Stochastic Models in Reliability, Network Security and System Safety: Essays Dedicated to Professor Jinhua Cao on the Occasion of His 80th Birthday

As one of the most popular reliability models, the previous several decades have witnessed remarkable developments and extensive applications of consecutive k systems, and a number of related models have been developed. In the paper, a summary of the state of the arts in the field is provided. After a brief introduction of conventional consecutive k systems, we focus on variants of the consecutive k systems by considering failure criteria (single failure criterion and multiple failure criteria), geometric structure of the system, states of components and the system, weight of each component, dependency of components. Finally, several future challenges deserving further studies are highlighted.

[1]  J. M. Kontoleon.  Optimum Allocation of Components in a Special 2-Port Network , 1978, IEEE Transactions on Reliability.

[2]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[3]  J. George Shanthikumar,et al.  Lifetime Distribution of Consecutive-k-out-of-n:F Systems With Exchangeable Lifetimes , 1985, IEEE Transactions on Reliability.

[4]  Stavros Papastavridis,et al.  Exact Reliability Formulas for Linear & Circular Consecutive-k-out-of-n:F Systems , 1985, IEEE Transactions on Reliability.

[5]  D. Malon,et al.  Optimal Consecutive-k-out-of-n:F Component Sequencing , 1985, IEEE Transactions on Reliability.

[6]  Stavros Papastavridis,et al.  Reliability of a Consecutive-k-out-of-n:F System for Markov-Dependent Components , 1987, IEEE Transactions on Reliability.

[7]  James C. Fu,et al.  On Reliability of a Large Consecutive-k-out-of-n:F System with (k - 1)-step Markov Dependence , 1987, IEEE Transactions on Reliability.

[8]  L. K. Chan,et al.  On consecutive-k-out-of-n: F systems , 1988 .

[9]  Y. C. Yao,et al.  Multistate consecutively-connected systems , 1989 .

[10]  Anthony A. Salvia,et al.  Two-dimensional consecutive-k-out-of-n:F models , 1990 .

[11]  W. Kuo,et al.  A consecutive-k-out-of-n:G system: the mirror image of a consecutive-k-out-of-n:F system , 1990 .

[12]  S. Papastavridis,et al.  Optimal-arrangement and importance of the components in a consecutive-k-out-of-r-from-n:F system , 1991 .

[13]  Markos V. Koutras,et al.  Consecutive k-out-of-n systems with maintenance , 1992 .

[14]  Michael Sfakianakis,et al.  Reliability of a consecutive k-out-of-r-from-n:F system , 1992 .

[15]  Michael Sfakianakis.  Optimal arrangement of components in a consecutive k-out-of-r-from n:F system , 1993 .

[16]  Markos V. Koutras,et al.  Distribution Theory of Runs: A Markov Chain Approach , 1994 .

[17]  T. Boehme,et al.  ON RELIABILITY ANALYSIS OF CONSECUTIVE-k-OUT-OF-n: F SYSTEMS AND THEIR GENERALIZATIONS - A SURVEY , 1994 .

[18]  Ming J. Zuo,et al.  Reliability of multistate consecutively-connected systems , 1994 .

[19]  Rong-Jaye Chen,et al.  An algorithm for computing the reliability of weighted-k-out-of-n systems , 1994 .

[20]  J. Malinowski,et al.  Reliability of circular consecutively-connected systems with multistate components , 1995 .

[21]  Z. M. Psillakis,et al.  A simulation algorithm for computing failure probability of a consecutive-k-out-of-r-from-n:F system , 1995 .

[22]  Markos V. Koutras.  Consecutive-k, r-out-of-n:DFM systems , 1997 .

[23]  Yeh Lam,et al.  Reliability of consecutive-k-out-of-n: G repairable system , 1998, Int. J. Syst. Sci..

[24]  Amos E. Gera.  A consecutive k-out-of-n: G system with dependent elements - a matrix formulation and solution , 2000, Reliab. Eng. Syst. Saf..

[25]  D. E. Dimla,et al.  On-line metal cutting tool condition monitoring.: I: force and vibration analyses , 2000 .

[26]  Yeh Lam,et al.  Repairable consecutive‐k‐out‐of‐n: F system with Markov dependence , 2000 .

[27]  Yeh Lam,et al.  A general model for consecutive-k-out-of-n: F repairable system with exponential distribution and (k-1)-step Markov dependence , 2001, Eur. J. Oper. Res..

[28]  Finn V. Jensen,et al.  Bayesian Networks and Decision Graphs , 2001, Statistics for Engineering and Information Science.

[29]  Luigi Portinale,et al.  Improving the analysis of dependable systems by mapping fault trees into Bayesian networks , 2001, Reliab. Eng. Syst. Saf..

[30]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[31]  Gregory Levitin,et al.  Multi-State System Reliability - Assessment, Optimization and Applications , 2003, Series on Quality, Reliability and Engineering Statistics.

[32]  Gregory Levitin,et al.  Linear multi-state sliding-window systems , 2003, IEEE Trans. Reliab..

[33]  Ming J. Zuo,et al.  Multi-State Consecutive- k -out-of- n Systems , 2003 .

[34]  Tomoaki Akiba,et al.  Survey of Reliability Studies of Multi-dimensional Consecutive-k-out-of-n:F Systems , 2003 .

[35]  Gregory Levitin.  Consecutive k-out-of-r-from-n system with multiple failure criteria , 2004, IEEE Transactions on Reliability.

[36]  Yi-Chih Hsieh,et al.  Reliability lower bounds for two-dimensional consecutive-k-out-of-n: F systems , 2004, Comput. Oper. Res..

[37]  Joanne Bechta Dugan,et al.  A discrete-time Bayesian network reliability modeling and analysis framework , 2005, Reliab. Eng. Syst. Saf..

[38]  Tomoaki Akiba,et al.  Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system , 2005 .

[39]  Gregory Levitin,et al.  The Universal Generating Function in Reliability Analysis and Optimization , 2005 .

[40]  Philippe Weber,et al.  Complex system reliability modelling with Dynamic Object Oriented Bayesian Networks (DOOBN) , 2006, Reliab. Eng. Syst. Saf..

[41]  Joanne Bechta Dugan,et al.  A continuous-time Bayesian network reliability modeling, and analysis framework , 2006, IEEE Transactions on Reliability.

[42]  Ming Jian Zuo,et al.  Recursive formulas for the reliability of multi-state consecutive-k-out-of-n:G systems , 2006, IEEE Transactions on Reliability.

[43]  Yung Wen Liu,et al.  Reliability measures for dynamic multistate nonrepairable systems and their applications to system performance evaluation , 2006 .

[44]  Ming Jian Zuo,et al.  Performance evaluation of generalized multi-state k-out-of-n systems , 2006, IEEE Transactions on Reliability.

[45]  Lin Ma,et al.  An analytical model for interactive failures , 2006, Reliab. Eng. Syst. Saf..

[46]  Yasuhiro Tsujimura,et al.  GENETIC ALGORITHM FOR SOLVING OPTIMAL COMPONENT ARRANGEMENT PROBLEM OF CIRCULAR CONSECUTIVE-K-OUT-OF-N: F SYSTEM , 2006 .

[47]  L. Cui,et al.  Reliabilities for (n, f, k (i, j)) and ⟨n, f, k (i, j)⟩ Systems , 2006 .

[48]  Lirong Cui,et al.  Reliability for Sparsely Connected Consecutive-$k$ Systems , 2007, IEEE Transactions on Reliability.

[49]  Liudong Xing,et al.  Reliability Evaluation of Phased-Mission Systems With Imperfect Fault Coverage and Common-Cause Failures , 2007, IEEE Transactions on Reliability.

[50]  Taha Radwan,et al.  Reliability evaluation of multi-state consecutive k-out-of-r-from-n : G system , 2007 .

[51]  Harry F. Martz,et al.  A fully Bayesian approach for combining multi-level information in multi-state fault tree quantification , 2007, Reliab. Eng. Syst. Saf..

[52]  John Quigley,et al.  Modelling the reliability of search and rescue operations with Bayesian Belief Networks , 2008, Reliab. Eng. Syst. Saf..

[53]  Luigi Portinale,et al.  Radyban: A tool for reliability analysis of dynamic fault trees through conversion into dynamic Bayesian networks , 2008, Reliab. Eng. Syst. Saf..

[54]  Nikolaos Limnios,et al.  Semi-Markov Chains and Hidden Semi-Markov Models toward Applications: Their Use in Reliability and DNA Analysis , 2008 .

[55]  Wei-Chang Yeh.  A Fast Algorithm for Searching All Multi-State Minimal Cuts , 2008, IEEE Transactions on Reliability.

[56]  Gang Xiao,et al.  Estimation of Dependability Measures and Parameter Sensitivities of a Consecutive-$k$-out-of-$n$: F Repairable System With $(k-1)$-Step Markov Dependence by Simulation , 2008, IEEE Transactions on Reliability.

[57]  Wei Li,et al.  Optimal design of multi-state weighted k-out-of-n systems based on component design , 2008, Reliab. Eng. Syst. Saf..

[58]  Wei Li,et al.  Reliability evaluation of multi-state weighted k-out-of-n systems , 2008, Reliab. Eng. Syst. Saf..

[59]  Curtis Smith,et al.  Bayesian inference in probabilistic risk assessment - The current state of the art , 2009, Reliab. Eng. Syst. Saf..

[60]  Manju Agarwal,et al.  Combined m -Consecutive- k -Out-of- n: F & Consecutive kc -Out-of- n: F Systems , 2009, IEEE Trans. Reliab..

[61]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[62]  Serkan Eryilmaz,et al.  Reliability Evaluation of Linear Consecutive-Weighted-k-Out-of-n: F System , 2009, Asia Pac. J. Oper. Res..

[63]  Philippe Weber,et al.  Evidential Networks for Reliability Analysis and Performance Evaluation of Systems With Imprecise Knowledge , 2009, IEEE Transactions on Reliability.

[64]  T. Yuge,et al.  Reliability of a consecutive (r, s)-out-of-(m, n):F lattice system with conditions on the number of failed components in the system , 2010 .

[65]  Shenggui Zhang,et al.  Integrated importance measures of multi-state systems under uncertainty , 2010, Comput. Ind. Eng..

[66]  Liudong Xing,et al.  Decision Diagram Based Methods and Complexity Analysis for Multi-State Systems , 2010, IEEE Transactions on Reliability.

[67]  Yi Ding,et al.  Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers , 2010 .

[68]  Yasuhiro Tsujimura,et al.  Proposal of Simulated Annealing Algorithms for Optimal Arrangement in a Circular Consecutive-k-out-of-n: F System , 2010 .

[69]  Lirong Cui,et al.  Reliability evaluation of generalised multi-state k-out-of-n systems based on FMCI approach , 2010, Int. J. Syst. Sci..

[70]  Soumaya Yacout,et al.  Evaluating the Reliability Function and the Mean Residual Life for Equipment With Unobservable States , 2010, IEEE Transactions on Reliability.

[71]  Dag Eirik Nordgård,et al.  Application of Bayesian networks for risk analysis of MV air insulated switch operation , 2010, Reliab. Eng. Syst. Saf..

[72]  Ian Jenkinson,et al.  The use of Bayesian network modelling for maintenance planning in a manufacturing industry , 2010, Reliab. Eng. Syst. Saf..

[73]  Yi-Kuei Lin,et al.  Network Reliability of a Time-Based Multistate Network Under Spare Routing With $p$ Minimal Paths , 2011, IEEE Transactions on Reliability.

[74]  M. Koutras,et al.  Signature and IFR Preservation of 2-Within-Consecutive $k$-out-of-$n$: $F$ Systems , 2011, IEEE Transactions on Reliability.

[75]  Wei Zhao,et al.  Two-dimensional linear connected-k system with trinary states and its reliability , 2011 .

[76]  Gregory Levitin,et al.  Linear m -Consecutive k -out-of-r -From- n: F Systems , 2011, IEEE Trans. Reliab..

[77]  Nima Khakzad,et al.  Safety analysis in process facilities: Comparison of fault tree and Bayesian network approaches , 2011, Reliab. Eng. Syst. Saf..

[78]  Gregory Levitin,et al.  Consecutive sliding window systems , 2011, Reliab. Eng. Syst. Saf..

[79]  Lirong Cui,et al.  Exact Reliability of a Linear Connected-(r, s)-out-of-(m, n): F System , 2011, IEEE Trans. Reliab..

[80]  Taha Radwan,et al.  Bounds for increasing multi-state consecutive k-out-of-r-from-n: F system with equal components probabilities , 2011 .

[81]  Gregory Levitin.  Linear m-gap-consecutive k-out-of-r-from-n: F systems , 2011, Reliab. Eng. Syst. Saf..

[82]  Yonghong Liu,et al.  Using Bayesian networks in reliability evaluation for subsea blowout preventer control system , 2012, Reliab. Eng. Syst. Saf..

[83]  Serkan Eryilmaz,et al.  Linear m -Consecutive- k , l -Out-of- n : F System , 2012, IEEE Trans. Reliab..

[84]  Benoît Iung,et al.  Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas , 2012, Eng. Appl. Artif. Intell..

[85]  Yu Xu,et al.  State Distributions of Multi-State Consecutive-$k$ Systems , 2012, IEEE Transactions on Reliability.

[86]  Enrico Zio,et al.  The Monte Carlo Simulation Method for System Reliability and Risk Analysis , 2012 .

[87]  Chris Jackson,et al.  Bayesian inference with overlapping data for systems with continuous life metrics , 2012, Reliab. Eng. Syst. Saf..

[88]  N. Limnios,et al.  Semi-Markov Processes and Reliability , 2012 .

[89]  M. Asadi,et al.  On the mean residual lifetime of consecutive k-out-of-n systems , 2012 .

[90]  Kirtee K. Kamalja,et al.  BIRNBAUM IMPORTANCE FOR CONSECUTIVE-k SYSTEMS , 2012 .

[91]  Sheng Tang,et al.  A Repairable Linear m -Consecutive-k -Out-of-n :F System , 2012 .

[92]  Hidemi Yamachi,et al.  Comparative Study of Several Simulated Annealing Algorithms for Optimal Arrangement Problems in a Circular Consecutive-k-out-of-n: F System , 2012 .

[93]  Gregory Levitin,et al.  BDD-based reliability evaluation of phased-mission systems with internal/external common-cause failures , 2013, Reliab. Eng. Syst. Saf..

[94]  Daniel Straub,et al.  Efficient Bayesian network modeling of systems , 2013, Reliab. Eng. Syst. Saf..

[95]  Qian Fan,et al.  Dynamic Bayesian networks based performance evaluation of subsea blowout preventers in presence of imperfect repair , 2013, Expert Syst. Appl..

[96]  Jian Liu,et al.  Proportional hazard modeling for hierarchical systems with multi-level information aggregation , 2014 .

[97]  S. Eryilmaz,et al.  Modeling and analysis of weighted-k-out-of-n: G system consisting of two different types of components , 2014 .

[98]  Seth D. Guikema,et al.  Bayesian Belief Networks for predicting drinking water distribution system pipe breaks , 2014, Reliab. Eng. Syst. Saf..

[99]  A. Kashikar,et al.  SIGNATURE AND RELIABILITY OF CONDITIONAL THREE-DIMENSIONAL CONSECUTIVE-(s, s, s)-OUT-OF-(s, s, m):F SYSTEM , 2014 .

[100]  K. K. Kamalja.  Birnbaum Reliability Importance for (n,f,k) and ⟨n,k,f⟩ System , 2014 .

[101]  Kirtee K. Kamalja,et al.  Computational Methods for Reliability and Importance Measures of Weighted-Consecutive-System , 2014, IEEE Transactions on Reliability.

[102]  Jian Liu,et al.  Bayesian modeling of multi-state hierarchical systems with multi-level information aggregation , 2014, Reliab. Eng. Syst. Saf..

[103]  Min Xie,et al.  Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems , 2014, Reliab. Eng. Syst. Saf..

[104]  Serkan Eryilmaz,et al.  Joint Reliability Importance in a Binary K-out-of-n: G System with Exchangeable Dependent Components , 2014 .

[105]  Oswaldo Morales-Nápoles,et al.  Analysis of axle and vehicle load properties through Bayesian Networks based on Weigh-in-Motion data , 2014, Reliab. Eng. Syst. Saf..

[106]  Jean-Baptiste Denis,et al.  Bayesian Networks , 2014 .

[107]  Gregory Levitin,et al.  Explicit and implicit methods for probabilistic common-cause failure analysis , 2014, Reliab. Eng. Syst. Saf..

[108]  Helge Langseth,et al.  Bayesian Networks in Reliability: Some Recent Developments , 2004 .

[109]  Pooja Mohan,et al.  GERT Analysis of Consecutive-k Systems: An Overview , 2014 .

[110]  Xiaoyan Zhu,et al.  Joint Reliability Importance in a Consecutive-k-out-of-n : F System and an m-Consecutive-k-out-of-n: F System for Markov-Dependent Components , 2015, IEEE Trans. Reliab..

[111]  Gregory Levitin,et al.  m/nCCS: linear consecutively connected systems subject to combined gap constraints , 2015, Int. J. Gen. Syst..

[112]  Matthew Collette,et al.  A dynamic discretization method for reliability inference in Dynamic Bayesian Networks , 2015, Reliab. Eng. Syst. Saf..

[113]  Gregory Levitin,et al.  Probabilistic common cause failures in phased-mission systems , 2015, Reliab. Eng. Syst. Saf..

[114]  Hong-Zhong Huang,et al.  Dynamic Reliability Assessment for Multi-State Systems Utilizing System-Level Inspection Data , 2015, IEEE Transactions on Reliability.

[115]  Luca Podofillini,et al.  Bayesian belief networks for human reliability analysis: A review of applications and gaps , 2015, Reliab. Eng. Syst. Saf..

[116]  Lirong Cui,et al.  Reliability and Birnbaum Importance for Sparsely Connected Circular Consecutive-$k $ Systems , 2015, IEEE Transactions on Reliability.

[117]  Marios K. Chryssanthopoulos,et al.  Bridge condition modelling and prediction using dynamic Bayesian belief networks , 2015 .

[118]  Shijia Du,et al.  Birnbaum Importance for Linear Consecutive-k-out-of-n Systems With Sparse d , 2015, IEEE Trans. Reliab..

[119]  Yu Liu,et al.  A multiphase dynamic Bayesian networks methodology for the determination of safety integrity levels , 2016, Reliab. Eng. Syst. Saf..

[120]  Daniel Straub,et al.  A discretization procedure for rare events in Bayesian networks , 2016, Reliab. Eng. Syst. Saf..

[121]  Lirong Cui,et al.  Reliability Modeling on Consecutive-$k_r $ -out-of-$n_r $:F Linear Zigzag Structure and Circular Polygon Structure , 2016, IEEE Transactions on Reliability.

[122]  Ming Jian Zuo,et al.  Selective Maintenance for Multistate Series Systems With S-Dependent Components , 2016, IEEE Transactions on Reliability.

[123]  Xiaohu Li,et al.  ON WEIGHTED K-OUT-OF-N SYSTEMS WITH STATISTICALLY DEPENDENT COMPONENT LIFETIMES , 2016, Probability in the Engineering and Informational Sciences.

[124]  E. Salehi,et al.  On reliability analysis of consecutive k-out-of-n systems with arbitrarily dependent components , 2016 .

[125]  Gregory Levitin,et al.  Optimal replacement and allocation of multi-state elements in k-within-m-from-r/n sliding window systems , 2016 .

[126]  Min Xie,et al.  A Real-Time Fault Diagnosis Methodology of Complex Systems Using Object-Oriented Bayesian Networks , 2016, Bayesian Networks in Fault Diagnosis.

[127]  Quan Liu,et al.  Object Oriented Bayesian Network for complex system risk assessment , 2016 .

[128]  Xiaoyan Zhu,et al.  Reliability and Joint Reliability Importance in a Consecutive-k-Within-m-out-of-n: F System With Markov-Dependent Components , 2016, IEEE Trans. Reliab..

[129]  Iris Tien,et al.  Algorithms for Bayesian network modeling and reliability assessment of infrastructure systems , 2016, Reliab. Eng. Syst. Saf..

[130]  David W. Coit,et al.  Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components , 2017, Reliab. Eng. Syst. Saf..

[131]  Elham Mahmoudi,et al.  Joint reliability and weighted importance measures of a k-out-of-n system with random weights for components , 2017, J. Comput. Appl. Math..

[132]  Yu Liu,et al.  Dynamic Reliability Assessment for Nonrepairable Multistate Systems by Aggregating Multilevel Imperfect Inspection Data , 2017, IEEE Transactions on Reliability.

[133]  Xiaoyang Zhu,et al.  A linear weighted (n, f, k) system for non-homogeneous Markov-dependent components , 2017 .

[134]  Gabriele Landucci,et al.  Application of dynamic Bayesian network to performance assessment of fire protection systems during domino effects , 2017, Reliab. Eng. Syst. Saf..

[135]  I. Nashwan.  Reliability and failure functions of some weighted systems , 2017 .

[136]  Lei Huang,et al.  Bayesian Networks in Fault Diagnosis , 2017, IEEE Transactions on Industrial Informatics.

[137]  Tao Jiang,et al.  Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences , 2017, Reliab. Eng. Syst. Saf..

[138]  Tao Jiang,et al.  Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment , 2018, Mechanical Systems and Signal Processing.

[139]  Kalpesh P. Amrutkar,et al.  Reliability and Reliability Importance of Weighted-$r$ -Within-Consecutive-$k$ -out-of-$n: F$, 2018, IEEE Transactions on Reliability.

[140]  Weiwen Peng,et al.  Reliability analysis of complex multi-state system with common cause failure based on evidential networks , 2018, Reliab. Eng. Syst. Saf..

[141]  Faisal Khan,et al.  Integrated offshore power operation resilience assessment using Object Oriented Bayesian network , 2018, Ocean Engineering.

[142]  Lin Ma,et al.  An integrated approach for system functional reliability assessment using Dynamic Bayesian Network and Hidden Markov Model , 2018, Reliab. Eng. Syst. Saf..

[143]  Jian Zheng,et al.  Optimal inspection planning of corroded pipelines using BN and GA , 2018 .

[144]  Anatoly Lisnianski,et al.  Recent Advances in Multi-state Systems Reliability , 2018 .

[145]  Syed Imtiaz,et al.  Dynamic availability assessment of safety critical systems using a dynamic Bayesian network , 2018, Reliab. Eng. Syst. Saf..

[146]  Nima Khakzad,et al.  Modeling wildfire spread in wildland-industrial interfaces using dynamic Bayesian network , 2019, Reliab. Eng. Syst. Saf..

[147]  Hui Xiao,et al.  Reliability of sliding window systems with two failure modes , 2019, Reliab. Eng. Syst. Saf..

[148]  Tao Jiang,et al.  Reliability assessment of multi-state phased-mission systems by fusing observation data from multiple phases of operation , 2019, Mechanical Systems and Signal Processing.

[149]  Xiaoyang Zhu,et al.  A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components , 2019 .

[150]  Yonghong Liu,et al.  A Bayesian network based method for reliability analysis of subsea blowout preventer control system , 2019, Journal of Loss Prevention in the Process Industries.

[151]  Daniel Straub,et al.  Risk-based optimal inspection strategies for structural systems using dynamic Bayesian networks , 2019, Structural Safety.

[152]  Tianxiang Yu,et al.  On capacity evaluation for multi-state weighted k-out-of-n system , 2019, Commun. Stat. Simul. Comput..

[153]  Wen Yao,et al.  Improved compression inference algorithm for reliability analysis of complex multistate satellite system based on multilevel Bayesian network , 2019, Reliab. Eng. Syst. Saf..

[154]  Faisal Khan,et al.  Resilience modeling of engineering systems using dynamic object-oriented Bayesian network approach , 2019, Comput. Ind. Eng..

[155]  Yu Liu,et al.  Optimal loading strategy for multi-state systems: Cumulative performance perspective , 2019, Applied Mathematical Modelling.

[156]  Yu Liu,et al.  Reliability assessment of systems subject to interval-valued probabilistic common cause failure by evidential networks , 2019, Journal of Intelligent & Fuzzy Systems.

[157]  Jing Lin,et al.  Application of Bayesian Networks in Reliability Evaluation , 2019, IEEE Transactions on Industrial Informatics.

[158]  Simon Jude,et al.  Comparison of automatic and guided learning for Bayesian networks to analyse pipe failures in the water distribution system , 2019, Reliab. Eng. Syst. Saf..

[159]  Ehsan Arzaghi,et al.  Multi-level optimization of maintenance plan for natural gas system exposed to deterioration process. , 2019, Journal of hazardous materials.

[160]  Lizhi Wang,et al.  Maintenance grouping optimization with system multi-level information based on BN lifetime prediction model , 2019, Journal of Manufacturing Systems.

[161]  Lirong Cui,et al.  Reliabilities of Some Multistate Consecutive-k Systems , 2020, IEEE Transactions on Reliability.