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Reliability and Life-Cycle Analysis of Deteriorating Systems pp 117–149Cite as

Continuous State Degradation Models

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

Abstract

In this and the following chapters, the focus is on mathematical models for degradation that are based on stochastic processes.

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Notes

  1. 1.

    Modeling the distribution of damage magnitudes is in general rather difficult, but data can be obtained, for example, from the so-called fragility curves , which describe the probability that the system reaches a certain damage level in terms of a specific demand parameter. Several approaches to compute these curves are available in the literature; see, for instance, [16].

References

  1. T. Nakagawa, Shock and Damage Models in Reliability (Springer, London, 2007)

    MATH  Google Scholar 

  2. M.S. Nikulin, N. Limnios, N. Balakrishnan, W. Kahle, C. Huber-Carol, Advances in Degradation Modeling: Applications to Reliability, Survival Analysis and Finance, Statistics for Industry Technology (Birkhauser, Boston, 2010)

    Book  MATH  Google Scholar 

  3. J.M. Van Noortwijk, A survey of the application of gamma processes in maintenance. Reliab. Eng. Syst. Saf. 94, 2–21 (2009)

    Article  Google Scholar 

  4. M.D. Pandey, Probabilistic models for condition assessment of oil and gas pipelines. Int. J. Non-Destr. Test. Eval. 31(5), 349–358 (1998)

    Google Scholar 

  5. M.D. Pandey, X.X. Yuan, J.M. van Noortwijk, The influence of temporal uncertainty of deterioration on life-cycle management of structures. Struct. Infrastruct. Eng. 5(2), 145–156 (2009)

    Article  Google Scholar 

  6. C. Park, W.J. Padgett, New cumulative damage models for failure using stochastic processes as initial damage. IEEE Trans. Reliab. 54, 530–540 (2005)

    Article  Google Scholar 

  7. J. Ghosh, J. Padgett, M. Sánchez-Silva, Seismic damage accumulation of highway bridges in earthquake prone regions. Earthq. Spectra 31(1), 115–135 (2015)

    Article  Google Scholar 

  8. M. Sánchez-Silva, G.-A. Klutke, D. Rosowsky, Life-cycle performance of structures subject to multiple deterioration mechanisms. Struct. Saf. 33(3), 206–217 (2011)

    Article  Google Scholar 

  9. M. Junca, M. Sánchez-Silva, Optimal maintenance policy for permanently monitored infrastructure subjected to extreme events. Probab. Eng. Mech. 33(1), 1–8 (2013)

    Article  Google Scholar 

  10. I. Iervolino, M. Giorgio, E. Chioccarelli, Gamma degradation models for earthquake-resistant structures. Struct. Saf. 45, 48–58 (2013)

    Article  Google Scholar 

  11. K.C. Kapur, L.R. Lamberson, Reliability in Engineering Design (Wiley, New York, 1977)

    Google Scholar 

  12. J.L. Bogdanoff, F. Kozin, Probabilistic models of fatigue crack growth. Eng. Fract. Mech. 20(2), 255–270 (1984)

    Article  MATH  Google Scholar 

  13. F. Kozin, J.L. Bogdanoff, Probabilistic models of fatigue crack growth: results and specifications. Nucl. Eng. Des. 115, 143–171 (1989)

    Article  MATH  Google Scholar 

  14. T.J. Aven, U. Jensen, Stochastic Models in Reliability. Series in Applications of Mathematics: Stochastic Modeling and Applied Probability (41) (Springer, New York, 1999)

    Google Scholar 

  15. W. Kahle, H. Wendt, On accumulative damage process and resulting first passage times. Appl. Stoch. Models Bus. Ind. 20, 17–26 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Federal Emergency Management Agency (FEMA), Earthquake loss estimation methodology: technical manual. National Institute of Building Sciences for the Federal Emergency Management Agency (FEMA), Washington (1997)

    Google Scholar 

  17. J.T. Duane, Learning curve approach to reliability monitoring. IEEE Trans. Aerosp. 2, 563–566 (1964)

    Article  Google Scholar 

  18. S. Zacks, Distributions of failure times associated with non-homogeneous compound poisson damage processes. Inst. Math. Stat.-Lect. Notes-Monogr. Ser. 45, 396–407 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. W. Kahle, H. Wendt, Parametric shock models, in Advances in Degradation Modeling, ed. by M.S. Nikulin, et al. (Birkhauser, Boston, 2010)

    Google Scholar 

  20. D.S. Reynolds, I.R. Savage, Random wear models in reliability theory. Adv. Appl. Probab. 3, 229–248 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  21. Z.W. Birnbaum, S.C. Saunders, A new family of life distributions. J. Appl. Probab. 6, 319–327 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Desmond, Stochastic models of failure in random environments. Can. J. Stat. 13, 171–183 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  23. W.J. Owen, W.J. Padgett, Accelerated test models for system strength based on birnbaum-saunders distribution. Life Data Anal. 5(2), 133–147 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. D.B. Kececioglu, M.X. Jiang, A unified approach to random-fatigue reliability quantification under random loading, in Proceedings of the Annals of Reliability Maintainability Symposium, pp. 308–313 (1998)

    Google Scholar 

  25. G.A. Whitmore, Estimating degradation by a Wiener diffusion process subject to measurement error. Lifetime Data Anal. 1, 307–319 (1995)

    Article  MATH  Google Scholar 

  26. K. Doksum, S.L. Normand, Gaussian models for degradation processes-part I: methods for the analysis of biomarker data. Lifetime Data Anal. 1(2), 131–144 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  27. G.A. Whitmore, F. Schenkelberg, Modeling accelerated degradation data using wiener diffusion with a time scale transformation. Lifetime Data Anal. 3, 27–45 (1997)

    Article  MATH  Google Scholar 

  28. G.A. Whitmore, M.J. Crowder, J.F. Lawless, Failure inference from a marker process based on a bivariate Wiener model. Lifetime Data Anal. 4, 229–251 (1998)

    Article  MATH  Google Scholar 

  29. W. Kahle, A Lehmann, The Wiener process as a degradation model: modeling and parameter estimation, in Advances in Degradation Modeling, ed. by M.S. Nikulin et al. (eds.) (Birkhauser, Boston, 2010)

    Google Scholar 

  30. W.J. Padgett, M.A. Tomlinson, Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Anal. 10, 191–206 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  31. P. Kiessler, G.-A. Klutke, Y. Yang, Availability of periodically inspected systems subject to Markovian degradation. J. Appl. Probab. 39, 700–711 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  32. Y. Lam, The Geometric Process and Its Applications (World Scientific Press, New Jersey, 2007)

    Book  MATH  Google Scholar 

  33. E. Çinlar, Z.P. Bazant, E. Osman, Stochastic process for extrapolating concrete creep. J. Eng. Mech. Div. 103(EM6), 1069–1088 (1977)

    Google Scholar 

  34. E. Çinlar, On a generalization of gamma processes. J. Appl. Probab. 17, 467–480 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  35. N.D. Singpurwalla, Survival in dynamic environments. Stat. Sci. 1, 86–103 (1995)

    Article  MATH  Google Scholar 

  36. P.A.P. Moran, The Theory of Storage (Methuen, London, 1959)

    MATH  Google Scholar 

  37. J.D. Baker, H.J. van Der Graph, J.M. van Noortwijk, Proceedings of the Eight International Conference on Structural Faults and Repair (Edinburgh Engineering Technics Press, London, 1999)

    Google Scholar 

  38. M. Abdel-Hameed, A gamma wear process. IEEE Trans. Reliab. 24(2), 152–153 (1975)

    Article  Google Scholar 

  39. R.P. Nicolai, G. Budai, R. Dekker, M. Vreijling, A comparison of models for measurable deterioration: an application to coatings on steel structures. Reliab. Eng. Syst. Saf. 92(12), 1635–1650 (2007)

    Article  Google Scholar 

  40. N.D. Singpurwalla, S.P. Wilson, Failure models indexed by two scales. Adv. Appl. Probab. 30(4), 1058–1072 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  41. V. Bagdonavicius, M.S. Nikulin, Estimation in degradation models with explanatory variables. Lifetime Data Anal. 7(1), 85–103 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  42. W. Wang, P.A. Scarf, M.A.J. Smith, On the applications of a model of condition-based maintenance. J. Oper. Res. Soc. 51(11), 1218–1227 (2000)

    Article  MATH  Google Scholar 

  43. A.N. Avramidis, P. L’Ecuyer, P.A. Tremblay, Efficient simulation of gamma and variance gamma processes, in Proceedings of the 2003 Winter Simulation Conference, IEEE, Ed. by S. Chick, P.J. Sçnzhs, D. Ferrin, D.J. Morrice, pp. 319–323, Piscataway, August (2003)

    Google Scholar 

  44. N.T. Kottegoda, R. Rosso, Probability, Statistics and Reliability for Civil and Environmental Engineers (McGraw Hill, New York, 1997)

    Google Scholar 

  45. A.H-S. Ang, W.H. Tang, Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering (Wiley, New York, 2007)

    Google Scholar 

  46. F. Dufresne, H.U. Gerber, E.S.W. Shiu, Risk theory with gamma process. ASTIN Bul. 21(2), 177–192 (1991)

    Article  Google Scholar 

  47. J.S.K. Chang, Y. Lam, D.Y.P. Leung, Statistical inference for geometric processes with gamma distributions. Comput. Stat. Data Anal. 47, 565–581 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  48. Y. Lam, Non-parametric inference for geometric processes. Commun. Stat. Theory Methods 21, 2083–2105 (1992)

    Article  MATH  Google Scholar 

  49. Y. Lam, A shock model for the maintenance problem of reparable systems. Comput. Oper. Res. 31, 1807–1820 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  50. Y. Lam, S.K. Chang, Statistical inference for geometric processes with lognormal distributions. Comput. Stat. Data Anal. 27, 99–112 (1998)

    Article  MathSciNet  Google Scholar 

  51. F.K.N. Leung, Statistical inferential analogies between arithmetic and geometric processes. Int. J. Reliab. Qual. Saf. Eng. 12, 323–335 (2005)

    Article  Google Scholar 

  52. S. Suresh, Fatigue of Materials, 2nd edn. (Cambridge University Press, Edimburgh, 1998)

    Book  Google Scholar 

  53. J. Rice, On generalized shot noise. Adv. Appl. Probab. 9, 553–565 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  54. T.L. Hsing, J.L. Teugels, Extremal properties of shot noise processes. Adv. Appl. Probab. 21, 513–525 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  55. E. Waymire, V.K. Gupta, The mathematical structure of rainfall representations 1: a review of stochastic rainfall models. Water Res. Res. 17, 1261–1272 (1981)

    Article  Google Scholar 

  56. R.B. Lund, A dam with seasonal input. J. Appl. Probab. 31, 526–541 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  57. R.B. Lund, The stability of storage models with shot noise input. J. Appl. Probab. 33, 830–839 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  58. L. Takacs, Stoch. Process. (Wiley, New York, 1960)

    Google Scholar 

  59. U. Sumita, J. Shanthikumar, General shock models associated with correlated renewal sequences. J. Appl. Probab. 20, 600–614 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  60. U. Sumita, Z. Jinshui, Analysis of correlated multivariate shock model generated from a renewal sequence. Department of Social Systems and Management: discussion paper series No. 1194; University of Tsukuba, Tsukuba, Japan (2008)

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Universidad de Los Andes, Bogotá, Colombia

    Mauricio Sánchez-Silva

  2. Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, USA

    Georgia-Ann Klutke

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  1. Mauricio Sánchez-Silva
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  2. Georgia-Ann Klutke
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Correspondence to Mauricio Sánchez-Silva .

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Sánchez-Silva, M., Klutke, GA. (2016). Continuous State Degradation Models. In: Reliability and Life-Cycle Analysis of Deteriorating Systems. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-20946-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-20946-3_5

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