Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network

This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition-based maintenance (CBM) into consideration. The Markov models of elements without repair and under CBM are established, and an absorbing set is introduced to determine the reliability of the repairable element. According to the state-transition relations between the states determined by the Markov process, a DBN model is built. In addition, its parameters for series and parallel systems, namely, conditional probability tables, can be calculated by referring to the conditional degradation probabilities. Finally, the power of a control unit in a failure model is used as an example. A dynamic fault tree (DFT) is translated into a Bayesian network model, and subsequently extended to a DBN. The results show the state probabilities of an element and the system without repair, with perfect and imperfect repair, and under CBM, with an absorbing set plotted by differential equations and verified. Through referring forward, the reliability value of the control unit is determined in different kinds of modes. Finally, weak nodes are noted in the control unit.

[1]  Philippe Weber,et al.  Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis , 2008, Reliab. Eng. Syst. Saf..

[2]  Claudio M. Rocco Sanseverino,et al.  Uncertainty propagation and sensitivity analysis in system reliability assessment via unscented transformation , 2014, Reliab. Eng. Syst. Saf..

[3]  Alyson G. Wilson,et al.  Bayesian networks for multilevel system reliability , 2007, Reliab. Eng. Syst. Saf..

[4]  Natasha Smith,et al.  Bayesian networks for system reliability reassessment , 2001 .

[5]  Xuesong Wei,et al.  A coupling vibration model of multi-stage pump rotor system based on FEM , 2016 .

[6]  Robertas Alzbutas,et al.  Bayesian Reliability of Gas Network Under Varying Incident Registration Criteria , 2016, Qual. Reliab. Eng. Int..

[7]  M. Sam Mannan,et al.  Bayesian network based dynamic operational risk assessment , 2016 .

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

[9]  Miroslaw J. Skibniewski,et al.  Bayesian-network-based safety risk analysis in construction projects , 2014, Reliab. Eng. Syst. Saf..

[10]  Bentolhoda Jafary,et al.  A universal generating function-based multi-state system performance model subject to correlated failures , 2016, Reliab. Eng. Syst. Saf..

[11]  Marco Grzegorczyk,et al.  A non-homogeneous dynamic Bayesian network with a hidden Markov model dependency structure among the temporal data points , 2016, Machine Learning.

[12]  Adel Karaa,et al.  Revisiting the bull and bear markets notions in the Tunisian stock market: New evidence from multi-state duration-dependence Markov-switching models , 2016 .

[13]  Malcolm J Price,et al.  Parameterization of treatment effects for meta‐analysis in multi‐state Markov models , 2011, Statistics in medicine.

[14]  Hong-Zhong Huang,et al.  Optimal Replacement Policy for Multi-State System Under Imperfect Maintenance , 2010, IEEE Transactions on Reliability.

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

[16]  Linlin Liu,et al.  A modified GO-FLOW methodology with common cause failure based on Discrete Time Bayesian Network , 2016 .

[17]  Luigi Portinale,et al.  A dynamic Bayesian network based framework to evaluate cascading effects in a power grid , 2012, Eng. Appl. Artif. Intell..

[18]  Enrico Zio,et al.  A multi-state model for the reliability assessment of a distributed generation system via universal generating function , 2012, Reliab. Eng. Syst. Saf..

[19]  Olexandr Yevkin,et al.  An Efficient Approximate Markov Chain Method in Dynamic Fault Tree Analysis , 2016, Qual. Reliab. Eng. Int..

[20]  Xuesong Wei,et al.  A superlinear iteration method for calculation of finite length journal bearing's static equilibrium position , 2017, Royal Society Open Science.

[21]  Andrés R. Masegosa,et al.  International Journal of Approximate Reasoning , 2022 .

[22]  Rania Hassan,et al.  Spacecraft Reliability-Based Design Optimization Under Uncertainty Including Discrete Variables , 2008 .

[23]  Luigi Portinale,et al.  Bayesian networks in reliability , 2007, Reliab. Eng. Syst. Saf..

[24]  Borut Mavko,et al.  A dynamic fault tree , 2002, Reliab. Eng. Syst. Saf..

[25]  Anatoly Lisnianski,et al.  A multi-state Markov model for a short-term reliability analysis of a power generating unit , 2012, Reliab. Eng. Syst. Saf..

[26]  Lijie Guo,et al.  An extended HAZOP analysis approach with dynamic fault tree , 2015 .

[27]  Malcolm J. Beynon,et al.  DS/AHP method: A mathematical analysis, including an understanding of uncertainty , 2002, Eur. J. Oper. Res..

[28]  Weimin Cui,et al.  Risk-based reconfiguration of safety monitoring system using dynamic Bayesian network , 2007, Reliab. Eng. Syst. Saf..

[29]  Yonghong Liu,et al.  Dynamic Bayesian network modeling of reliability of subsea blowout preventer stack in presence of common cause failures , 2015 .

[30]  Nima Khakzad,et al.  Dynamic safety assessment of natural gas stations using Bayesian network. , 2017, Journal of hazardous materials.

[31]  T. Vasanthi,et al.  Reliability Analysis of Mobile Ad Hoc Networks Using Universal Generating Function , 2016, Qual. Reliab. Eng. Int..

[32]  Marcelo Ramos Martins,et al.  Application of Bayesian Belief networks to the human reliability analysis of an oil tanker operation focusing on collision accidents , 2013, Reliab. Eng. Syst. Saf..