicatorsofdependability.
Intermsofthenumberoflinguisticvariables,itcanbeinferredthatsevenisthemaximumcount
ofvariablesthatapersoncanrationallyrecognizesimultaneouslywhileretainingthesamemeaning
[39].
Takingthisstatementintoaccount,thefiveratings(linguisticvariables),definedasfollows:
excellent(exc),good(good),average(aver),adequate(adeq),andpoor(poor),willbeconsideredin
thispaper.Linguisticvariables(ratings)aregivenintheformoftriangularfuzzynumbers,andtheir
graphicrepresentationispresentedinthefollowingfigure.
Correspondingfuzzynumbersofthementionedlinguisticvariablesaredefinedby(according
toFigure6):𝜇󰇛1, 0.25, 0, 0, 0󰇜,
𝜇󰇛0.25, 1, 0.25, 0, 0󰇜,
𝜇󰇛0, 0.25, 1, 0.25, 0󰇜,
𝜇󰇛0, 0, 0.25, 1, 0.25󰇜,
(1)
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𝜇󰇛0, 0, 0, 0.25, 1󰇜.
Partialindicatorst,e,u,d,m,smorecloselydeterminesthepartialindicatorM‐maintenance
convenience,whileM–maintainabilitytogetherwithR‐reliabilityandF‐logisticsupportdetermine
theD‐dependabilityofthesystem.ItwillbeshowninthefollowinghowthedependabilityDis
determinedbasedonindicatorsofmaintainabilityM,reliabilityRandlogisticalsupportF,whilethe
maintenanceconvenienceMisobtainedsimilarlybasedonpartialindicatorst,e,u,d,m,s.
Figure6.Fuzzysets.
TheideaofthisworkistoobtainamoreaccurateassessmentofthedependabilityofCCS
systemsattheopenpitGacko.Thisassessmentwasidentifiedasthebestpossibleamongtheworst
expectedratingsofthepartialavailabilityindicators(R,M,andF).LetthepartialindicatorsR,M,F
beshownintheformofthefollowingtriangularfuzzynumbers
𝜇𝜇
,𝜇
,𝜇,
𝜇
,𝜇
, 𝜇󰇛𝜇
,𝜇
,𝜇,
𝜇
,𝜇
󰇜,𝜇󰇛𝜇
,𝜇
,𝜇,
𝜇
,𝜇
󰇜. (2)
Inthenextstep,themax‐mincompositionisperformedonthem.Ifthementionedpartial
indicatorsR,M,Fareobserved,itispossibletomake𝐶5125combinationsofcorresponding
membershipfunctions,whichwillbefurtherdenotedwith
𝜇 󰇛𝜇
, 𝜇
,𝜇
),𝑖,
𝑗
,𝑘 ∈󰇝1, 2, 3, 4, 5󰇞(3)
Eachofthesecombinationsrepresentsonepossibleassessmentofthedependabilityandthe
followingtwovaluescanbeassociatewithit
Ω󰇟󰇠
 (4)
and𝑚min𝜇
,𝜇
, 𝜇
(5)
Ωtakesvaluesfromtheset󰇝1, 2, 3, 4, 5󰇞,andeachofthementionedvaluescanbeassociated
withthenumber𝜇whichrepresentsthemaximumvalueof
𝑚 of all those combinations for which Ωisequalto𝑙,za𝑙∈󰇝1, 2, 3, 4, 5󰇞,thatis
𝜇min𝑚∶ Ω𝑙.(6)
Inthisway,aratingforthedependabilityof𝐷isobtained
𝜇󰇛𝜇,𝜇,𝜇,𝜇,𝜇󰇜(7)
Usingthebest‐fitmethod,see[11],totransformtheobtainedratingsintobelongingtothefuzzy
set,determinedby(2),thedistanceisusedthatisdefinedby
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𝑑𝑑󰇛𝜇,𝜇 󰇜
󰇛𝜇 𝜇,󰇜
 , 𝜇𝜇,,𝜇,,𝜇,,𝜇,,𝜇,,(8)
For𝜇∈𝜇,𝜇 , 𝜇,𝜇 , 𝜇 .Smallvalues𝑑indicateproximitytothelinguistic
variable𝜇 .Accordingly,let𝑑betheminimumvalueoftheobtaineddistances𝑑,𝑑,𝑑,𝑑,𝑑,
thenthereciprocalvalueoftherelativedistancescanbeassociatedtoeachofthemthatisdetermined
by:𝛼𝑑
𝑑, 𝑖∈󰇝1, 2, 3, 4, 5󰇞.(9)
Ifforsomeithedistancevalue 𝑑isequalto0,thenthecorrespondingvalueofthereciprocal
valueofrelativedistanceis𝛼1, whiletheothervaluesofthereciprocalrelativedistancesare
equalto0.Thenormalizedvaluesofthusobtainedreciprocalvaluesoftherelativedistancesare
determinedby:𝛽𝛼
𝛼𝛼𝛼𝛼𝛼,𝑖∈󰇝1, 2, 3, 4, 5󰇞(10)
andpresentbelongingtotheappropriaterating:
𝐴󰇛𝛽,"excʺ󰇜,𝛽,"goodʺ,󰇛𝛽,"averʺ󰇜,𝛽,"adeqʺ,𝛽,"poorʺ(11)
Intheend,theappropriatelinguisticratingisobtainedasfollows:
𝑍5𝛽4𝛽3𝛽2𝛽1𝛽
𝛽𝛽𝛽𝛽𝛽 (12)
Inasimilarway,aratingformaintainabilityMisobtainedfromthelinguisticvariablest,e,u,d,
m,swhichislaterusedtodeterminethedependabilityD.
Figure7showsthefuzzymodelalgorithmfordependabilityevaluation.
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8
Start
Exp ert
evaluation
(Questionnaire)
Statistical processing
Fuzz y propos ition
Fuzz y composition
Best-fit m ethod
Data classification
Fuzzification
Fuzzy inference model
Identifica tion
Evaluation of
dependability
End
Situation analysis
Input- numerica l
values
Inpu t – fuz zy values
Output –fuzzy
values
Numerical value
Figure7.Algorithmoffuzzymodelforevaluationthedependability[11].
4.2.CaseStudy–OpenPitGacko
4.2.1.ResultsofExpertEvaluation
Determinationofthedependabilityofthesystemanditspartialindicatorswasprocessed
throughtheresultsobtainedthroughquestionnairesrelatedtotheexpertevaluationofthepartial
indicatorsofoperationalsafety.Thequestionnairecontaineddetaileddescriptionsofthepartial
indicatorsthemselves.Intheexpertevaluation,10expertsweresurveyed.Thefirst5expertsare
representativesoftheGackoMine(expertsfromthisfieldwithmanyyearsofworkonthesesystems
‐minimum10yearsofworkexperience),andtheother5expertsareexternalexpertswithmanyyears
ofexperienceinthefieldofopenpitmining.Ratingsareexpressedusingmembershipfunctions
representingpredefinedlinguisticvariablesrangingfromʹpoorʹtoʹexcellentʹwithinascaleof0to1.
Additionally,aparametercanbeassociatedwithmultiplelinguisticvariablessimultaneously,
ensuringthatthetotalsumofratingsequals1.Thefollowingtablesgivetheresultsofexpert
evaluationforeachpartoftheCCSsystem.ThelayoutofonequestionnaireisgiveninFigure8.
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Figure8.Layoutofquestionnaire.
Table1.ResultsofexpertevaluationforCrusherSB1515.
ExpertTypepooradeqavergoodexcExpertTypepooradeqavergoodexc
1
R00.50.500
6
R0000.60.4
t00.20.800t00.40.600
e00.60.400e00.20.800
u0.20.8000u00.10.900
d00.50.500d00.40.600
m00.30.700m00.30.700
s00.10.900s00.70.300
F0.40.6000F0.20.8000
2
R000.30.70
7
R000.30.70
t000.350.650t000.20.80
e000.20.80e0000.40.6
u000.60.40u00.40.600
d0.20.8000d0000.60.4
m0.50.5000m000.20.80
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s00.70.300s000.30.70
F00.30.700F00.40.600
3
R000.30.70
8
R0000.80.2
t000.40.60t00.40.600
e000.450.550e00.30.700
u00.250.7500u00.60.400
d00.10.900d000.20.80
m0.40.6000m000.70.30
s00.60.400s00.40.600
F00.30.700F00.10.900
4
R000.10.90
9
R0000.90.1
t000.20.80t00.30.700
e00.50.500e000.20.80
u0.40.6000u000.40.60
d00.40.600d000.20.80
m0.30.7000m000.70.30
s0.250.75000s00.30.700
F0.150.85000F0.20.8000
5
R000.30.70
10
R000.60.40
t00.30.700t00.30.700
e00.70.300e00.40.600
u00.40.600u00.60.400
d0.30.7000d00.10.900
m00.60.400m00.70.300
s0.30.7000s00.20.800
F00.30.700F00.40.600
Table2.ResultsofexpertevaluationforCrusherSB1315.
ExpertTypepooradeqavergoodexcExpertTypepooradeqavergoodexc
1
R0000.60.4
6
R0000.60.4
t000.20.80t00.40.600
e0000.70.3e00.20.800
u0.450.55000u00.10.900
d000.10.90d00.40.600
m00.30.700m00.30.700
s00.20.800s00.70.300
F000.40.60F0.20.8000
2
R000.30.70
7
R000.30.70
t0000.30.7t000.20.80
e0000.40.6e0000.40.6
u000.20.80u00.40.600
d000.40.60d0000.60.4
m0.50.5000m000.20.80
s000.80.20s000.30.70
F000.20.80F00.40.600
3
R000.30.70
8
R0000.80.2
t000.40.60t00.40.600
e000.450.550e00.30.700
u00.250.7500u00.60.400
d00.10.900d000.20.80
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m0.40.6000m000.70.30
s00.60.400s00.40.600
F00.30.700F00.10.900
4
R000.10.90
9
R0000.90.1
t000.20.80t00.30.700
e00.50.500e000.20.80
u0.40.6000u000.40.60
d00.40.600d000.70.30
m0.30.7000m000.40.60
s0.250.75000s00.30.700
F0.150.85000F0.20.8000
5
R000.30.70
10
R000.60.40
t00.30.700t00.30.700
e00.70.300e00.40.600
u00.40.600u00.60.400
d0.30.7000d00.10.900
m00.60.400m00.70.300
s0.30.7000s00.20.800
F00.30.700F00.40.600
Table3.Resultsofexpertevaluationforbeltconveyors.
ExpertTypepooradeqavergoodexcExpertTypepooradeqavergoodexc
1
R00.50.500
6
R0000.60.4
t00.20.800t00.40.600
e00.60.400e00.20.800
u0.20.8000u00.10.900
d00.50.500d00.40.600
m00.30.700m00.30.700
s00.10.900s00.70.300
F0.40.6000F0.20.8000
2
R000.30.70
7
R000.30.70
t000.350.650t000.20.80
e000.20.80e0000.40.6
u000.60.40u00.40.600
d0.20.8000d0000.60.4
m0.50.5000m000.20.80
s00.70.300s000.30.70
F00.30.700F00.40.600
3
R000.30.70
8
R0000.80.2
t000.40.60t00.40.600
e000.450.550e00.30.700
u00.250.7500u00.60.400
d00.10.900d000.20.80
m0.40.6000m000.70.30
s00.60.400s00.40.600
F00.30.700F00.10.900
4
R000.10.90
9
R0000.90.1
t000.20.80t00.30.700
e00.50.500e000.20.80
u0.40.6000u000.40.60
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d00.40.600d000.70.30
m0.30.7000m000.40.60
s0.250.75000s00.30.700
F0.150.85000F0.20.8000
5
R000.30.70
10
R000.60.40
t00.30.700t00.30.700
e00.70.300e00.40.600
u00.40.600u00.60.400
d0.30.7000d00.10.900
m00.60.400m00.70.300
s0.30.7000s00.20.800
F00.30.700F00.40.600
4.3.DeterminationthePartialIndicatorofMaintainabilityM
Onthebasisofthesubmittedresults,thefollowingestimateswereobtainedforeachanalyzed
partoftheCCSsystem.
Table4.RatingsofmaintainabilityindicatorsforCrusherSB1515,CrusherSB1315andbelt
conveyors.
 CrusherSB1515CrusherSB1315Beltconveyors
 pooradeqavergoodexcpooradeqavergoodexcpooradeqavergoodexc
t0.00000.28500.52500.19000.00000.13000.48000.32000.07000.00000.07000.35500.44500.13000.0000
e0.06000.25500.41500.27000.00000.34000.43000.20000.03000.00000.08000.38500.41500.12000.0000
u0.00000.10000.46500.37500.06000.00000.36000.35000.24500.04500.00000.14000.53000.33000.0000
d0.04000.17000.44000.30000.05000.12000.43000.35000.10000.00000.00400.22000.49000.25000.0000
m0.00000.17000.34000.37000.12000.07000.30000.33000.21000.09000.00700.18000.27000.37000.1100
s0.00000.07000.43000.44500.00550.00000.17000.45000.32500.05500.00000.08000.43000.46000.0300
Table5.Finalratingforpartialindicatorst,e,ud,m,s,forCrusherSB1515,CrusherSB1315andbelt
conveyorsintheformoffuzzynumber.
 CrusherSB1515CrusherSB1315Beltconveyors
 pooradeqavergoodexcpooradeqavergoodexcpooradeqavergoodexc
t0.07130.41630.64380.32130.04750.25000.59250.45750.15000.01750.15880.48380.56630.24130.0325
e0.12380.37380.54630.37380.06750.44750.56500.31500.08000.00750.17630.50880.54130.22380.0300
u0.02500.21630.58380.50630.15380.09000.44750.50130.34380.10630.03500.27250.64750.46250.0825
d0.82500.29000.55750.42550.12500.22750.54750.48250.18750.02500.09500.35250.60750.37250.0625
m0.04250.25500.47500.48500.21250.14500.40000.45750.31500.14250.11500.26500.40750.46500.2025
s0.01750.17750.55880.56630.16630.04250.28250.57380.45130.13630.02000.18750.56500.57500.1450
Onthebasisoftheobtainedratingsintheformoffuzzynumbers,theratingsobtainedusingthe
max‐mincompositionforthespecifiedpartsofthesystemareshowninthefollowingtable.
Table6.Ratingsobtainedforthepartialindicatorofmaintainabilityusingthemax‐min
composition.
M‐maintainabilitypooradeqavergoodexc
CrusherSB15150.12500.48450.48500.41630.0713
CrusherSB13150.02500.31500.45750.45750.2275
Beltconveyors0.06250.46500.46500.46500.0950
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Figure9.DistributionofoutputvaluesforindicatorMmaintainabilityforCrusherSB1515usingmax‐
mincomposition.
Figure10.DistributionofoutputvaluesforindicatorMmaintainabilityforCrusherSB1315using
max‐mincomposition.
Figure11.DistributionofoutputvaluesforindicatorMmaintainabilityforbeltconveyorsusingmax‐
mincomposition.
4.4.DeterminationofPartialIndicatorsofReliabilityandLogisticalSupportofPartsoftheContinuousPrats
ofCombinedSystem‐RandF
Onthebasisofthesubmittedresults,thefollowingestimateswereobtainedforeachanalyzed
partofthecontinuoussystemwhenthesetwopartialindicatorsareconcerned.
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Table9.RatingsofpartialreliabilityandlogisticalsupportforCrusherSB1515,CrusherSB1315and
beltconveyors.
 CrusherSB1515 CrusherSB1315Beltconveyors
 pooradeqavergoodexcpooradeqavergoodexcpooradeqavergoodexc
R0.070
0
0.640
0
0.240
0
0.050
0
0.000
0
0.270
0
0.620
0
0.110
0
0.000
0
0.000
0
0.070
0
0.650
0
0.240
0
0.040
0
0.000
0
F
0.000
0
0.000
0
0.420
0
0.485
0
0.095
0
0.000
0
0.260
0
0.370
0
0.325
0
0.045
0
0.000
0
0.000
0
0.460
0
0.500
0
0.040
0
Usingtheestimatedvaluesforthepartialindicatorsforsystemmaintainability,thefinalratings
forthepartialindicatorsR,M,andFforCrusherSB1515,CrusherSB1315andbeltconveyorsinthe
fuzzynumberform.
Table10.CorrespondingfuzzynumbersforCrusherSB1515,CrusherSB1315andbeltconveyors.
 CrusherSB1515CrusherSB1315Beltconveyors
 pooradeqavergoodexcpooradeqavergoodexcpooradeqavergoodexc
R0.230
0
0.717
5
0.412
5
0.110
0
0.125
0
0.425
0
0.715
0
0.265
0
0.027
5
0.000
0
0.232
5
0.727
5
0.412
5
0.100
0
0.010
0
M0.125
0
0.484
5
0.485
0
0.416
3
0.071
3
0.025
0
0.315
0
0.457
5
0.457
5
0.227
5
0.062
5
0.465
0
0.465
0
0.465
0
0.095
0
F0.000
0
0.105
0
0.541
3
0.613
8
0.216
3
0.065
0
0.352
5
0.516
3
0.428
8
0.126
3
0.000
0
0.115
0
0.585
0
0.625
0
0.165
0
Basedontheobtainedratingsintheformoffuzzynumber,theratingsobtainedusingthemax‐
mincompositionforthespecifiedpartsoftheCCSsystemareshowninthefollowingtable.
Table11.Obtainedratingsforoperationalsafetyusingthemax‐mincomposition.
D‐dependabilitypoo
r
adeqave
r
g
oodexc
CrusherSB15150.07130.41250.48500.48500.1050
CrusherSB13150.02750.26500.30330.30330.2478
Beltconveyors0.09500.41250.46500.46500.6250
Figure12.DistributionofoutputvaluesforDdependabilityforCrusherSB1515usingmax‐min
composition.
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Figure13.DistributionofoutputvaluesforDdependabilityforCrusherSB1315usingmax‐min
composition.
Figure14.DistributionofoutputvaluesforDdependabilityforbeltconveyorsusingmax‐min
composition.
4.5.DependabilityoftheCCSSystemattheOpenPitGacko
Onthebasisofobtainedratingsfordependabilityofthesystemparts,theoverallratingof
dependabilitywasobtainedusingthemax‐mincompositionandreadsasfollows:
(0.07125,0.3033,0.30333,0.30333,0.105).
Furtheranalysisshowsthatthecorrespondingvaluesobtainedbythebestfitmethodareequal
to:
(1.02977,0.78942,0.71215,0.77866,0.99645).
Thecorrespondingreciprocalvaluesoftherelativedistances𝛼are:
(0.69156,0.90211,1,0.91458,0.71468),
whilethevaluesofnormalizedreciprocalvalues𝛽areequalto:
(0.16376,0.21362,0.23680,0.21657,0.16923).
Appropriatelinguisticevaluation𝑍
 2.9860.
Onascaleof1‐5,thementionedsysteminoperationhasacenterofgravityoflinguistic
assessmentforthemax‐mincompositionof2.9860.Dependabilityis59%.
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Figure15.DistributionofoutputvaluesforDdependabilityforCCSsystemusingmax‐min
composition.
5.VerificationofFuzzyModel
Theverificationmodelisbasedontheresultsofsystematicmonitoringoftheworkofthe
continuouspartofthecombinedsystem,whichiscarriedoutbyaspeciallydesignatedservicewithin
GackoMineandThermalPowerPlant.Theeffectivesystemoperatingtimerepresentsthetotal
operatingtimeintheobservedperiodandiscalculatedbysubtractingthetotaldowntime(failures)
fromthecalendarfund.Theoperationofeachsystemisaccompaniedbycertainfailuresthathavea
directimpactontheutilizationandreliabilityofthesystem.Thesefailurescanbeplannedor
unplanned.Planneddowntimereferstopredefinedtechnologicaloperationsandregularservice
maintenance.Unplannedfailuresareunpredictableandarenotanintegralpartofthesystemʹs
workinghours.Thedepartmentinchargeofmonitoringtheoperationoftheanalyzedsystemkeeps
recordsthatincludethebeginning,duration,andtypeoffailures.Theserecordsaremaintainedona
shiftordailybasis,andanofficialmonthlyreportisissuedontheoperationofthesystemasawhole,
includingthecontinuouspart.
Failuresarecategorizedintothefollowinggroups:
technologicalfailures,
electricalfailures,
mechanicalfailures,
shiftofworkers,
equipmentoverhaul,
dailyreview,
weatherconditions.
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Figure16.TheauthorsofthearticlewithrepresentativesoftheGackomineduringatourofthefield
(privatearchive).
ThefollowingfigureshowsthepercentageparticipationbytypesoffailuresfortheCCSsystem
byyear.
Figure17.ThepercentageoffailuresoftheCCSsystemintheperiodfrom2018‐2023.years.
Thisgraphshowsthepercentageparticipationofdifferenttypesoffailuresintheoperationof
theCCSsystemintheperiodfrom2018to2023.Thekeyindicatorsofthegraphareasfollows:
Technologicalfailuresareconsistentlyhighandvariesfrom20.1%to33.4%peryear,which
accountsforthelargestpartoftotaldowntime(29%foraperiodof6years).
Shiftofworkersandequipmentoverhaularealsosignificantdowntimefactorswithoverall
percentagesof23%and22%.
Electricalfailuresandmechanicalfailureshavearelativelysmallershare,butshowvariations
betweenyears.
Weatherconditionshavetheleastparticipationintotaldowntime(0.5%foraperiodof6years).
Dailyreviewvariesbyyear,butrecordsasignificantparticipationof17%fortheentireobserved
period.
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Overalldatashowthattechnologicalfailures,shiftofworkersandequipmentoverhaularethe
mostdominantfactorsintheoperationoftheCCSsystem,whileweatherconditionsaretheleast
significant.
DependabilityoftheCCSsystemintheperiod2018‐2023isshowninthefollowingfigure(Figure
18).
Figure18.DependabilityofthecontinuouspartoftheCCSsystemintheperiodfrom2018‐2023.
years.
DataonthedependabilityoftheCCSsysteminpercentagesfortheperiodfrom2018to2023
showslightvariations.In2018and2020,thesystemhadthehighestdependabilityof55%.In2019,
dependabilitywasthelowest,at46%.Thiswastheresultofasignificantpercentageoffailuresrelated
tothedailyinspectionofequipment,whichwassignificantlyhigherin2019comparedtoallothers
years.In2021and2022,dependabilitywasstableat53%,while2023sawaslightdropto51%.Overall,
systemdependabilityvariesbetween46%and55%overtheobservedperiod.Theaveragevalueof
dependabilityfortheperiodof6yearsis52.16%.
6.Conclusions
Thispaperpresentsamodelforevaluatingthedependabilityoftechnicalsystemsusingfuzzy
logic.Itbreaksdowndependabilityintodifferentindicatorsandcombinesthemusingthemax‐min
compositionmethod.
UnlikeconventionalmodelsthatrelyonITmonitoringsystems,thisapproachincorporates
expertassessmentsfromindividualsdirectlyinvolvedinmachineoperationandmaintenance.Its
simplicityandrelianceonexpertjudgmentmakeiteasytoimplementwithoutextensivedata
collection.
Thismodeloffersafastwaytoassesssystemsafetyandprovidesvaluableinsightsforenhancing
specificindicatorsandoveralldependability.Byfollowingthemodelʹsrecommendations,companies
canstreamlinemaintenanceactivities,analyzeworkflows,pinpointweaknesses,andoptimizethe
lifecyclesofmachinerytoloweroperationalexpenses.
Fieldexperienceconfirmsthatthemodelaccuratelyreflectsthedependabilityofanalyzed
systems,consideringfactorssuchassystemcomponents,structure,age,workingconditions,and
organizationalinfluences.Whencomparingthereliabilitydataobtainedthroughthefuzzylogic
modelwiththeactualfielddatacollectedovertheperiodfrom2018to2023,thereisastrong
correlation.Thedependabilityobtainedbythemodelis59%,andbasedonhistoricaldataforaperiod
of6years,theaveragevalueofdependabilityis52.6%.Thisconsistencyunderscoresthemodelʹs
effectivenessincapturingthereal‐worldperformanceanddependabilityoftheCCSsystems.
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19
Moreover,thehistoricaldataʹsalignmentwiththemodelʹsoutputvalidatestheuseoffuzzylogic
inpredictingandimprovingdependability.Thisapproachnotonlyfacilitatesproactivemaintenance
andriskmanagementbutalsosupportsstrategicdecision‐makingbyprovidingasophisticated
understandingofsystemvulnerabilities.Theadaptabilityofthemodeltodifferentminingcontexts
anditsrelianceonexpertknowledgefurtherenhanceitspracticalityandrobustness.Ultimately,this
modelservesasavaluabletoolforminingcompaniesaimingtoachievegreatersustainability,
efficiency,andcost‐effectivenessintheiroperations.
Futureresearchcouldexplorefurtherrefinementofthismodelbyintegratingitwithadvanced
dataanalyticsandmachinelearningtechniquestoenhancepredictiveaccuracyandadaptability.
Additionally,expandingtheapplicationofthismodeltootherindustriesbeyondminingcouldreveal
broaderinsightsandbenefits,establishingitasaversatiletoolfordependabilityassessmentacross
varioussectors.Thecontinuedevolutionandvalidationofthismodelwillensureitsrelevanceand
efficacyintheever‐changinglandscapeoftechnicalsystemmanagement.
AuthorContributions:Conceptualization,N.S.andM.G.;methodologyN.S.,M.G.andP.M..;Writing–review
andeditingN.S.,P.M.,D.K.,A.D.,andM.G.,supervisionS.S.,N.S.andM.G.Allauthorshavereadandagreed
tothepublishedversionofthemanuscript.
Funding:ThisworkwasfinanciallysupportedbytheMinistryofScience,TechnologicalDevelopmentand
InnovationoftheRepublicofSerbia,Contractonrealizationandfinancingthescientificresearchworkofthe
MiningandMetallurgyInstituteBorin2024,ContractNo.:451‐03‐66/2024‐03/200052.
Acknowledgments:
•GratitudetoMinistryofScience,TechnologicalDevelopmentandInnovationoftheRepublicofSerbia
•MiningandMetallurgyInstituteBor,Zelenibulevar35,Bor
•GackoMineandThermalPowerPlant
ConflictsofInterest:Theauthorsdeclarenoconflictofinterest.
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