A geometric Brownian motion model for field degradation data

International Journal of Materials and Product Technology

Volumn 20, Issue 1-3, 2003, Pages 51-72

  Elsayed, E A ^a   Liao, H T ^a  

^a DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING   (United States)

Author keywords

Brownian motion; Degradation model; Field data; Reliability estimation

Indexed keywords

CIVIL ENGINEERING; DEGRADATION; FAILURE (MECHANICAL); MATERIALS TESTING; MATHEMATICAL MODELS; PARAMETER ESTIMATION; RELIABILITY; STRESSES;

ACCELERATED LIFE TESTING; CIVIL ENGINEERING STRUCTURE; FIELD DATA; GEOMETRIC BROWNIAN MOTION DEGRADATION RATE MODEL;

BROWNIAN MOVEMENT;

EID: 1542753870     PISSN: 02681900     EISSN: None     Source Type: Journal    
DOI: 10.1504/ijmpt.2004.003912     Document Type: Article

References (21)

1. Crk, V. (2000) 'Reliability assessment from degradation data', Proceedings Annual Reliability and Maintainability Symposium, pp. 155-161.
2. Eghbali, G. (2000) Reliability Estimate Using Accelerated Degradation Data, Ph.D. Thesis No. 17, Department of Industrial Engineering, Rutgers University, January.
3. Eghbali, G. and Elsayed, E.A. (2001) 'Reliability estimate using degradation data', in Mastorakis, N.E. and Pecorelli-Peres, L.A. (Eds.): Advances in Systems Science: Measurement, Circuits and Control, Electrical and Computer Engineering Series, WSES Press, pp.425-430.
4. Elsayed, E.A. (1996) Reliability Engineering, Addison Wesley Longman Inc.
5. Lu, J.C. and Meeker, W.Q. (1993) 'Using degradation measures to estimate a time-to-failure distribution', Technometrics, Vol. 35, No. 2, May pp. 161-174.
6. Meeker, W.Q., Escobar, L.A. and Lu, J.C. (1998) 'Accelerated degradation tests: modelling and analysis', Technometrics, Vol. 40, No. 2, May pp.89-99.
7. Shiau, J.J.H. and Lin, H.H. (1999) 'Analysing accelerated degradation data by nonparametric regression', IEEE Transaction on Reliability, Vol. 48, No. 2, June pp. 149-158.
8. Yang, K. and Xue, J. (1996) 'Continuous state reliability analysis', Proceedings of the Annual Reliability and Maintainability Symposium 1996, IEEE, Piscataway, NJ, USA, pp. 251-257.
9. Faragher, E.B., Chantler, E.N. and Roberts, C.T. (1985) 'A statistical evaluation of the rate of degradation of copper releasing IUCDs', Statistician, Royal Statistical Society, Vol. 34, No. 2, pp.243-248.
10. Jorgensen, G.J., Kim, H.M. and Wendelin, T.J. (1996) 'Durability studies of solar reflector materials exposed to environment stresses', in Herling, R.J. (Ed.): Durability Testing of Nonmetallic Materials, ASTM STP 1294, American Society for Testing and Materials.
11. Elsayed, E.A. (1997) Reliability Prediction Based on Degradation Data, INFORMS, Dallas.
12. Sheldon, M.R. (1997) Introduction to Probability Models, 6th ed., Academic Press, pp.524-526.
13. Doksum, K.A. and Hóyland, A. (1992) 'Models for variable-stress accelerated life testing experiments based on Wiener process and the inverse Gaussian distribution', Technometrics, Vol. 34, No. 1, pp. 74-82.
14. Lu, Y.I. and Storer, B. (2001) 'A tampered Brownian motion process model for partial step-stress accelerated life testing', Journal of Statistical Planning and Inference, Vol. 94, pp.15-24.
15. Pieper, V., Domine, M. and Kurth, P. (1997) 'Level crossing problem and drift reliability', Mathematical Methods of Operations Research, Vol. 45, pp.347-354.
16. Bhattacharyya, G.K. and Fries, A. (1982) 'Fatigue-failure models - Birnbaum-Saunders vs. inverse Gaussian', IEEE Transaction on Reliability, Vol. R-31, pp.439-440.
17. Dufresne, D. (2001) 'The integral of geometric Brownian motion', Advanced Applied Probability, Vol. 33, pp.223-241.
18. Yor, M. (1992) 'On some exponential function of Brownian motion', Advanced Applied Probability, Vol. 24, pp.509-531.
19. Bosq, D. (1998) Nonparametric Statistics for Stochastic Processes - Estimation and Prediction, 2nd ed., Springer-Verlag Inc., New York, pp.170-172.
20. Kotelnikov, V.A. (1959) The Theory of Optimum Noise Immunity, McGraw-Hill, New York.
21. Ettouney, M. and Elsayed, E.A. (1999) 'Reliability estimation of degraded structural components subject to corrosion', Proceedings 5th ISSAT International Conference on Reliability and Quality in Design, August 11-13, Las Vegas, Nevada, pp.291-295.