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References
- 1
- Air Accident Investigation Branch (AAIB), UK Department of Environment, Transport and Regions (1996) Bulletin No: 12/96 Ref: EW/G96/10/16 Category: 1.3. Available at http://www.open.gov.uk/aaib/ .
- 2
- Bannantine, J.A., Comer, J.J. and Handrock, J.L. (1990) Fundamentals of Metal fatigue analysis, Englewood Cliffs, New Jersey : Prentice-Hall.
- 3
- Berger, J.O. (1990) ``Robust Bayesian Analysis - Sensitivity to the Prior,'' Journal of Statistical Planning and Inference, 25: (3), pp. 303-328.
- 4
- Beretta, S. and Clerici, P. (1996) ``Microcrack Propagation and Microstructural Parameters of Fatigue Damage,'' Fatigue & Fracture of Engineering Materials & Structures, 19: (9), pp. 1107-1115.
- 5
- Bernardo, J.M., Smith, A.F.M. (1994) Bayesian Theory, Chichester, UK : Wiley.
- 6
- Blom, A.F., Hedlund, A., Zhao, W., Fathulla, A., Weiss, B. and Stickler, R. (1986) ``Short Fatigue Crack Growth Behaviour in Al2024 and Al7475,'' in [32]. pp. 37-66.
- 7
- Brooks, S.P. and Roberts, G.O. (1998) ``Assessing Convergence of Markov Chain Monte Carlo Algorithms,'' Statistics and Computing, 8: (4), pp. 319-335.
- 8
- Brown, M.W. (1986) ``Interfaces Bewtween Short, Long, and Non-Propagating Cracks,'' in [32]. pp. 423-440.
- 9
- Chib, S. and Greenberg, E. (1995) ``Understanding the Metropolis-Hastings Algorithm,'' The American Statistician 49: (4), pp. 327-335.
- 10
- Connor, L.R. and Morell, A.J.H. (1964), Statistics in Theory and Practice, London : Pitman.
- 11
- Cowles, M.K., and Carlin, B.P., (1996) ``Markov Chain Monte-Carlo Convergence Diagnostics: a Comparitive Study,'' Journal of the American Statistical Association, 91, pp. 883-904.
- 12
- Cox, B.N. and Morris, W.L. (1987) ``A Probabilistic Model of Short Fatigue Crack Growth,'' Fatigue and Fracture of Engineering Materials and Structures 10: (5), pp. 419-428.
- 13
- Cox, B.N. and Morris, W.L. (1987) ``Model Based Statistical Analysis of Short Fatigue Crack Growth in Ti6A1-25n-4Zr-6Mo,'' Fatigue and Fracture of Engineering Materials and Structures 10: (6), pp. 429-446.
- 14
- Crandall, S.H. and Mark, W.D. (1963) Random Vibration in Mechanical Systems, New York : Academic Press.
- 15
- Dowling, N.E. (1972) ``Fatigue Failure Predictions for Complicated Stress Strain Histories,'' Journal of Materials, 7: (1), pp. 71-87.
- 16
- French, S. and Smith, J.Q., (1997) The Practice of Bayesian Analysis, London : Arnold.
- 17
- Gao, N., Brown, M.W. and Miller, K.J. (1995) ``Crack Growth Morphology and Microstructural Changes in 316 Stainless Steel Under Creep-Fatigue Cycling,'' Fatigue & Fracture of Engineering Materials & Structures 18: (12), pp. 1407-1421.
- 18
- Gelman, A. and Rubin, D.B. (1992) ``Inference from Iterative Simulation Using Multiple Sequences,'' (with discussion), Statistical Science, 7, pp. 457-511.
- 19
- Hastings, W.K. (1970) ``Monte Carlo Sampling Methods Using Markov Chains and their Applications,'' Biometrika, 57, pp. 97-109.
- 20
- Jarner, S.F. (1999) ``Geometric Ergodicity of Metropolis Algorithms,'' contributed paper at 22nd Research Students Conference in Probability and Statistics, Bristol, U.K.
- 21
- Jeffrey, H. (1961), Theory of Probability, 3rd edition, Oxford: Clarendon Press.
- 22
- Kachanov, L.M. (1986) Introduction to Continuum Damage Mechanics, Netherlands : Martinus-Nijhoff Publishers.
- 23
- Kirkner, D.J., Sobczyk, K. and Spencer, B.F. (1999) ``On the Relationship of the Cumulative Jump Model for Random Fatigue to Empirical Data,'' Probabilistic Engineering Mechanics 14: (3), pp. 257-267.
- 24
- Kitagawa, H. and Takahashi, S. (1976) ``Applicability of Fracture Mechanics to Very Small Cracks or the Cracks in the Early Stage,'' Proc. 2nd Int. Conf. Mech. Behaviour of Materials, Boston.
- 25
- Kleijnen, J.P.C. (1974) Statistical Techniques in Simulation, New York : Marcel Dekker.
- 26
- Lauritzen, S.L. and Spiegelhalter, D.J. (1988) ``Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems,'' Journal of the Royal Statistical Society. Series B (Methodological), 50, pp. 157-224.
- 27
- Lee, P.M. (1997) Bayesian Statistics: An Introduction, 2nd edition, London : Arnold.
- 28
- McCormack, B.A.O. (1997) On Damage Accumulation in Cemented Hip Replacements, PhD Thesis, National University of Ireland : Dublin.
- 29
- McCormack, B.A.O., Walsh, C.D., Wilson, S.P. and Prendergast, P.J. (1998) ``A Statistical Analysis of Microcrack Accumulation in PMMA Under Fatigue Loading: Applications to Orthopaedic Implant Fixation,'' International Journal of Fatigue 20: (8), pp. 581-593.
- 30
- Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) ``Equations of State Calculations by Fast Computing Machines,'' Journal of Chemical Physics, 21, pp. 1087-1092.
- 31
- Miller, K.J., Mohamed, H.J. and de los Rios, E.R. (1986) ``Fatigue Damage Accumulation Above and Below the Fatigue Limit,'' in [32]. pp. 491-512.
- 32
- Miller, K.J. and de los Rios, E.R. (1986) The Behaviour of Short Fatigue Cracks, London : Mechanical Engineering Publications.
- 33
- Mood, A., Graybill, F. and Boes, D. (1963) ``Introduction to the Theory of Statistics,'' New York : McGraw-Hill.
- 34
- Morgenthal, G.W. (1961) ``The Theory and Application of Simulations in Operations Research,'' in Progress in Operations Research eds. Ackoff, R.L., New York : Wiley.
- 35
- Murdoch, D.J. and Green, P.J. (1998) ``Exact Sampling from a Continuous State Space,'' Scandinavian Journal of Statistics, 25:(3), pp. 483-502.
- 36
- Murdoch, D.J. and Rosenthal, J.S. (1998) ``Regeneration Methods and Exact Sampling,'' contributed paper at Sixth Valencia International Meeting on Bayesian Statistics Alcossebre, Spain.
- 37
- O'Hagan, A. (1998) ``Eliciting Expert Beliefs in Substantial Practical Applications,'' Statistician 47: (1), pp. 21-35.
- 38
- O'Hagan, A. (1994) Kendall's Advanced Theory of Statistics Volume 2B, London : Arnold.
- 39
- Plumtree, A. and Schäfer, S. (1986) ``Initiation and Short Crack Behaviour in Aluminium Alloy Castings,'' in [32]. pp. 215-228.
- 40
- Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1996) Numerical Recipes in C - The Art of Scientific Computing, 2nd edition reprint, Cambridge, U.K. : Cambridge University Press.
- 41
- Rice, J.R. (1968) ``A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,'' Journal of Applied Mechanics, Transactions ASME
- 42
- Rice, S.O. (1944) ``Mathematical Analysis of Random Noise,'' Bell Systems Technical Journal, 23, pp. 282-332. 24, pp. 46-156 (1945). Also published (1954) in Selected Papers on Noise and Stochastic processes ed. Wax, N., New York: Dover.
- 43
- Roberts, G.O. and Rosenthal, J. ``Convergence of Slice Sampler Markov Chains,'' Journal of the Royal Statistical Society. Series B (Methodological), 61 : (3), pp. 643-660.
- 44
- Robinson, M. and Crowder, M. (1999) ``Statistical Modelling of Fatigue Crack Growth,'' at Young Statisticians Meeting 1999, Bristol, England. Available at http://www.mcs.surrey.ac.uk/Personal/M.Robinson/Posters/ .
- 45
- Rolfe, S.T. and Barsom, J.M. (1977) Fracture and Fatigue Control in Structures, New Jersey: Prentice Hall.
- 46
- Royal Statistical Society Conference (1997) Practical Bayesian Statistics 4, University of Nottingham, England.
- 47
- Smith, I.F.C. (1986) ``Applying Fatigue Research to Engineering Design,'' in
[32], pp. 15-26.
- 48
- Sobczyk, K. and Trebecki, J. (1991) ``Cumulative Jump Correlated Model for Random Fatigue,'' Engineering Fracture Mechanics, 40: (1), pp. 201-210.
- 49
- Sobczyk, K. and Trebecki, J. (1990) ``Maximum Entropy Principle in Stochastic Dynamics,'' Probabilistic Engineering Mechanics 5: (3), pp. 102-110.
- 50
- Spiegelhalter, D.J., Best, N.G., Gilks, W.R. and Inskip, H. (1995) ``Hepatitis B: a Case Study in MCMC Methods,'' in Markov Chain Monte Carlo in Practice, eds. Gilks, W.R., Richardson, S. and Spiegelhalter, D.J., London : Chapman and Hall. pp. 21-43.
- 51
- Spiegelhalter, D.J., Thomas, A. and Best, N. (1998) WinBUGS 1.1.1 Software Package. See also [52].
- 52
- Spiegelhalter, D.J., Thomas, A., Best, N. and Gilks, W. (1996) BUGS Bayesian inference Using Gibbs Sampling Manual (version ii), http://www.mrc-bsu.cam.ac.uk/bugs/ .
- 53
- Taylor, D., Li, J. and Giese, A. (1995) ``Short Fatigue Crack Growth in Cast Iron Described Using P-a Curves,'' International Journal of Fatigue 17 : (3), pp. 201-206.
- 54
- Tierney, L. (1994) ``Markov Chains for Exploring Posterior Distributions,'' Annals of Statistics, 22: (4), pp. 1701-1728.
- 55
- van Noortwijk, J., Kok, M. and Cooke, R.M. (1997) ``Optimal Decisions that Reduce Flood Damage along the Meuse: an Uncertainty Analysis,'' in [16].
- 56
- Wakefield, J. (1996) ``The Bayesian Analysis of Population Pharmacokinetic Models,'' Journal of the American Statistical Association, 91: (433), pp. 62-75
- 57
- Walsh, C.D. and Wilson, S.P. (1998) ``Reliability Modelling and Inference Through Fatigue Crack Growth,'' in Frontiers in Reliability, eds. Basu, A.P., Basu, S.K. and Mukhopadhyay, S., Singapore : World Scientific Publishing Company. pp. 397-410.
- 58
- Yang, J.N., Salivar, G.C. and Annis, C.G. (1983) ``Statistical Modeling of Fatigue-Crack Growth in a Nickel Based Superalloy,'' Engineering Fracture Mechanics, 18: (2), pp. 257-270.
- 59
- Yushanov, S.P. and Joshi, S.P. (1995) ``Stochastic Modeling of Fracture Processes in Fiber-Reinforced Composites,'' AIAA Journal, 33: (9), pp. 1689-1697.
- 60
- Zhao, Y.X., Gao, Q. and Wang, J.N. (1999) ``Interaction and Evolution of Short Fatigue Cracks,'' Fatigue & Fracture of Engineering Materials & Structures 22: (6), pp. 459-467.
Cathal Walsh
Sat Jan 22 17:09:53 GMT 2000