Engineering Reliability and Risk Assessment PDF
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Advances in Reliability Science Engineering Reliability and RISK ASSESSMENT Editedby HARISHGARG School of Mathematics,Thapar Institute of Engineering and Technology, Deemed tobe University, Patiala,Punjab, India MANGEYRAM Graphic EraDeemed to beUniversity, Dehradun, Uttarakhand, India; Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2023ElsevierInc.Allrightsreserved. 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Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluating andusinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuch informationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,including partiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assume anyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability, negligenceorotherwise,orfromanyuseoroperationofanymethods,products,instructions,orideas containedinthematerialherein. ISBN:978-0-323-91943-2 ForinformationonallElsevierpublicationsvisitour websiteathttps://www.elsevier.com/books-and-journals Publisher:MatthewDeans AcquisitionsEditor:BrianGuerin EditorialProjectManager:ClodaghHolland-Borosh ProductionProjectManager:KameshR CoverDesigner:MarkRogers TypesetbyTNQTechnologies Contributors Daniel O. Aikhuele FacultyofEngineeringandBuiltEnvironment,UniversityofJohannesburg,Johannesburg,South Africa Joydip Dhar ABV-IndianInstituteofInformationTechnologyandManagement,Gwalior,MadhyaPradesh, India Long Ding State Key Laboratory of Fire Science,University of Science and Technology of China, Hefei, Anhui, China Ahmed El-Awady Departmentof Environmental Engineering Sciences, Facultyof Graduate Studies and Environmental Research, Ain Shams University,Cairo, Egypt Ameneh Farahani Departmentof Industrial Engineering,Ooj Institute of Higher Education, Qazvin, Iran Zawar Hussain Departmentof Statistics, Faculty of Computing, The Islamia University of Bahawalpur, Bahawalpur, Pakistan Desmond E.Ighravwe FacultyofEngineeringandBuiltEnvironment,UniversityofJohannesburg,Johannesburg,South Africa Jie Ji State Key Laboratory of Fire Science,University of Science and Technology of China, Hefei, Anhui, China Komal Departmentof Mathematics, School of Physical Sciences, DoonUniversity, Dehradun, Uttarakhand, India Girish Kumar Delhi Technological University, Delhi, India Mohit Kumar DepartmentofBasicSciences,InstituteofInfrastructureTechnologyResearchandManagement, Ahmedabad,India Ajay Kumar ABV-IndianInstituteofInformationTechnologyandManagement,Gwalior,MadhyaPradesh, India M.K. Loganathan KazirangaUniversity, Jorhat, Assam, India ix x Contributors Reetu Malhotra ChitkaraUniversityInstituteofEngineeringandTechnology,ChitkaraUniversity,Punjab,India A.J. NakhalAkel Department of Mechanicaland Aerospace Engineering,Sapienza University,Rome,Italy Ram Niwas Department of Statistics, GoswamiGanesh Dutta Sanatan Dharma College, Chandigarh, India N. Paltrinieri Department of Mechanicaland Industrial Engineering,Norwegian Universityof Science and Technology, Trondheim, Norway R.Patriarca Department of Mechanicaland Aerospace Engineering,Sapienza University,Rome,Italy Kumaraswamy Ponnambalam Department of Systems Design Engineering,Facultyof Engineering,Universityof Waterloo, Waterloo,ON, Canada Vishal Pradhan ABV-IndianInstituteofInformationTechnologyandManagement,Gwalior,MadhyaPradesh, India Anum Shafiq School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China Ahmad Shoja Department of Mathematics and Statistics, Roudehen Branch,Islamic Azad University, Roudehen, Iran Tabassum NazSindhu Department of Statistics, Quaid-i-Azam University,Islamabad, Pakistan Zhaojun Steven Li Department of Industrial Engineeringand Engineering Management, Springfield, MA, United States Hamid Tohidi Department of Industrial Engineering,South Tehran Branch, Islamic Azad University, Tehran, Iran HuiminWang School of Mechanicaland Electrical Engineering, University of Electronic Scienceand Technology of China, Chengdu,China Om Yadav North Dakota University, Fargo,United States CHAPTER 1 Bayesian networks for failure analysis of complex systems using different data sources Ahmed El-Awady1 and Kumaraswamy Ponnambalam2 1DepartmentofEnvironmentalEngineeringSciences,FacultyofGraduateStudiesandEnvironmentalResearch,AinShams University,Cairo,Egypt;2DepartmentofSystemsDesignEngineering,FacultyofEngineering,UniversityofWaterloo, Waterloo,ON,Canada 1. Introduction Failureanalysisisanimportantandchallengingaspectofthestudyofcomplexsystems.A systemisdefinedtobeconsistingofcomponents,subsystems,inputs,andoutputswithin systemboundaries.Theinputsprovidephysicalresourcesandinformationtothesubsys- tems,whichareinteractingamongeachothertoproducesomeoutputs.Allinteractions areassumedtotakeplacewithinsystemboundaries.Acomplexsystemcanbedefinedasa system structure that is composed of usually a large number of components that have complexinteractions,[1].Anyfailureinperformingtherequiredinteractionsamongsys- temcomponents,oranyfailureingettingtheexpectedoutput/result,isconsideredtobe contributing to system failure [2]. Thus, analysis of a system with its components is a crucial step in determining the difficulties and complexities that the system will experi- enceatanystage.However,intherealworld,performanceofbothinputsandsubsystems isaffectedbyprobabilisticuncertainty,andhence,afailuremaycomewithanassociated probability.Themaingoalofthischapteristoevaluatetheprobabilityoffailureofcom- plex systems, while finding the failure causes using Bayesian Networks (BNs). For any given system with its inputs and subsystems, probabilistic failure analysis depends on finding the probability of not getting the required or estimated output of that system. The required output of the BN analysis may be the effect that is produced from certain causes (i.e., prediction reasoning), or the determination of the cause responsible for certain results and effects (i.e., diagnostic reasoning), both in probabilistic measures. Thus,determiningthecauseeeffectrelationisanimportantfirststepintheprobabilistic failure analysis, which allows for better understanding to enhance the system reliability and take decisions for mitigating the negative effects or better enhancing the causes. In this chapter, the graph representation of systems is conducted using BNs, which allow for representing marginal, conditional, and joint probability measures affecting system components;BNanalysisprovidestheabilitytodecomposealargesystemintoamanage- ablenumberofsubsystemsfortheirownanalysisandintheendaggregatingtheseresults EngineeringReliabilityandRiskAssessment ©2023ElsevierInc. ISBN978-0-323-91943-2,https://doi.org/10.1016/B978-0-323-91943-2.00001-0 Allrightsreserved. 1 2 EngineeringReliabilityandRiskAssessment toprovidethewholesystemresults.Representingsystemsofengineeringapplicationsus- ingBNsisaffectedbymultiplefactorsthataffecttheprobabilisticquantificationprocess. Theaimofthischapteristorevealthedifferentapproachesthatfacilitatetheprobabilistic quantification of BNs and hence, facilitate prediction of system failures. 2. Risk, reliability, and uncertainty Therearemanydefinitionsofrisk.Twocommondefinitionsofriskare:(i)probabilityof failure and (ii) the product of the probability of an undesired outcome (failure) and the consequences of that outcome [3e12]. The development of risk estimates or the deter- minationofrisksinagivencontextiscalledRiskAnalysis,whileRiskAssessmentisthe processofevaluatingtherisksanddeterminingthebestcourseofaction.Uncertaintyof outcomes is a common concept in all definitions of risk. Uncertainty may be defined as thestateofhavinglimitedknowledgesurroundingexistingeventsandfutureoutcomes, orimperfectabilitytoassignacharacterstatetoaprocessthatformsasourceofdoubt,[3]. Thus,uncertaintyisan intrinsicpropertyofriskandispresentinallaspectsof riskman- agementincludingriskanalysisandriskassessment[4].Generally,riskanalysisisasystem- atic tool that facilitates the identification of the weak elements of a complex system and thehazardsthatmainlycontributetotherisk.InRef.[13],hazardanalysisisdescribedas “investigating an accident before it occurs,” with the aim of identifying potential causes of accidents that can lead to losses. According to Refs. [11,12,14, and 15], availability is the ability of a component or system to function at a specified interval of time. This is closely related to what is called “Reliability,” which describes the ability of a system or component to function under statedconditionsforaspecifiedperiodoftime.Reliabilityengineeringisasubdiscipline of systems engineering that emphasizes dependability in the lifecycle management of a product. In reliability engineering programsdwhere reliability plays a key role in the cost effectiveness of systemsdtestability, maintainability, and maintenance are parts of these programs. In reliability engineering, estimation, prevention, and management of high levels of lifetime engineering uncertainty and risks of failure are common areas to bedealtwith.Theoretically,reliabilityisdefinedastheprobabilityofsuccess(Probability ofsuccess¼1-Probabilityoffailure).Sometimes,probabilisticstabilityanalysisisreferred toas“reliabilityanalysis.”Duringfailureprobabilityestimation,reliabilityanalysiscannot beusedsolely,andtheresultsofsuchanalysismustbemoderatedusingengineeringjudg- ment and appropriate models as useful tools in estimating conditional probabilities. In some literature, according to Refs. [6,12,16, and 17], uncertaintydwhich is a common concept for expressing inaccuraciesdmeans that a number of different values canexistforaquantity,whileriskmeansthepossibilityoflossasaresultofuncertainties. Accordingly, any uncertain variable, which can take various values over a range, should be provided with an uncertainty analysis that is used to assess output uncertainty and to Bayesiannetworksforfailureanalysisofcomplexsystemsusingdifferentdatasources 3 identifythemostefficientwaystoreducethatuncertaintyaccordingtothecontributing variables. Hence, in terms of statistical concepts, uncertainty can be thought about as a statistical variable and can be calculated using well-verified statistical procedures. In a broadappliedstatisticalsense,thevaluereportedforameasurementdescribesthecentral tendency(mean);whiletheuncertaintydescribesthestandarddeviation(deviationfrom themean).Ideally, thismeasureof uncertaintyis calculatedfrom repeatedtrials or tobe takenfromestimatesinwholeorpartinmanyengineeringtestsorresearchexperiments. Thus, risk analysis forces the engineer to confront uncertainties directly and to use best estimates and predictions, especially, while taking decisions regarding the safety of large technological (complex) systems.Increasingly, such decisions are being basedon the re- sultsofprobabilisticriskassessments,whichmustbeassociatedwithadequatequantifica- tion of the uncertainties. Uncertain parameters can be treated as random variables with appropriateprobabilitydistributions.Suchdistributionsareassignedonthebasisofavail- abledata(whichisoftenscarce),combinedwiththejudgmentofexperts(whichcanvary widely), adding another element of uncertainty into the uncertainty analysis itself. This means that there might be different sources of uncertainty due to data available, limited knowledge,and subjectivejudgment,and uncertaintyhere is assumedto beavailablein probabilistictermseitherfromdataorfromexpertjudgmentorlogicalinference,[3,16]. Acomplexsystemhasasystemstructurethatiscomposedofamanycomponentsthat havecomplexinteractionsandmayberepresentedasanetworkwherethenodesrepre- sent system components and the edges (links) are their interactions. Given any complex system that includes inputs, outputs, subsystems, and boundaries, it is reasonable to as- sumethatallofthesesystemcomponentsareinteractingeitherdirectlywithoneanother or indirectly. In order to estimate the probability of failure for such system, the interac- tions should be represented mathematically including any probability measures. A full representation of the system facilitates its analysis from the failure point of view. The mainobstacleinfailureanalysisofcomplexsystemsishowtorepresentthesystemcom- ponents and their basic and conditional probabilities. BNs are found to solve this prob- lem. BN provides a graphical representation of any system using basic probabilities, for system inputs, and conditional probabilities, for subsystems and their interactions. One of the main advantages of using BNs is the ability of integrating all types of data (social, environmental, technical, etc.) seamlessly in one representation. This is because of the probabilistic nature of the BNs, as everything is represented as a probability. 3. Bayesian networks (BNs) AccordingtoRefs.[18e22],BNs,orbeliefnetworks,areprobabilisticgraphicalmodels usedtorepresentknowledgeaboutanuncertaindomainusingacombinationofprinci- plesfromgraphtheory,probabilitytheory,computerscience,andstatistics.Inthegraph, nodes (vertices) are representing random variables, and the edges (arcs) represent the 4 EngineeringReliabilityandRiskAssessment interrelationships (conditional probabilistic dependencies) among these variables, which canbeestimatedusingknownstatisticalandcomputationalmethods.BNscanmodelthe quantitative strength of the interrelationships among variables (nodes), allowing their probabilitiestobeupdatedusinganynewavailabledataandinformation.BNisagraph- icalstructureknownasadirectedacyclicgraph(DAG),whichispopularinsomefieldsof learning (statistics, machine learning, and artificial intelligence). This means that a set of directed edges are used to connect the set of nodes, where these edges represent direct statistical dependencies among variables, with the constraint of not having any directed cycles (i.e., cannot return to any node by following directed arcs). Thus, the definition of parent nodes and child nodes is obvious. The directed edge is often directed from a parent node to a child node, which means that any child node depends on its parent node(s). BNs are mathematically rigorous, understandable, and efficient in computing joint probability distribution over a set of random variables, along with being useful in riskanalysis.Also,BNsdduetotherequirementsofbeingDAGsdaremoreeasilysolv- able than Markov networks. In BNs, there are two main types of reasoning (inference support): one e predictive reasoning (top-down or forward reasoning), in which evi- dencenodesareconnectedthroughparentnodes(causetoeffect),andtwoediagnostic reasoning (bottom-up or backward reasoning), in which evidence nodes are connected throughchildnodes(effecttocause).Firstly,thetopologyoftheBNshouldbespecified (structuring of graphical causality model), then, the interrelationships among connected nodes should be quantified, i.e., conditional probability distributions using conditional probability tables (CPTs). Also, the basic probabilities of basic (evidence) nodes should be determined using basic probability tables (BPTs). As the number of parent nodes, and/or their states, increases, the CPTs get very large. Fig. 1.1 introduces the different Figure1.1 TypesofreasoninginBNs[22]. Bayesiannetworksforfailureanalysisofcomplexsystemsusingdifferentdatasources 5 typesofreasoninginBNs.Nodeswithoutanyarrowsdirectedintothemarecalledroot nodes, and they have prior (basic) probability tables, while nodes without children are called leaf nodes. Nodes with arrows directed into them are called child nodes, while nodeswitharrowsdirectedfromthemarecalledparentnodes.Thepriorbasicprobability tables,fortherootnodes,andtheconditionalprobabilitytables,fortheparentandchild relationships,maybeobtainedfromhistoricaldatabasecurrentlyavailable,whichcanbe updatedincaseof havinganynew dataorinformation. Generally,quantifyingBNs de- pends on four sources of data: statistical and historical data, judgment based on experience (i.e. expert judgment), existing physical models (or empirical models), and logic inference. Where no such sufficient data exist, either subjective probabilities from experts or detailed simulation models can be used to estimate condi- tional probabilities, which is discussed in details later in this chapter. ThemainchallengeinBNsisthatstatisticaldatamustbeavailableinordertoestimate probabilities. When the system is fully represented, the failure probability could beesti- mated using Bayesian equations. An alternative use of the BN is to evaluate the perfor- mance of the system components and their interactions to get some information about the failure causes. If the postfailure analysis stage is taken into consideration, determina- tion of causes and mitigation or treatment actions should be considered in order to improve the performance and limit the overall system failure. An example of BN with seven variables is shown in Fig. 1.2. The joint probability function of random variables in a BN can be expressed as shown in Eq. (1.1): Figure1.2 AnexampleofBNwithsevenvariables[23].
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