A birnbaum-saunders accelerated life model

IEEE Transactions on Reliability

Volumn 49, Issue 2, 2000, Pages 224-229

  Owen, W Jason ^a   Padgett, William J ^b  

^a Univ of New Hampshire   (United States)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

Cycles to failure, fatigue life, laplace method, maximum likelihood, percentile estimation

Indexed keywords

FATIGUE OF MATERIALS; FATIGUE TESTING; INFERENCE ENGINES; LAPLACE TRANSFORMS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; SERVICE LIFE;

ASYMPTOTIC STANDARD DEVIATION; BIRNBAUM-SAUNDERS DISTRIBUTION; FISHER INFORMATION MATRIX; GENERAL LINEAR MODEL; LOMER S-CONFIDENCE BOUNDS; MEAN TIME TO FAILURE; PERCENTILE ESTIMATION;

PROBABILITY DISTRIBUTIONS;

EID: 0034197743     PISSN: 00189529     EISSN: None     Source Type: Journal    
DOI: 10.1109/24.877342     Document Type: Article

References (24)

1. S. D. Durham and W. J. Padgett, "A cumulative damage model for system failure with application to carbon fibers and composites," Technometrics, vol. 39, pp. 34-44, Feb. 1997.
2. S. D. Durham, J. D. Lynch, and W. J. Padgett, et al., "Localized loadsharing rules and Markov-Weibull fibers: A comparison of microcomposite data with Monte Carlo simulations," J. Composite Materials, vol. 31, pp. 1856-1882, Sep. 1997.
3. S. D. Durham and W. J. Padgett, "A probabilistic stress-strength model and its application to fatigue failure in gun barrels," J. Statistical Planning and Inference, vol. 29, pp. 67-74, Sep./Oct. 1991.
4. W. J. Owen and W. J. Padgett, "Birnbaum-Saunders-type models for system strength assuming multiplicative damage," in Frontiers in Reliability Analysis, A. P. Basu, Ed: Indian Assoc. for Productivity, Quality and Reliability, World Scientific, 1998.
5. Z. W. Birnbaum and S. C. Saunders, "Estimation for a family of life distributions with applications to fatigue," J. Applied Probability, vol. 6, pp. 328-347, 1969.
6. N. R. Mann, R. E. Schafer, and N. D. Singpurwalla, Methods for Statistical Analysis of Reliability and Life Data: John Wiley & Sons, 1974.
7. W. J. Padgett, S. D. Durham, and A. M. Mason, "Weibull analysis of the strength of carbon fibers using linear and power law models for the length effect," J. Composite Materials, vol. 29, pp. 1873-1884, Oct. 1995.
8. Z. W. Birnbaum and S. C. Saunders, "A new family of life distributions," J. Applied Probability, vol. 6, pp. 319-327, 1969.
9. S. C. Saunders, "A family of random variables closed under reciprocation," J. American Statistical Assoc., vol. 69, pp. 533-539, Jun. 1974.
10. A. F. Desmond, "Stochastic models of failure in random environments," Canadian J. Statistics, vol. 13, pp. 171-183, Sep. 1985.
11. A. F. Desmond, "On the relationship between two fatigue-life models," IEEE Trans. Reliability, vol. R-35, pp. 167-169, Jun. 1986.
12. W. J. Owen and W. J. Padgett, "Acceleration models for system strength based on Birnbaum-Saunders distributions," Lifetime Data Analysis, vol. 5, pp. 133-147, Jun. 1999.
13. M. Engelhardt, L. J. Bain, and F. T. Wright, "Inferences on the parameters of the Birnbaum-Saunders fatigue life distribution based on maximum likelihood estimation," Technometrics, vol. 23, pp. 251-256, Aug. 1981.
14. W. J. Padgett, "On Bayes estimation of reliability for the Birnbaum-Saunders fatigue life model," IEEE Trans. Reliability, vol. R-31, pp. 436-438, Dec. 1982.
15. J. A. Achcar, "Inferences for the Birnbaum-Saunders fatigue life model using Bayesian methods," Computational Statistics and Data Analysis, vol. 15, pp. 367-380, 1993.
16. L. Tierney, R. E. Kass, and J. B. Kadane, "Fully exponential Laplace approximations to expectations and variances of nonpositive functions," J. American Statistical Assoc., vol. 84, pp. 710-716, Sep. 1989.
17. J. R. Rieck and J. R. Nedelman, "A log-linear model for the Birnbaum-Saunders distribution," Technometrics, vol. 33, pp. 51-60, Feb. 1991.
18. J. R. Rieck, "Statistical analysis for the Birnbaum-Saunders fatigue life distribution," Ph.D. dissertation, Dept. of Mathematical Sciences, Clemson University, 1989.
19. B. Efron and D. V. Hinkley, "Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information," Biometrika, vol. 65, pp. 457-482, Aug. 1978.
20. S. F. Arnold, Mathematical Statistics: Prentice Hall, 1990.
21. W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data: John Wiley & Sons, 1998.
22. E. L. Lehmann, Theory of Point Estimation: John Wiley & Sons, 1983.
23. R. E. Kass, L. Tierney, and J. B. Kadane, "The validity of posterior expansions based on Laplace's method," in Essays in Honor of George A. Barnard, J. Hodges, Ed: North-Holland, 1990.
24. Z. W. Birnbaum and S. C. Saunders, "A statistical model for life-length of materials," J. American Statistical Assoc., vol. 53, pp. 151-160, Mar. 1958.