Deep learning of system reliability under multi-factor influence based on space fault tree

  • Tie-Jun Cui
  • Sha-sha Li
S.I. : Emergence in Human-like Intelligence towards Cyber-Physical Systems


For the fault tree analysis, a basic event probability is often complicated. The probability is not constant and even can be represented by function. In order to analyze the system reliability and related characteristics, we represent the probabilities of the basic events by functions. The variables of the function are n influencing factors on the basic events. We extend the top event probability from the constant value to n + 1-dimensional space considering n influencing factors, and the probability is n + 1th dimension. Further research the n + 1-dimensional space with related mathematical methods, and then, transform the system probability analysis into the problem of mathematic. The above ideas are the space fault tree (SFT). In SFT, component fault probability distribution replace basic event probability and system fault probability distribution replace top event probability. In this paper, we research the electrical system fault probability distribution and explain the related construction process. The main factors influencing the system are working temperature c and working time t. This paper constructs the three-dimensional fault probability distribution of the components and the system, and the probability importance and criticality importance of the components. With partial derivation of the system fault probability distribution by the c and t, we study the change trend of the fault probability. The optimal replacement schemes of components and the scheme considering the cost are obtained. The results show SFT is feasible and reasonable to analyze the fault probability of system under multi-factor influence and suitable for deep learning of the characteristics of the system reliability change.


Safety system engineering Space fault tree System reliability Multi-factor influence Deep learn 



The author wishes to thank all his friends for their valuable critics, comments and assistances on this paper. This study was partially supported by the grants (Grant Nos. 51704141, 51674127, 51474121) from the Natural Science Foundation of China.

Compliance with ethical standards

Conflict of interest

No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. All the authors listed have approved the manuscript that is enclosed.


  1. 1.
    Isoda N, Kadohira M, Sekiguchi S, Schuppers M, Stärk KDC (2013) Review: evaluation of foot-and-mouth disease control using fault tree analysis. Transbound Emerg Dis 62(3):233–244CrossRefGoogle Scholar
  2. 2.
    Zytoon MA, El-Shazly AH, Noweir MH, Al-Zahrani AA (2013) Quantitative safety analysis of a laboratory-scale bioreactor for hydrogen sulfide biotreatment using fault tree analysis. Process Saf Prog 32(4):376–386CrossRefGoogle Scholar
  3. 3.
    Ferdous R, Khan F, Sadiq R, Amyotte P, Veitch B (2011) Fault and event tree analyses for process systems risk analysis: uncertainty handling formulations. Risk Anal 31(1):86–107CrossRefGoogle Scholar
  4. 4.
    Flage R, Baraldi P, Zio E, Aven T (2012) Probability and possibility-based representations of uncertainty in fault tree analysis. Risk Anal 33(1):121–133CrossRefGoogle Scholar
  5. 5.
    Pedroni N, Zio E (2013) Uncertainty analysis in fault tree models with dependent basic events. Risk Anal 33(6):1146–1173CrossRefGoogle Scholar
  6. 6.
    Wang D, Zhang Y, Jia X, Jiang P, Guo B (2015) Handling uncertainties in fault tree analysis by a hybrid probabilistic–possibilistic framework. Qual Reliab Eng Int 32(3):1137–1148CrossRefGoogle Scholar
  7. 7.
    Remenyte-Prescott R, Andrews JD (2009) An efficient real-time method of analysis for non-coherent fault trees. Qual Reliab Eng Int 25(2):129–150CrossRefGoogle Scholar
  8. 8.
    Ge D, Li D, Chou Q, Zhang R, Yang Y (2014) Quantification of highly coupled dynamic fault tree using IRVPM and SBDD. Qual Reliab Eng Int 32(1):139–151CrossRefGoogle Scholar
  9. 9.
    Åslund J, Biteus J, Frisk E, Krysander M, Nielsen L (2007) Safety analysis of autonomous systems by extended fault tree analysis. Int J Adapt Control Signal Process 21(2):287–298MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cui Y, Shi J, Wang Z (2015) Analog circuits fault diagnosis using multi-valued Fisher’s fuzzy decision tree (MFFDT). Int J Circuit Theory Appl 44(1):240–260CrossRefGoogle Scholar
  11. 11.
    Ekaette E, Lee RC, Cooke DL, Iftody S, Craighead P (2008) Probabilistic fault tree analysis of a radiation treatment system. Risk Anal 27(6):1395–1410CrossRefGoogle Scholar
  12. 12.
    Yousfi Steiner N, Hissel D, Moçotéguy P, Candusso D, Marra D, Pianese C, Sorrentino M (2012) Application of fault tree analysis to fuel cell diagnosis. Fuel Cells. 12(2):302–309CrossRefGoogle Scholar
  13. 13.
    Rahmat MK, Khairil M (2009) Slobodan Jovanovic. Reliability modelling of uninterruptible power supply systems using fault tree analysis method. Eur Trans Electr Power 19(2):814–826CrossRefGoogle Scholar
  14. 14.
    Zhaoguang Peng Y, Miller A, Johnson C, Zhao T (2016) Risk assessment of railway transportation systems using timed fault trees. Qual Reliab Eng Int 32(1):181–194CrossRefGoogle Scholar
  15. 15.
    Huang H-Z, Zhang H, Li Y (2012) A new ordering method of basic events in fault tree analysis. Qual Reliab Eng Int 28(3):297–305CrossRefGoogle Scholar
  16. 16.
    Mo Y, Zhong F, Liu H, Yang Q, Cui G (2013) Efficient ordering heuristics in binary decision diagram–based fault tree analysis. Qual Reliab Eng Int 29(3):307–315CrossRefGoogle Scholar
  17. 17.
    Ge D, Yang Y (2015) Reliability analysis of non-repairable systems modeled by dynamic fault trees with priority AND gates. Appl Stoch Models Bus Ind 31(6):809–822MathSciNetCrossRefGoogle Scholar
  18. 18.
    Merle G, Roussel J-M, Lesage J-J, Perchet V, Vayatis N (2014) Quantitative analysis of dynamic fault trees based on the coupling of structure functions and monte carlo simulation. Qual Reliab Eng Int 32(1):7–18CrossRefGoogle Scholar
  19. 19.
    Yevkin O (2015) An efficient approximate markov chain method in dynamic fault tree analysis. Qual Reliab Eng Int 32(4):1509–1520CrossRefGoogle Scholar
  20. 20.
    Merle G, Roussel J-M, Lesage J-J (2014) Quantitative analysis of dynamic fault trees based on the structure function. Qual Reliab Eng Int 30(1):143–156CrossRefGoogle Scholar
  21. 21.
    Zhang X-p, Wang J, Hu M-l (2011) Application of FTA in safety assessment of row piles of excavation engineering. Chin J Geotech Eng 33(6):960–965Google Scholar
  22. 22.
    Xue-bin W (2010) A prototype for integrating HAZOP/Fault tree analysis. Dalian University of Technology, DalianGoogle Scholar
  23. 23.
    Shi-jie N (2011) Study on hazard analysis by FTA and comprehensive assessment index system in construction work field. Chongqing University, ChongqingGoogle Scholar
  24. 24.
    Yi X (2009) Complex fault tree qualitative and quantitative analysis method research and Application. Kunming University of Science and Technology, KunmingGoogle Scholar
  25. 25.
    Lei LU, Wenjie XIAO (2010) An improved fuzzy fault tree analysis method. Electr Opt Control 17(11):93–96Google Scholar
  26. 26.
    Qi J-x, Chen Q, Sun X-h (2010) Application of fuzzy fault tree assessment on chloroethylene polymerization reactor. J Tianjin Univ Technol 26(4):79–82Google Scholar
  27. 27.
    Gao L-h, Tian J, Li S-w (2011) Fuzzy comprehensive assessment model of vehicle safety states based on fault tree analysis. J Jilin Univ (Eng Technol Edit) 41(1):95–100Google Scholar
  28. 28.
    An L-m (2010) Application of fuzzy and fault tree on fire accident analyse. Taiyuan University of Technology, TaiyuanGoogle Scholar
  29. 29.
    Teixeira CAR, Cavalca KL (2008) Reliability as an added-value factor in an automotive clutch system. Qual Reliab Eng Int 24(2):229–248CrossRefGoogle Scholar
  30. 30.
    Ahadi A, Ghadimi N, Mirabbasi D (2015) An analytical methodology for assessment of smart monitoring impact on future electric power distribution system reliability. Complexity 21(1):99–113CrossRefGoogle Scholar
  31. 31.
    Guo S-X, Li Y (2017) Robust reliability method and reliability-based performance optimization for non-fragile robust control design of dynamic system with bounded parametric uncertainties. Optimal Control Appl Methods 38(2):279–292MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Yi X-j, Shi J, Dhillon BS et al (2017) A new reliability analysis method for repairable systems with multifunction modes based on goal-oriented methodology. Qual Reliab Eng Int. Google Scholar
  33. 33.
    Noorossana R, Sabri-Laghaie K (2016) System reliability with multiple failure modes and time scales. Qual Reliab Eng Int 32(3):1109–1126CrossRefGoogle Scholar
  34. 34.
    Xiao F, Zhang Z, Yin X (2017) Reliability evaluation of the centralized substation protection system in smart substation. Trans Electr Electr Eng 12(3):317–327CrossRefGoogle Scholar
  35. 35.
    Huda ASN, Živanović R (2017) Improving distribution system reliability calculation efficiency using multilevel Monte Carlo method. Int Trans Electr Energy Syst. Google Scholar
  36. 36.
    Hou Y, Wang X, Guo J (2017) Quasi Monte Carlo method for reliability evaluation of power system based on dimension importance sorting. Int Trans Electr Energy Syst. Google Scholar
  37. 37.
    El-Khoury O, Shafieezadeh A (2017) Reliability-based control algorithms for nonlinear hysteretic systems based on enhanced stochastic averaging of energy envelope. Earthq Eng Struct Dyn 46(14):2381–2397CrossRefGoogle Scholar
  38. 38.
    Cui T-J, Wang P-Z, Li S-S (2017) The function structure analysis theory based on the factor space and space fault tree. Cluster Comput 20(2):1387–1398CrossRefGoogle Scholar
  39. 39.
    Cui T-J, Li S-S (2017) Study on the relationship between system reliability and influencing factors under big data and multi-factors. Cluster Comput. Google Scholar
  40. 40.
    LI S-S, Cui T-J, Liu J (2017) Study on the construction and application of cloudization space fault tree. Cluster Comput. Google Scholar
  41. 41.
    Cui T-J, Li S-S (2018) Study on the construction and application of discrete space fault tree modified by fuzzy structured element. Cluster Comput. Google Scholar
  42. 42.
    Xiang-nan B, Yu-ying Z (2008) Topology of power system reliability in more electric aircraft. J Beijing Univ Aeronaut Astronaut 34(10):1210–1213Google Scholar
  43. 43.
    Chen-lei F (2012) The reliability study of repairable system. Changsha University of Science and Technology, ChangshaGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.College of Safety Science and EngineeringLiaoning Technical UniversityFuxinChina
  2. 2.Key Laboratory of Mine Thermodynamic Disasters and Control of Ministry of EducationFuxinChina
  3. 3.Tunnel and Underground Structure Engineering Center of LiaoningDalian Jiaotong UniversityDalianChina

Personalised recommendations