Within the ongoing efforts of development and advancement, this book presents an overview of methods for assessing and optimizing system reliability. We address different types of system reliability assessment and optimization problems and the different approaches for their solutions. We consider the development and advancement in the fields of operations research, reliability, and optimization theory to tackle the reliability assessment and optimization of complex systems in different technological domains.
The book is directed to graduate students, researchers and practitioners in the areas of system reliability, availability, maintainability and Safety (RAMS), and it is intended to provide an overview of the state of knowledge of and tools for reliability assessment and system optimization. It is organized in three parts to introduce fundamentals, and illustrate methods and applications.
The first part reviews the concepts, definitions and metrics of reliability assessment and the formulations of different types of reliability optimization problems depending on the nature of the decision variables and considering redundancy allocation and maintenance and testing policies. Plenty of numerical examples are provided to accompany the understanding of the theoretical concepts and methods.
The second part covers multi-state system (MSS) modeling and reliability evaluation, Markov processes, Monte Carlo simulation (MCS), and uncertainty treatment under poor knowledge. The reviewed methods range from piecewise-deterministic Markov processes (PDMPs) to belief functions.
The third part of the book is devoted to system reliability optimization. In general terms, system reliability optimization involves defining the decision variables, the constraints and the single or multiple objective functions that describe the system reliability performance and involves searching for the combination of values of the decision variables that realize the target values the objective functions. Different formulations and methods are described with precise mathematical details and illustrative numerical examples, covering mathematical programming, evolutionary algorithms, multi-objective optimization (MOO) and optimization under uncertainty, including robust optimization (RO).
Applications of the assessment and optimization methods to real-world cases are also given, concerning for example the reliability of renewable energy systems. From this point of view, the book bridges the gap between theoretical development and engineering practice.
Acknowledgments
Live long and prosper, RAMS and system reliability! The authors would express the deepest appreciations to the great scholars along the line of honors and achievements for their inspirations and role modeling.
Many thanks to the postgraduate students in Tsinghua: Tianli Men, Hanxiao Zhang, Ruochong Liu, Chen Zhang and Chuanzhou Jia. Thanks for their priceless efforts in editing, depicting, and proofreading in various chapters.
The authors would like to specially thank the Wiley colleagues for their continuous and kindhearted monitoring and encouragement throughout the years.
At last, this work is supported in part by the National Natural Science Foundation of China under a key project grant No. 71731008 and the Beijing Natural Science Foundation grant No. L191022.
List of Abbreviations
ABCartificial bee colony algorithmACOant colony optimizationAGANas-good-as-newB&Bbranch-and-boundBBAbasic belief assignmentBDDbinary decision diagramBFSbasic feasible solutionBSSbinary state systemBSSPSbinary-state series-parallel systemcdfcumulative distribution functionCGcolumn generationCLTCentral Limit TheoremCTMCcontinuous time Markov chainCVaRconditional value-at-riskDCdirect currentDEdeterministic equivalentDEdifferential evolutionDGdistributed generationDMdecision makerDPdynamic programmingDTMCdiscrete time Markov chainEAevolutionary algorithmENSenergy not suppliedEENSexpected energy not suppliedEVelectrical vehiclesFVfinite-volumeGAgenetic algorithmGDgenerational distanceHCTMChomogeneous CTMCHPIShigh-pressure injection systemHUGFhybrid UGFHVhyper-volumeICTMCinhomogeneous CTMCILPinteger linear programmingIPinteger programmingLOLinear optimizationLPlinear programmingLPMLP master problemMCMCMarkov Chain Monte CarloMCSMonte Carlo simulationMCS-OPFMonte Carlo simulation – optimal power flowMCVminimal cut vectorMDDmulti-valued decision diagramMHMetropolis-HastingsMIPmixed integer programmingMOOmulti-objective optimizationMPmathematical programmingMPVminimal path vectorMRCMarkov renewal chainMSMain supply power spotMSCSmulti-state coherent systemMSMmulti-state modelMSMSmulti-state monotone systemMSSmulti-state systemMTBFmean time between failuresMTBRmean time between repairsMTTFmean time to failureNLPnon-linear programmingNPGAniched Pareto GANPPnuclear power plantNSGA-IIfast non-dominated sorting genetic algorithmOPFoptimal power flowpdfprobability density functionPDMPpiecewise-deterministic Markov processpmfprobability mass functionP-o-FPhysics-of-FailurePSOparticle swarm optimizationPVsolar photovoltaicRAMreliability, availability, and maintainabilityRAMSRAM and Safety criteriaRAMS+CRAMS and CostRAPredundancy allocation problemRCrobust counterpartRESTARTRepetitive Simulation Trials After Reaching ThresholdsRFNrandom-fuzzy numberRLPMrestricted LPMROrobust optimizationSMPsemi-Markov processSODEsingle-object DESOEAsingle-objective EASOGAsingle-objective GASOOsingle-objective optimizationSOPSOsingle-objective PSOSPstochastic programmingSPEAstrength Pareto evolutionary algorithmSPEA 2improved strength Pareto evolutionary algorithmSSOsocial spider optimizationSTstorage deviceTDMSMtime-dependent MSMTIMSMtime-independent MSMTSTabu searchUGFuniversal generating functionVEGAvector-evaluated GAWwind turbine
Notations
Notations: Part I
| t | time point |
| nf(t) | number of failed items |
| ns(t) | number of the survived items |
| n0 | sample size |
| T | random variable of the failure time |
| F(t) | cdf of failure time |
| f(t) | pdf of failure time |
| R(t) | reliability at time t |
| h(t) | hazard function at time t |
| H(t) | cumulative hazard function at time t |
| Q^(t) | estimate of the unreliability |
| R^(t) | estimate of the reliability |
| D(t) | component or system demand at time t |
| G(t) | performance function at time t |
| MTTF | mean time to failure |
| X | random variable |
| a | crack length |
| N | load cycle |
| Q | total volume of wear debris produced |
| Rs(t) | reliability of the system at time t |
| (⋅) | unreliability function of the system |
| C | cost |
| x | decision variable |
| g(x) | inequality constraints |
| h(x) | equality constraints |
| f(x) | criterion function |
| D=(V, A) | directed graph |
| d(⋅) | length of the shortest path |
Notations: Part II
| t | time point |
| S | state set |
| M | perfect state |
| x=(x1,…,xn) | component state vector |
| X=(X1,…,Xn) | state of all components |
| ϕ(⋅) | structure function of the system |
| gi | performance level of component i |
| λkji | transition rate of component i from state k to state j |
| Qkji(t) | kernel of the SMP analogous to λkji of the CTMC |
| Tni | time of the n-th transition of component i |
| Gni | performance of component i at the n-th transition |
| θjki(t) | probability that the process of component i starts from state j at time t |
| AφW(t) | availability with a minimum on performance of total φ at time t |
| ui(z) | universal generating function of component i |
| pij=Pr(Xi=j) | probability of component i being at
|