A Multiphase Dynamic Bayesian Network Methodology for the Determination of Safety Integrity Levels

  • Baoping CaiEmail author
  • Yonghong Liu
  • Zengkai Liu
  • Yuanjiang Chang
  • Lei Jiang


A novel safety integrity level (SIL) determination methodology based on multiphase dynamic Bayesian networks (MDBNs) for safety instrumented systems is proposed. Proof test interval phase and proof test phase are modeled separately using dynamic Bayesian networks and integrated together to form the MDBNs. The unified structure models of MDBNs for k-out-of-n architectures are constructed, and the procedures of automatic creation of conditional probability tables are developed. The target failure measures, that is, probability of failure on demand, average probability of failure on demand, probability of failing safely, average probability of failing safely, and SIL of safety instrumented systems operating in a low-demand mode, are evaluated using the proposed MDBNs. The effects of time interval of MDBNs, common cause weight, imperfect proof test, and repair on model precision are researched. User-friendly SIL determination software is developed by using MATLAB GUI to assist engineers in determining the SIL value.


Multiphase dynamic Bayesian networks Safety integrity level Safety instrumented system KooM architecture KooMD architecture 



The authors wish to acknowledge the financial support of Hong Kong Scholars Program (No. XJ2014004), National Natural Science Foundation of China (No. 51309240), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130133120007), China Postdoctoral Science Foundation (No. 2015M570624), Applied Basic Research Programs of Qingdao (No. 14-2-4-68-jch), Science and Technology Project of Huangdao District (No. 2014-1-48), Fundamental Research Funds for the Central Universities (No. 14CX02197A), Theme-based Research Scheme of University Grants Council (No. T32-101/15-R), and Key Project of National Natural Science Foundation of China (No. 71532008).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Baoping Cai
    • 1
    Email author
  • Yonghong Liu
    • 1
  • Zengkai Liu
    • 1
  • Yuanjiang Chang
    • 1
  • Lei Jiang
    • 2
  1. 1.China University of PetroleumQingdaoChina
  2. 2.Southwest Jiaotong UniversityChengduChina

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