A review on degradation models in reliability analysis

  • Nima Gorjian
  • Lin Ma
  • Murthy Mittinty
  • Prasad Yarlagadda
  • Yong Sun


With increasingly complex engineering assets and tight economic requirements, asset reliability becomes more crucial in Engineering Asset Management (EAM). Improving the reliability of systems has always been a major aim of EAM. Reliability assessment using degradation data has become a significant approach to evaluate the reliability and safety of critical systems. Degradation data often provide more information than failure time data for assessing reliability and predicting the remnant life of systems. In general, degradation is the reduction in performance, reliability, and life span of assets. Many failure mechanisms can be traced to an underlying degradation process. Degradation phenomenon is a kind of stochastic process; therefore, it could be modelled in several approaches. Degradation modelling techniques have generated a great amount of research in reliability field. While degradation models play a significant role in reliability analysis, there are few review papers on that. This paper presents a review of the existing literature on commonly used degradation models in reliability analysis. The current research and developments in degradation models are reviewed and summarised in this paper. This study synthesises these models and classifies them in certain groups. Additionally, it attempts to identify the merits, limitations, and applications of each model. It provides potential applications of these degradation models in asset health and reliability prediction.


Hide Markov Model Degradation Model Remain Useful Life Gamma Process Failure Time Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Meeker WQ & Escobar LA. (1998) Statistical methods for reliability data: J. Wiley.Google Scholar
  2. 2.
    Meeker WQ & Escobar LA. (1993) A review of recent research and current issues in accelerated testing. International Statistical Review, 61(1), 147-168.CrossRefGoogle Scholar
  3. 3.
    Singpurwalla ND. (2006) The hazard potential: introduction and overview. Journal of the American Statistical Association, 101(476), 1705-1717.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Singpurwalla ND. (1995) Survival in dynamic environments. Statistical Science 10(1), 86–103.MATHCrossRefGoogle Scholar
  5. 5.
    Van Noortwijk JM. (2007) A survey of the application of gamma processes in maintenance. Reliability Engineering & System Safety, In Press, Corrected Proof, 20.Google Scholar
  6. 6.
    Ma L. (2007) Condition monitoring in engineering asset management. APVC. p. 16.Google Scholar
  7. 7.
    Rausand M. (1998) Reliability centered maintenance. Reliability Engineering & System Safety, 60(2), 121-132.CrossRefGoogle Scholar
  8. 8.
    Blischke WR & Murthy DNP. (2000) Reliability : modeling, prediction, and optimization. New York: Wiley.MATHGoogle Scholar
  9. 9.
    Zuo MJ, Renyan J & Yam RCM. (1999) Approaches for reliability modeling of continuous-state devices. IEEE Transactions on Reliability, 48(1), 9-18.CrossRefGoogle Scholar
  10. 10.
    Meeker WQ, L. A. Escobar & Lu CJ. (1998) Accelerated degradation tests: Modeling and analysis. Technometrics, 40(2), 89.CrossRefGoogle Scholar
  11. 11.
    Yang K & Xue J. (1996) Continuous state reliability analysis. Annual Reliability and Maintainability Symposium. pp. 251-257.Google Scholar
  12. 12.
    Montoro-Cazorla D & Perez-Ocon R. (2006) Reliability of a system under two types of failures using a Markovian arrival process. Operations Research Letters, 34(5), 525-530.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Yang G. (2002) Environmental-stress-screening using degradation measurements. IEEE Transactions on Reliability, 51(3), 288-293.CrossRefGoogle Scholar
  14. 14.
    Yang K & Yang G. (1998) Degradation reliability assessment using severe critical values. International Journal of Reliability, Quality and Safety Engineering, 5(1), 85-95.CrossRefGoogle Scholar
  15. 15.
    Borris S. (2006) Total productive maintenance. New York: McGraw-Hill.Google Scholar
  16. 16.
    Endrenyi J & Anders GJ. (2006) Aging, maintenance, and reliability - approaches to preserving equipment health and extending equipment life. Power and Energy Magazine, IEEE, 4(3), 59-67.CrossRefGoogle Scholar
  17. 17.
    Jardine AKS, Lin D & Banjevic D. (2006) A review on machinery diagnostics and prognostics implementing conditionbased maintenance. Mechanical Systems and Signal Processing, 20(7), 1483-1510.CrossRefGoogle Scholar
  18. 18.
    Heng A, Zhang S, Tan ACC & Mathew J. (2008) Rotating machinery prognostics: State of the art, challenges and opportunities. Mechanical Systems and Signal Processing, In Press, Corrected Proof.Google Scholar
  19. 19.
    Vachtsevanos GJ, Lewis FL, Roemer M, Hess A & Wu B. (2006) Intelligent fault diagnosis and prognosis for engineering systems. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  20. 20.
    Zhang L, Li X & Yu J. (2006) A review of fault prognostics in condition based maintenance. Sixth International Symposium on Instrumentation and Control Technology: Signal Analysis, Measurement Theory, Photo-Electronic Technology, and Artificial Intelligence China. pp. 6357521-6. SPIE.Google Scholar
  21. 21.
    Sikorska J. (2008) Prognostic modelling options for remaining useful life estimation: CASWA Pty Ltd & University of Western Australia.Google Scholar
  22. 22.
    Jiang R & Yan X. (2007) Condition monitoring on diesel engines. 25.Google Scholar
  23. 23.
    Kothamasu R, Huang S & VerDuin W. (2006) System health monitoring and prognostics — a review of current paradigms and practices. The International Journal of Advanced Manufacturing Technology, 28(9), 1012-1024.CrossRefGoogle Scholar
  24. 24.
    Katipamula S & Brambley MR. (2005) Methods for fault detection, diagnostics, and prognostics for building systems—a review, part I. International Journal of HVAC&R Research, 11(1), 3-25.Google Scholar
  25. 25.
    Goh KM, Tjahjono B, Baines TS & Subramaniam S. (2006) A review of research in manufacturing prognostics. IEEE International Conference on Industrial Informatics. pp. 1-6.Google Scholar
  26. 26.
    Ma Z & Krings AW. (2008) Survival analysis approach to reliability, survivability and prognostics and health management. IEEE Aerospace Conference. pp. 1-20.Google Scholar
  27. 27.
    Pusey HC & Roemer MJ. (1999) An assessment of turbomachinary condition monitoring and failure prognosis technology. The Shock and Vibration Digest, 31(5), 365-371.CrossRefGoogle Scholar
  28. 28.
    Weibull W. (1951) A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18(3), 293-297.MATHGoogle Scholar
  29. 29.
    Chelidze D & Cusumano JP. (2004) A dynamical systems approach to failure prognosis. Transactions of the ASME, 126, 2.CrossRefGoogle Scholar
  30. 30.
    Chen A & Wu GS. (2007) Real-time health prognosis and dynamic preventive maintenance policy for equipment under aging Markovian deterioration. International Journal of Production Research, 45(15), 3351.MATHCrossRefGoogle Scholar
  31. 31.
    Luo J, Bixby A, Pattipati K, Liu Q, Kawamoto M & Chigusa S. (2003) An interacting multiple model approach to modelbased prognostics. Bixby A (Ed.). IEEE International Conference on Systems, Man and Cybernetics. pp. 189-19.Google Scholar
  32. 32.
    Kulkarni SS & Achenbach JD. (2008) Structural health monitoring and damage prognosis in fatigue. Structural Health Monitoring, 7(1), 37-49.CrossRefGoogle Scholar
  33. 33.
    Wang W & Zhang W. (2008) An asset residual life prediction model based on expert judgments. European Journal of Operational Research, 188(2), 496-505.MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Jardine AKS. (2002) Optimizing condition based maintenance decisions. Annual Reliability and Maintainability Symposium. pp. 90-97. IEEE.Google Scholar
  35. 35.
    Eleuteri A, Tagliaferri R, Milano L, De Placido S & De Laurentiis M. (2003) A novel neural network-based survival analysis model. Neural Networks, 16(5-6), 855-864.CrossRefGoogle Scholar
  36. 36.
    Li C, Tao L & Yongsheng B. (2007) Condition residual life evaluation by support vector machine. 8th International Conference on Electronic Measurement and Instruments. pp. 441-445.Google Scholar
  37. 37.
    Liao H. (2004) Degradation models and design of accelerated degradation testing plans. United States -- New Jersey: Rutgers The State University of New Jersey - New Brunswick.Google Scholar
  38. 38.
    Jiang R & Jardine AKS. (2008) Health state evaluation of an item: A general framework and graphical representation. Reliability Engineering & System Safety, 93(1), 89-99.CrossRefGoogle Scholar
  39. 39.
    Lu CJ & Meeker WQ. (1993) Using degradation measures to estimate a time-to-failure distribution. Technometrics, 35(2), 161-174.MATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Engel SJ, Gilmartin BJ, Bongort K & Hess A. (2000) Prognostics, the real issues involved with predicting life remaining. IEEE Aerospace Conference Proceedings pp. 457-469.Google Scholar
  41. 41.
    Yuan X. (2007) Stochastic modeling of deterioration in nuclear power plant components. Ontario -- Canada: University of Waterloo.Google Scholar
  42. 42.
    Crk V. (2000) Reliability assessment from degradation data. Annual Reliability and Maintainability Symposium. pp. 155-161.Google Scholar
  43. 43.
    Crk V. (1998) Component and system reliability assessment from degradation data. United States -- Arizona: The University of Arizona.Google Scholar
  44. 44.
    Lu S, Lu H & Kolarik WJ. (2001) Multivariate performance reliability prediction in real-time. Reliability Engineering & System Safety, 72(1), 39-45.CrossRefGoogle Scholar
  45. 45.
    Gordon NJ, Salmond DJ & Smith AFM. (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proceedings "F" Radar and Signal Processing. pp. 107-113.Google Scholar
  46. 46.
    Arulampalam MS, Maskell S, Gordon N & Clapp T. (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2), 174-188.CrossRefGoogle Scholar
  47. 47.
    Nachlas JA. (2005) Reliability engineering : probabilistic models and maintenance methods. Boca Raton: Taylor & Francis.MATHGoogle Scholar
  48. 48.
    Xue J & Yang K. (1997) Upper and lower bounds of stress-strength interference reliability with random strengthdegradation. IEEE Transactions on Reliability, 46(1), 142-145.CrossRefGoogle Scholar
  49. 49.
    Sweet AL. (1990) On the hazard rate of the lognormal distribution. IEEE Transactions on Reliability, 39(3), 325-328.MATHCrossRefGoogle Scholar
  50. 50.
    Huang W & Askin RG. (2004) A generalized SSI reliability model considering stochastic loading and strength aging degradation. IEEE Transactions on Reliability, 53(1), 77-82.CrossRefGoogle Scholar
  51. 51.
    Esary JD & Marshall AW. (1973) Shock models and wear processes. The Annals of Probability, 1(4), 627-649.MATHCrossRefMathSciNetGoogle Scholar
  52. 52.
    Lemoine AJ & Wenocur ML. (1985) On failure modeling. Naval Research Logistics, 32(3), 497-508.MATHCrossRefMathSciNetGoogle Scholar
  53. 53.
    Li N, Xie W-C & Haas R. (1996) Reliability-based processing of Markov chains for modeling pavement network deterioration. Transportation Research Record, 1524(-1), 203-213.CrossRefGoogle Scholar
  54. 54.
    Pijnenburg M. (1991) Additive hazards models in repairable systems reliability. Reliability Engineering and System Safety, 31(3), 369-390.CrossRefGoogle Scholar
  55. 55.
    Kallen MJ & van Noortwijk JM. (2006) Optimal periodic inspection of a deterioration process with sequential condition states. International Journal of Pressure Vessels and Piping, 83(4), 249-255.CrossRefGoogle Scholar
  56. 56.
    Welte TM, Vatn J & Heggest J. (2006) Markov state model for optimization of maintenance and renewal of hydro power components. International Conference on Probabilistic Methods Applied to Power Systems pp. 1-7.Google Scholar
  57. 57.
    Papazoglou IA. (2000) Semi-Markovian reliability models for systems with testable components and general test/outage times. Reliability Engineering & System Safety, 68(2), 121-133.CrossRefGoogle Scholar
  58. 58.
    Ross SM. (1996) Stochastic processes (2nd ed.). New York: Wiley.MATHGoogle Scholar
  59. 59.
    Whitmore G & Schenkelberg F. (1997) Modelling accelerated degradation data using wiener diffusion with a time scale transformation. Lifetime Data Analysis, 3(1), 27-45.MATHCrossRefGoogle Scholar
  60. 60.
    Bagdonavicius V & Nikulin MS. (2001) Estimation in degradation models with explanatory variables. Lifetime Data Analysis, 7(1), 85-103.MATHCrossRefMathSciNetGoogle Scholar
  61. 61.
    Doksum KA. (1991) Degradation rate models for failure time and survival data. CWI Quarterly, 4, 195-203.MATHGoogle Scholar
  62. 62.
    Singpurwalla ND. (2006) Reliability and risk : a Bayesian perspective. New York: J. Wiley & Sons.MATHGoogle Scholar
  63. 63.
    Van Noortwijk JM, Van der Weide JAM, Kallen MJ & Pandey MD. (2007) Gamma processes and peaks-over-threshold distributions for time-dependent reliability. Reliability Engineering & System Safety, 92(12), 1651-1658.CrossRefGoogle Scholar
  64. 64.
    Van Noortwijk JM & Frangopol DM. (2004) Two probabilistic life-cycle maintenance models for deteriorating civil infrastructures. Probabilistic Engineering Mechanics, 19(4), 345-359.CrossRefGoogle Scholar
  65. 65.
    Lawless J & Martin C. (2004) Covariates and random effects in a Gamma process model with application to degradation and failure. Lifetime Data Analysis, 10(3), 213.MATHCrossRefMathSciNetGoogle Scholar
  66. 66.
    Singpurwalla N. (1997) Gamma processes and their generalizations: an overview. Engineering Probabilistic Design and Maintenance for Flood Protection, 67–75.Google Scholar
  67. 67.
    Tang LC & Shang CD. (1995) Reliability prediction using nondestructive accelerated-degradation data: case study on power supplies. IEEE Transactions on Reliability 44(4), 562-566.CrossRefGoogle Scholar
  68. 68.
    Meeker WQ & LuValle MJ. (1995) An accelerated life test model based on reliability kinetics. Technometrics, 37(2), 133-146.MATHCrossRefGoogle Scholar
  69. 69.
    Zhang C, Chuckpaiwong I, Liang SY & Seth BB. (2002) Mechanical component lifetime estimation based on accelerated life testing with singularity extrapolation. Mechanical Systems and Signal Processing, 16(4), 705-718.CrossRefGoogle Scholar
  70. 70.
    Shiau J-JH & Lin H-H. (1999) Analyzing accelerated degradation data by nonparametric regression. IEEE Transactions on Reliability, 48(2), 149-158.CrossRefGoogle Scholar
  71. 71.
    Pham H. (2006) Reliability modeling, analysis and optimization. Singapore: World Scientific.CrossRefGoogle Scholar
  72. 72.
    Nelson W. (1990) Accelerated testing: statistical models, test plans, and data analyses. New York: John Wiley & Sons.Google Scholar
  73. 73.
    Gorjian N, Ma L, Mittinty M, Yarlagadda P & Sun Y. (2009) A review on reliability models with covariates The 4rd World Congress on Engineering Asset Management, Athens-Greece. Springer.Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Nima Gorjian
    • 1
    • 2
  • Lin Ma
    • 1
    • 2
  • Murthy Mittinty
    • 3
  • Prasad Yarlagadda
    • 2
  • Yong Sun
    • 1
    • 2
  1. 1.Cooperative Research Centre for Integrated Engineering Asset Management (CIEAM)BrisbaneAustralia
  2. 2.School of Engineering SystemsQueensland University of Technology (QUT)BrisbaneAustralia
  3. 3.School of Mathematical SciencesQueensland University of Technology (QUT)BrisbaneAustralia

Personalised recommendations