Analysis of strength distributions of multi-modal failures using the EM algorithm

Journal of Statistical Computation and Simulation

Volumn 76, Issue 7, 2006, Pages 619-636

  Park, Chanseok ^a   Padgett, W J ^a,b  

^a CLEMSON UNIVERSITY   (United States)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Censoring; Competing risks; EM algorithm; Inverse gaussian (Wald); Likelihood function; Lognormal; Masking; Missing data; MLE; Weibull

Indexed keywords

EID: 77951583195     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/10629360500108970     Document Type: Article

References (38)

1. Johnson, J.W. and Thorne, D.J., 1969, Effect of internal polymer flaws on strength of carbon fibres prepared from an acrylic precursor. Carbon, 7, 659-660.
2. Jones, B.F. and Wilkins, J.S., 1972, A technique for the analysis of fracture strength data for carbon fibres. Fibre Science and Technology, 5, 315-320.
3. Layden, G.K., 1973, Fracture behaviour of boron filaments. Journal of Materials Science, 8, 1581-1589.
4. Boggio, J.V. and Vingsbo, O., 1976, Tensile strength and crack nucleation in boron fibres. Journal of Materials Science, 11, 273-282.
5. Beetz, C.P., 1982, The analysis of carbon fibre strength distributions exhibiting multiple modes of failure. Fibre Science Technology, 16, 45-59.
6. Martineau, P., Lahaye, M., Pailler, R., Naslain, R., Couzi, M. and Cruege, F., 1984, SiC filament/titanium matrix composites regraded as model composites: Part 1 filament micro-analysis and strength characterization. Journal of Materials Science, 19, 2731-2748.
7. Simon, G. and Bunsell, A.R., 1984, Mechanical and structural characterization of the nicalon silicon carbide fibre. Journal of Materials Science, 19, 3649-3657.
8. Chi, Z., Chou, T.-W. and Shen, G., 1984, Determination of single fibre strength distribution from fibre bundle testings. Journal of Materials Science, 19, 3319-3324.
9. Goda, K. and Fukunaga, H., 1986, The evaluation of the strength distribution of silicon carbide and alumina fibres by a multi-modalWeibull distribution. Journal of Materials Science, 21, 4475-4480.
10. Wagner, D.H., 1989, Stochastic concepts in the study of size effects in the mechanical strength of highly oriented polymeric materials. Journal of Polymer Science, B-27, 115-148.
11. Stoner, E.G., Edie, D.D. and Durham, S.D., 1994, An end-effect model for the single-filament tensile test. Journal of Materials Science, 29, 6561-6574.
12. Meeker, W.Q. and Escobar, L.A., 1998, Statistical Methods for Reliability Data (NewYork: JohnWiley&Sons).
13. Taylor, H.M., 1994, The Poisson-Weibull flaw model for brittle fiber strength. In: J. Galambos, J. Lechner and E. Simiu (Eds) Extreme Value Theory (Amsterdam: Kluwer), pp. 43-59.
14. Phoenix, S.L. and Sexsmith, R.G., 1972, Clamp effects in fiber testing. Journal of Composite Materials, 29, 1873-1884.
15. Padgett, W.J., Durham, S.D., and Mason, A.M., 1995, Weibull analysis of the strength of carbon fibers using linear and power law models for the length effect. Journal of Composite Materials, 29, 1873-1884.
16. Durham, S.D. and Padgett, W.J., 1997, A cumulative damage model for system failure with application to carbon fibers and composites. Technometrics, 39, 34-44.
17. Moeshberger, M.L. and David, H.A., 1971, Life tests under competing causes of failure and the theory of competing risks. Biometrics, 27, 909-933.
18. Cox, D.R., 1959, The analysis of exponentially distributed lifetimes with two types of failures. Journal of the Royal Statistical Society B, 21, 411-421.
19. Herman, R.J. and Patell, R.K.N., 1971, Maximum likelihood estimation for multi-risk model. Technometrics, 13, 385-396.
20. Miyakawa, M., 1984, Analysis of incomplete data in competing risks model. IEEE Transactions on Reliability, 33, 293-296.
21. Usher, J.S. and Hodgson, T.J., 1988, Maximum likelihood analysis of component reliability using masked system life-test data. IEEE Transactions on Reliability, 37, 550-555.
22. Usher, J.S. and Guess, F.M., 1989, An iterative approach for estimating component reliability from masked system life data. Quality and Reliability Engineering International, 5, 257-261.
23. Guess, F.M., Usher, J.S., and Hodgson, T.J., 1991, Estimating system and component reliabilities under partial information of the cause of failure. Journal of Statistical Planning and Inference, 29, 75-85.
24. Reiser, B., Guttman, I., Lin, D.K.J., Guess, F.M. and Usher, H.S., 1995, Bayesian inference for masked system lifetime data. Applied Statistics, 44, 79-90.
25. Kundu, D. and Basu, S., 2000, Analysis of incomplete data in presence of competing risks. Journal of Statistical Planning and Inference, 87, 221-239.
26. Ishioka, T. and Nonaka, Y., 1991, Maximum likelihood estimation of Weibull parameters for two independent competing risks. IEEE Transactions on Reliability, 40, 71-74.
27. Park, C. and Kulasekera, K.B., 2004, Parametric inference of incomplete data with competing risks among several groups. IEEE Transactions on Reliability, 53, 11-21.
28. Albert, J.R.G. and Baxter, L.A., 1995, Applications of the EM algorithm to the analysis of life length data. Applied Statistics, 44, 323-341.
29. Park, C., 2005, Parameter estimation of incomplete data in competing risks using the EM algorithm. IEEE Transactions on Reliability, in press.
30. Park, C. and Padgett, W.J., 2004, Analysis of strength distributions of multi-modal failures using the EM algorithm. Technical Report no. 220, Department of Statistics, University of South Carolina.
31. R Development Core Team, 2004, R: A language and environment for statistical computing (Vienna, Austria: R Foundation for Statistical Computing) (ISBN 3-900051-07-0).
32. Blom, G., 1958, Statistical Estimates and Transformed Beta Variates (NewYork:Wiley).
33. Wilk, M.B. and Gnanadesikan, R., 1968, Probability plotting methods for the analysis of data. Biometrika, 55, 1-17.
34. Kaplan, E.L. and Meier, P., 1958, Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481.
35. Aalen, O.O., 1978, Nonparametric estimation of partial transition probabilities in multiple decrement models. Annals of Statistics, 6, 534-545.
36. Harwell, M., 1995, Microbond tests for ribbon fibers. MS thesis, Clemson University.
37. Kuhn, J.W. and Padgett, W.J., 1997, Local bandwidth selection fro kernel density estimation from right-censored data based on asymptotic mean absolute error. Nonlinear Analysis, Theory, Methods and Applications, 30, 4375-4384.
38. Farnum, N.R. and Booth, P., 1997, Uniqueness of maximum likelihood estimators of the 2-parameter Weibull distribution. IEEE Transactions on Reliability, 46, 523-525.