Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

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Abstract

In today’s technologically driven industrial environments, ensuring system reliability has become paramount. The chapter examines the various mathematical models employed to assess, predict, and enhance the reliability of industrial systems. Beginning with a foundational understanding of reliability, the chapter talks about traditional probabilistic models, such as exponential and Weibull distributions, and modern stochastic processes and Bayesian approaches. Special attention is given to the suitability and accuracy of models in addressing real-world industrial challenges. Practical applications are highlighted through case studies, demonstrating how these models have been instrumental in mitigating system failures, reducing downtimes, and optimizing maintenance strategies. The chapter also explores the intersection of data analytics and reliability modelling, emphasizing the increasing role of machine learning and artificial intelligence in forecasting and improving industrial system reliability. The study concludes with a forward-looking perspective on emerging trends in reliability modelling and the potential avenues for future research.

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References

  1. Rausand M, Hoyland A (2004) System reliability theory: models, statistical methods, and applications, p 664. https://doi.org/10.1109/WESCON.1996.554026

  2. Hollnagel E (1998) Chapter 2—The need of HRA. In: Hollnagel (eds) Cognitive Reliability and error analysis method (CREAM). Elsevier, Oxford, pp 22–51. https://doi.org/10.1016/B978-008042848-2/50002-6

  3. Yazdi Y (2019) Acquiring and sharing tacit knowledge in failure diagnosis analysis using intuitionistic and Pythagorean assessments. J Fail Anal Prev 19(2019). https://doi.org/10.1007/s11668-019-00599-w

  4. Li Y-F, Huang H-Z, Mi J, Peng W, Han X (2022) Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability. Ann Oper Res 311:195–209. https://doi.org/10.1007/s10479-019-03247-6

    Article  MathSciNet  Google Scholar 

  5. Yazdi M, Adesina KA, Korhan O, Nikfar F (2019) Learning from Fire Accident at Bouali Sina petrochemical complex plant. J Fail Anal Prev. https://doi.org/10.1007/s11668-019-00769-w

    Article  Google Scholar 

  6. Mannan MS, Reyes-Valdes O, Jain P, Tamim N, Ahammad M (2016) The Evolution of process safety: current status and future direction. Annu Rev Chem Biomol Eng 7:135–162. https://doi.org/10.1146/annurev-chembioeng-080615-033640

    Article  Google Scholar 

  7. Tong Q, Yang M, Zinetullina A (2020) A dynamic Bayesian network-based approach to resilience assessment of engineered systems. J Loss Prev Process Ind 65:104152. https://doi.org/10.1016/j.jlp.2020.104152

    Article  Google Scholar 

  8. Li H, Yazdi M (2022) Develo** failure modes and effect analysis on offshore wind turbines using two-stage optimization probabilistic linguistic preference relations BT. In: Li H, Yazdi M (eds) Advanced decision-making methods and applications in system safety and reliability problems: approaches. Springer, Cham, pp 47–68. https://doi.org/10.1007/978-3-031-07430-1_4

  9. Conley S, Franco G, Faloona I, Blake DR, Peischl J, Ryerson TB (2016) Methane emissions from the 2015 Aliso Canyon blowout in Los Angeles, CA, Science (80-.). 351 (2016) 1317 LP–1320. https://doi.org/10.1126/science.aaf2348

  10. PMI (2017) Project management body of knowledge (pmbok® guide). Project Management Institute, Inc. Newt. Square, PA, USA

    Google Scholar 

  11. Rausand M, Haugen S (2020) Risk assessment: theory, methods, and applications. Wiley, 2020.

    Google Scholar 

  12. Kwak YH, Anbari FT (2006) Benefits, obstacles, and future of six sigma approach. Technovation 26:708–715

    Article  Google Scholar 

  13. MacDuffie JP, Krafcik J (1992) Integrating technology and human resources for high-performance manufacturing: evidence from the international auto industry, Transform Organ 209226

    Google Scholar 

  14. Li H, Peng W, Adumene S, Yazdi M (2023) A sustainable circular economy in energy infrastructure: application of supercritical water gasification system BT. In: Li H, Peng W, Adumene S, Yazdi M (eds) Intelligent reliability and maintainability of energy infrastructure assets. Springer, Cham, pp 119–135. https://doi.org/10.1007/978-3-031-29962-9_8

  15. Trivedi KS, Bobbio A (2017) Reliability and availability engineering: modeling, analysis, and applications. Cambridge University Press

    Google Scholar 

  16. Saraswat S, Yadava GS (2008) An overview on reliability, availability, maintainability and supportability (RAMS) engineering. Int J Qual Reliab Manag. 25:330–344

    Article  Google Scholar 

  17. Spanos A (2019) Probability theory and statistical inference: Empirical modeling with observational data. Cambridge University Press

    Google Scholar 

  18. Jaynes ET (1967) Foundations of probability theory and statistical mechanics. In: Delaware seminar in the foundations of physics. Springer, pp 77–101

    Google Scholar 

  19. Ash RB (2008) Basic probability theory. Courier Corporation

    Google Scholar 

  20. Freund RJ, Wilson WJ (2003) Statistical methods. Elsevier

    Google Scholar 

  21. Pfeiffer PE (2013) Concepts of probability theory. Courier Corporation

    Google Scholar 

  22. Joyce J (2003) Bayes’ theorem

    Google Scholar 

  23. Li H, Yazdi M (2022) Reliability analysis of correlated failure modes by transforming fault tree model to Bayesian network: a case study of the MDS of a CNC machine Tool BT. In: Li H, Yazdi M (eds) Advanced decision-making methods and applications in system safety and reliability problems: approach. Springer, Cham, pp 15–28. https://doi.org/10.1007/978-3-031-07430-1_2

  24. Li H, Yazdi M (2022) Integration of the Bayesian network approach and interval type-2 fuzzy sets for develo** sustainable hydrogen storage technology in large metropolitan areas BT. In: Li H, Yazdi M (eds) Advanced decision-making methods and applications in system safety and reliability problem. Springer, Cham, pp 69–85. https://doi.org/10.1007/978-3-031-07430-1_5

  25. Coburn CE, Turner EO (2011) Research on data use: a framework and analysis. Meas Interdiscip Res Perspect 9:173–206

    Article  Google Scholar 

  26. Ahlqvist E, Storm P, Käräjämäki A, Martinell M, Dorkhan M, Carlsson A, Vikman P, Prasad RB, Aly DM, Almgren P (2018) Novel subgroups of adult-onset diabetes and their association with outcomes: a data-driven cluster analysis of six variables. Lancet Diabetes Endocrinol 6:361–369

    Article  Google Scholar 

  27. Jiang H, Zhang H, Zhang K, Cui X (2018) Neurocomputing Data-driven adaptive dynamic programming schemes for non-zero-sum games of unknown discrete-time nonlinear systems. Neurocomputing 275:649–658. https://doi.org/10.1016/j.neucom.2017.09.020

    Article  Google Scholar 

  28. Bonett DG, Wright TA (2015) Cronbach’s alpha reliability: Interval estimation, hypothesis testing, and sample size planning. J Organ Behav 36:3–15

    Article  Google Scholar 

  29. Javanmard A, Montanari A (2014) Confidence intervals and hypothesis testing for high-dimensional regression. J Mach Learn Res 15:2869–2909

    MathSciNet  Google Scholar 

  30. Aydogdu M, Firat M (2015) Estimation of failure rate in water distribution network using fuzzy clustering and LS-SVM methods. Water Resour Manag 29:1575–1590

    Article  Google Scholar 

  31. Yazdi M (2022) A brief review of using linguistic terms in system safety and reliability analysis BT. In: Yazdi M (ed) Linguistic methods under fuzzy information in system safety and reliability analysis. Springer, Cham, pp 1–4. https://doi.org/10.1007/978-3-030-93352-4_1

  32. Yazdi M, Golilarz NA, Nedjati A, Adesina KA (2021) An improved lasso regression model for evaluating the efficiency of intervention actions in a system reliability analysis. Neural Comput Appl. https://doi.org/10.1007/s00521-020-05537-8

    Article  Google Scholar 

  33. Bowles JB (2002) Commentary-caution: constant failure-rate models may be hazardous to your design. IEEE Trans Reliab 51:375–377

    Article  Google Scholar 

  34. Lariviere MA (2006) A note on probability distributions with increasing generalized failure rates. Oper Res 54:602–604

    Article  MathSciNet  Google Scholar 

  35. Adamidis K, Loukas S (1998) A lifetime distribution with decreasing failure rate. Stat Probab Lett 39:35–42

    Article  MathSciNet  Google Scholar 

  36. Sharma RK, Kumar D, Kumar P (2008) Fuzzy modeling of system behavior for risk and reliability analysis. Int J Syst Sci 39:563–581. https://doi.org/10.1080/00207720701717708

    Article  MathSciNet  Google Scholar 

  37. Markowski AS, Mannan MS, Bigoszewska A (2009) Fuzzy logic for process safety analysis. J Loss Prev Process Ind 22:695–702. https://doi.org/10.1016/j.jlp.2008.11.011

    Article  Google Scholar 

  38. Klutke G-A, Kiessler PC, Wortman MA (2003) A critical look at the bathtub curve. IEEE Trans Reliab 52:125–129

    Article  Google Scholar 

  39. Hajivassiliou VA, Ruud PA (1994) Classical estimation methods for LDV models using simulation. Handb Econom 4:2383–2441

    MathSciNet  Google Scholar 

  40. Isermann R (1984) Process fault detection based on modeling and estimation methods—A survey. Automatica 20:387–404

    Article  Google Scholar 

  41. Langley A (1999) Strategies for theorizing from process data. Acad Manag Rev 24:691–710

    Article  Google Scholar 

  42. Tranfield D, Denyer D, Smart P (2003) Towards a methodology for develo** evidence-informed management knowledge by means of systematic review. Br J Manag 14:207–222

    Article  Google Scholar 

  43. Spokoiny V (2012) Parametric estimation. Finite sample theory

    Google Scholar 

  44. Epanechnikov VA (1969) Non-parametric estimation of a multivariate probability density. Theory Probab Appl 14:153–158

    Article  MathSciNet  Google Scholar 

  45. Ullah A (1988) Non-parametric estimation of econometric functionals. Can J Econ 625–658

    Google Scholar 

  46. O’Connor AN (2011) Probability distributions used in reliability engineering. RiAC

    Google Scholar 

  47. Short TA (2018) Distribution reliability and power quality. CRC Press

    Google Scholar 

  48. Elsayed EA (2012) Overview of reliability testing. IEEE Trans Reliab 61:282–291

    Article  Google Scholar 

  49. Gnedenko BV, Belyayev YK, Solovyev AD (2014) Mathematical methods of reliability theory. Academic Press

    Google Scholar 

  50. Hallinan AJ Jr (1993) A review of the Weibull distribution. J Qual Technol 25:85–93

    Article  Google Scholar 

  51. Lai CD, **e M, Murthy DNP (2003) A modified Weibull distribution. IEEE Trans Reliab 52:33–37

    Article  Google Scholar 

  52. Denson W (1998) The history of reliability prediction. IEEE Trans Reliab 47:SP321–SP328

    Google Scholar 

  53. Li H, Peng W, Adumene S, Yazdi M (2023) Advances in failure prediction of subsea components considering complex dependencies BT. In: Li H, Peng W, Adumene S, Yazdi M (eds) Intelligent reliability and maintainability of energy infrastructure assets. Springer, Cham, pp 93–105. https://doi.org/10.1007/978-3-031-29962-9_6

  54. Li H, Yazdi M (2022) How to deal with toxic people using a fuzzy cognitive map: improving the health and wellbeing of the human system BT. In: Li H, Yazdi M (eds) Advanced decision-making methods and applications in system safety and reliability problems: approaches, case studies, multi-criteria D. Springer, Cham, pp 87–107. https://doi.org/10.1007/978-3-031-07430-1_6

  55. **ng L, Tannous O, Dugan JB (2011) Reliability analysis of nonrepairable cold-standby systems using sequential binary decision diagrams. IEEE Trans Syst Man Cybern A Syst Humans 42(2011):715–726

    Google Scholar 

  56. Vaurio JK (1994) The theory and quantification of common cause shock events for redundant standby systems. Reliab Eng Syst Saf 43:289–305

    Article  Google Scholar 

  57. Weber P, Jouffe L (2006) Complex system reliability modelling with dynamic object oriented Bayesian networks (DOOBN). Reliab Eng Syst Saf 91:149–162. https://doi.org/10.1016/j.ress.2005.03.006

    Article  Google Scholar 

  58. Yazdi M, Nedjati A, Zarei E, Abbassi R (2020) A novel extension of DEMATEL approach for probabilistic safety analysis in process systems. Saf Sci 121:119–136. https://doi.org/10.1016/j.ssci.2019.09.006

    Article  Google Scholar 

  59. Ball MO (1986) Computational complexity of network reliability analysis: an overview. IEEE Trans Reliab 35:230–239

    Article  Google Scholar 

  60. Reibman AL, Veeraraghavan M (1991) Reliability modeling: an overview for system designers. Computer (Long Beach Calif) 24(1991):49–57

    Google Scholar 

  61. Yazdi M, Mohammadpour J, Li H, Huang H-Z, Zarei E, Pirbalouti RG, Adumene S (2023) Fault tree analysis improvements: a bibliometric analysis and literature review. Qual Reliab Eng Int (n/a). https://doi.org/10.1002/qre.3271

  62. Flood JE (1007) Telecommunication networks. IET

    Google Scholar 

  63. Heydt GT (2010) The next generation of power distribution systems. IEEE Trans Smart Grid. 1:225–235

    Article  Google Scholar 

  64. Bast H, Delling D, Goldberg A, Müller-Hannemann M, Pajor T, Sanders P, Wagner D, Werneck RF (2016) Route planning in transportation networks. Algor Eng Sel Results Surv 19–80

    Google Scholar 

  65. Dekker S (2016) Drift into failure: From hunting broken components to understanding complex systems. CRC Press

    Google Scholar 

  66. Chan D, Mo J (2017) Life cycle reliability and maintenance analyses of wind turbines. Energy Procedia 110(2017):328–333. https://doi.org/10.1016/j.egypro.2017.03.148

  67. Yazdi M, Khan F, Abbassi R (2021) Microbiologically influenced corrosion (MIC) management using Bayesian inference. Ocean Eng. https://doi.org/10.1016/j.oceaneng.2021.108852

  68. Ferreira LL, Albano M, Silva J, Martinho D, Marreiros G, Di Orio G, Maló P, Ferreira H (2017) A pilot for proactive maintenance in industry 4.0. In: 2017 IEEE 13th international workshop on factory communication systems. IEEE, pp 1–9

    Google Scholar 

  69. Adumene S, Okwu M, Yazdi M, Afenyo M, Islam R, Orji CU, Obeng F, Goerlandt F, (2021) Dynamic logistics disruption risk model for offshore supply vessel operations in Arctic waters. Marit Transp Res 2(2021):100039. https://doi.org/10.1016/j.martra.2021.100039

  70. Li H, Peng W, Adumene S, Yazdi M (2023) Operations management of critical energy infrastructure: a sustainable approach BT. In: In: Li H, Peng W, Adumene S, Yazdi M (eds) Intelligent reliability and maintainability of energy infrastructure assets. Springer, Cham, pp 39–52. https://doi.org/10.1007/978-3-031-29962-9_3

  71. Yazdi M, Khan F, Abbassi R, Quddus N (2022) Resilience assessment of a subsea pipeline using dynamic Bayesian network. J Pipeline Sci Eng 2(2022):100053. https://doi.org/10.1016/j.jpse.2022.100053

  72. Arifujjaman M, Iqbal MT, Quaicoe JE (2009) Reliability analysis of grid connected small wind turbine power electronics. Appl Energy 86:1617–1623

    Article  Google Scholar 

  73. Albasrawi MN, Jarus N, Joshi KA, Sarvestani SS (2014) Analysis of reliability and resilience for smart grids. In: 2014 IEEE 38th annual computer software and applications conference. IEEE, pp 529–534

    Google Scholar 

  74. Yuanidis P, Styblinski MA, Smith DR, Singh C (1994) Reliability modeling of flexible manufacturing systems. Microelectron Reliab 34:1203–1220

    Article  Google Scholar 

  75. Pecht MG, Nash FR (1994) Predicting the reliability of electronic equipment. Proc IEEE 82:992–1004

    Article  Google Scholar 

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Yazdi, M. (2024). Mathematical Models for Industrial System Reliability. In: Advances in Computational Mathematics for Industrial System Reliability and Maintainability. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-53514-7_2

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