Skip to main content

RUL Estimation Based on a Nonlinear Diffusion Degradation Process

  • Chapter
  • First Online:
Data-Driven Remaining Useful Life Prognosis Techniques

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

  • 1938 Accesses

Abstract

Because of limited natural resources, considerably increased safety and environmental concerns, and the drive to reduce operating costs, critical assets need to be managed over their entire life cycles—from design, manufacture, sale, and operation to their end of life in order to optimize life cycle management and reduce negative impact on the environment [1, 2]. For safety-critical equipment, such as aviation control systems and nuclear power generators, the accurate and early estimation of failure is critical in order to avoid catastrophic events that may cause severe damage to equipment, loss of human lives, and environmental disasters.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bayus BL (1998) An analysis of product lifetimes in a technologically dynamic industry. Manag Sci 44:763–775

    Article  MATH  Google Scholar 

  2. Mazhar MI, Kara S, Kaebernick H (2007) Remaining life estimation of used components in consumer products life cycle data analysis by Weibull and artificial neural networks. J Oper Manag 25:1184–1193

    Article  Google Scholar 

  3. Pecht M (2008) Prognostics and health management of electronics. John Wiley, New Jersey

    Book  Google Scholar 

  4. Altay N, Green WGIII (2006) OR/MS research in disaster operations management. Eur J Oper Res 175:475–493

    Article  MATH  Google Scholar 

  5. Block HW, Savits TH, Singh H (2002) A criterion for burn-in that balances mean residual life and residual variance. Oper Res 50:290–296

    Article  MathSciNet  MATH  Google Scholar 

  6. Elwany AH, Gebraeel NZ (2008) Sensor-driven prognostic models for equipment replacement and spare parts inventory. IIE Trans 40:629–639

    Article  Google Scholar 

  7. Fan CY, Chang PC, Fan PS (2010) A system dynamics modeling approach for a military weapon maintenance supply system. Int J Prod Econ (2010). doi:10.1016/j.ijpe.2010.07.015

  8. Huh WT, Janakiraman G, Muckstadt JA, Rusmevichientong P (2009) Asymptotic optimality of order-up-to policies in lost sales inventory systems. Manag Sci 55(3):404–420

    Article  MATH  Google Scholar 

  9. Jardine AKS, Lin D, Banjevic D (2006) A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mech Syst Signal Process 20(7):1483–1510

    Article  Google Scholar 

  10. Papakostas N, Papachatzakis P, Xanthakis V, Mourtzis D, Chryssolouris G (2010) An approach to operational aircraft maintenance planning. Decis Support Syst 48:604–612

    Article  Google Scholar 

  11. Tomlin B (2006) On the value of mitigation and contingency strategies for managing supply chain disruption risks. Manag Sci 52(5):639–657

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang W (2007) A two-stage prognosis model in condition based maintenance. Eur J Oper Res 182:1177–1187

    Article  MATH  Google Scholar 

  13. Maillart LM, Ivy JS, Ransom S, Diehl K (2008) Assessing dynamic breast cancer screening policies. Oper Res 56:1411–1427

    Article  Google Scholar 

  14. Ryu YU, Chandrasekaran R, Jacob V (2004) Prognosis using an isotonic prediction technique. Manag Sci 50:777–785

    Article  Google Scholar 

  15. Derman C, Lieberman GJ, Ross SM (1984) On the use of replacements to extend system life. Oper Res 32:616–627

    Article  MathSciNet  MATH  Google Scholar 

  16. Leemis LM (1987) Variate generation for accelerated life and proportional hazards models. Oper Res 35:892–894

    Article  Google Scholar 

  17. Shen Y, Tang LC, Xie M (2009) A model for upside-down bathtub-shaped mean residual life and its properties. IEEE Trans Reliab 58(3):425–431

    Article  Google Scholar 

  18. Chen Z, Zheng S (2005) Lifetime distribution based degradation analysis. IEEE Trans Reliab 54:3–10

    Article  Google Scholar 

  19. Escobar LA, Meeker WQ (2006) A review of accelerated test models. Stat Sci 21(4):552–577

    Article  MathSciNet  MATH  Google Scholar 

  20. Gebraeel N, Pan J (2008) Prognostic degradation models for computing and updating residual life distributions in a time-varying environment. IEEE Trans Reliab 57(4):539–550

    Article  Google Scholar 

  21. Lu CJ, Meeker WQ (1993) Using degradation measures to estimate a time-to-failure distribution. Technometrics 35(2):161–174

    Article  MathSciNet  MATH  Google Scholar 

  22. Nelson W (1990) Accelerated testing: statistical models, test plans, and data analysis. Wiley, New York

    Book  MATH  Google Scholar 

  23. Wang X, Xu D (2010) An inverse Gaussian process model for degradation data. Technometrics 52(2):188–197

    Article  MathSciNet  Google Scholar 

  24. Singpurwalla ND (1995) Survival in dynamic environments. Stat Sci 10(1):86–103

    Article  MATH  Google Scholar 

  25. Cox DR (1999) Some remarks on failure-times, surrogate markers, degradation, wear, and the quality of life. Lifetime Data Anal 5:307–314

    Article  MathSciNet  MATH  Google Scholar 

  26. Aalen OO, Gjessing HK (2001) Understanding the shape of the hazard rate: a process point of view (with discussion). Stat Sci 16(1):1–22

    MATH  Google Scholar 

  27. Lee M-LT, Whitmore GA (2006) Threshold regression for survival analysis: modeling event times by a stochastic process reaching a boundary. Stat Sci 21(4):501–513

    Article  MathSciNet  MATH  Google Scholar 

  28. Karlin S, Taylor HM (1981) A second course in stochastic processes. Academic press, California

    MATH  Google Scholar 

  29. Lefebvre M, Aoudia DA (2011) Two-dimensional diffusion processes as models in lifetime studies. Int J Syst Sci. doi:10.1080/00207721.2011.563870

  30. Chhikara RS, Folks JL (1977) The inverse Gaussian distribution as a lifetime model. Technometrics 19(4):461–468

    Article  MATH  Google Scholar 

  31. Gebraeel N, Lawley MA, Li R, Ryan JK (2005) Residual-life distributions from component degradation signals: a Bayesian approach. IIE Trans 37:543–557

    Article  Google Scholar 

  32. Park C, Padgett WJ (2005) Accelerated degradation models for failure based on geometric Brownian motion and gamma processes. Lifetime Data Anal 11(4):511–527

    Article  MathSciNet  MATH  Google Scholar 

  33. Doksum KA, Hoyland A (1992) Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics 34(1):74–82

    Article  MathSciNet  MATH  Google Scholar 

  34. Wang X (2010) Wiener processes with random effects for degradation data. J Multivar Anal 101(2):340–351

    Article  MathSciNet  MATH  Google Scholar 

  35. Whitmore GA, Schenkelberg F (1997) Modeling accelerated degradation data using Wiener diffusion with a time scale transformation. Lifetime Data Anal 3:27–45

    Article  MATH  Google Scholar 

  36. Cox DR, Miller HD (1965) The theory of stochastic processes. Methuen and Company, London

    MATH  Google Scholar 

  37. Buonocore A, Caputo L, Pirpzzi E, Ricciardi LM (2011) The first passage time problem for Gauss-diffusion processes: algorithmic approaches and applications to LIF neuronal model. Methodol Comput Appl Prob 13(1):29–57

    Article  MathSciNet  MATH  Google Scholar 

  38. Mehr CB, McFadden JA (1965) Certain property of Gaussian processes and their first-passage times. J R Stat Soc Ser B 27:505–522

    MATH  Google Scholar 

  39. Nardo ED, Nobile AG, Pirozzi E, Ricciardi LM (2001) A computational approach to first-passage-time problems for Gauss-Markov processes. Adv Appl Prob 33:453–482

    Article  MathSciNet  MATH  Google Scholar 

  40. Ricciardi LM (1976) On the transformation of diffusion processes into the Wiener process. J Math Anal Appl 54:185–199

    Article  MathSciNet  MATH  Google Scholar 

  41. Heng A, Zhang S, Tan CC, Mathew J (2009) Rotating machinery prognostics: state of the art, challenges and opportunities. Mech Syst Signal Process 23:724–739

    Article  Google Scholar 

  42. Si XS, Wang W, Hu CH, Zhou DH (2011) Remaining useful life estimation-A review on the statistical data driven approaches. Eur J Oper Res 213(1):1–14

    Article  MathSciNet  Google Scholar 

  43. Bondesson L (1979) A general result on infinite divisibility. Ann Prob 7(6):965–979

    Article  MathSciNet  MATH  Google Scholar 

  44. Tseng ST, Tang J, Ku LH (2003) Determination of optimal burn-in parameters and residual life for highly reliable products. Naval Res Logist 50:1–14

    Article  MathSciNet  MATH  Google Scholar 

  45. Tseng ST, Peng CY (2004) Optimal burn-in policy by using an integrated Wiener process. IIE Trans 36:1161–1170

    Article  Google Scholar 

  46. Lee MY, Tang J (2007) A modified EM-algorithm for estimating the parameters of inverse Gaussian distribution based on time-censored Wiener degradation data. Statistica Sinica 17:873–893

    MathSciNet  MATH  Google Scholar 

  47. Tang J, Su TS (2008) Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model. Naval Logist Res 55:265–276

    Article  MathSciNet  MATH  Google Scholar 

  48. Padgett WJ, Tomlinson MA (2004) Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Anal 10:191–206

    Article  MathSciNet  MATH  Google Scholar 

  49. Park C, Padgett WJ (2005) New cumulative damage models for failure using stochastic processes as initial damage. IEEE Trans Reliab 54(3):530–540

    Article  Google Scholar 

  50. Park C, Padgett WJ (2006) Stochastic degradation models with several accelerating variables. IEEE Trans Reliab 55(2):379–390

    Article  Google Scholar 

  51. Joseph VR, Yu IT (2006) Reliability improvement experiments with degradation data. IEEE Trans Reliab 55(1):149–157

    Article  Google Scholar 

  52. Balka J, Desmond AF, McNicholas PD (2009) Review and implementation of cure models based on first hitting times for Wiener processes. Lifetime Data Anal 15:147–176

    Article  MathSciNet  MATH  Google Scholar 

  53. Peng CY, Tseng ST (2009) Mis-specification analysis of linear degradation models. IEEE Trans Reliab 58(3):444–455

    Article  Google Scholar 

  54. Wang W, Carr M, Xu W, Kobbacy AKH (2011) A model for residual life prediction based on Brownian motion with an adaptive drift. Microelectron Reliab 51(2):285–293

    Article  Google Scholar 

  55. Tseng ST, Peng CY (2007) Stochastic diffusion modeling of degradation data. J Data Sci 5:315–333

    Google Scholar 

  56. Si XS, Hu CH, Yang JB, Zhou ZJ (2011) A new prediction model based on belief rule base for system’s behavior prediction. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2011.2130527

  57. Woodman OJ (2007) An introduction to inertial navigation, Technical report, Published by the University of Cambridge Computer Laboratory, http://www.cl.cam.ac.uk/techreport/

  58. Kharoufeh JP, Cox SM (2005) Stochastic models for degradation-based reliability. IIE Trans 37:533–542

    Article  Google Scholar 

  59. Kloeden P, Platen E (1995) Numerical solution of stochastic differential equations. Springer, New York

    MATH  Google Scholar 

  60. Park JI, Bae SJ (2010) Direct prediction methods on lifetime distribution of organic light-emitting diodes from accelerated degradation tests. IEEE Trans Reliab 59(1):74–90

    Article  Google Scholar 

  61. Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New York

    Google Scholar 

  62. Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data. Wiley, New York

    Book  MATH  Google Scholar 

  63. Durbin J (1985) The first-passage density of a continuous Gaussian process to a general boundary. J Appl Prob 22:99–122

    Article  MathSciNet  MATH  Google Scholar 

  64. Barker CT, Newby MJ (2009) Optimal non-periodic inspection for a multivariate degradation model. Reliab Eng Syst Safety 94:33–43

    Article  Google Scholar 

  65. Oakland JS (2008) Stat Process Control, 6th edn. Butterworth-Heinemann, Woburn

    Google Scholar 

  66. Taylor AE (1952) L’Hospital’s rule. Am Math Mon 59(1):20–24

    Article  MathSciNet  MATH  Google Scholar 

  67. Lagarias JC, Reeds JA, Wright MH, Wright PE (1998) Convergence properties of the nelder-mead simplex method in low dimensions. SIAM J Optim 9(1):112–147

    Article  MathSciNet  MATH  Google Scholar 

  68. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–722

    Article  MathSciNet  MATH  Google Scholar 

  69. Wilk MB, Gnanadesikan R (1968) Probability plotting methods for the analysis data. Biometrika 55(1):1–17

    Google Scholar 

  70. Beskos A, Papaspiliopoulos O, Roberts GO, Fearnhead P (2006) Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes. J R Stat Assoc Ser B 68(3):333–382

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiao-Sheng Si .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 National Defense Industry Press and Springer-Verlag GmbH Germany

About this chapter

Cite this chapter

Si, XS., Zhang, ZX., Hu, CH. (2017). RUL Estimation Based on a Nonlinear Diffusion Degradation Process. In: Data-Driven Remaining Useful Life Prognosis Techniques. Springer Series in Reliability Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54030-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-54030-5_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-54028-2

  • Online ISBN: 978-3-662-54030-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics