Inferences for the Fatigue Life Model Based on the Birnbaum–Saunders Distribution

References

• Achcar , J. A. 1993 . Inferences for the Birnbaum–Saunders fatigue life model using bayesian methods . Computational Statistics and Data Analysis , 15 ( 15 ) : 367 – 380 .
   Google Scholar
• Balakrishnan , N. and Aggarwala , R. 2000 . “ Progressive Censoring:Theory ” . In Methods and Applications Boston : Birkhauser .
   Google Scholar
• Barndorff-Nielsen , O. E. and Cox , D. R. 1994 . Inference and Asymptotics London : Chapman & Hall .
   Google Scholar
• Bhattacharyya , G. K. and Fries , A. 1980 . Fatigue failure models—Birnbaum–Saunders vs. inverse Gaussian . IEEE Transactions on Reliability , 31 : 439 – 440 .
   Google Scholar
• Birnbaum , Z. W. and Saunders , S. C. 1969 . A new family of life distribution . Journal of Applied Probability , 6 : 319 – 327 .
   Google Scholar
• Chang , D. S. and Tang , L. C. 1993 . Reliability bounds and critical time for the Birnbaum–Saunders distribution . IEEE Transactions on Reliability , 42 ( 3 ) : 464 – 469 .
   Google Scholar
• Chang , D. S. and Tang , L. C. 1994 . Percentile bounds and tolerance limits for the Birnbaum–Saunders distribution . Communications in Statistics, Part A Theory and Methods , 23 ( 10 ) : 2853 – 2863 .
   Google Scholar
• Davison , A. C. and Hinkley , D. V. 1997 . Bootstrap Methods and Their Applications . Cambridge. ,
   Google Scholar
• Desmond , A. F. 1986 . On the relationship between two fatigue-life models . IEEE Transactions on Reliability , 35 : 167 – 169 .
   Google Scholar
• Desmond , A. F. and Yang , Z. 1995 . Shortest prediction intervals for the Birnbaum–Saunders distribution . Communication in Statistics, Part A Theory and Methods , 24 ( 6 ) : 1383 – 1401 .
   Google Scholar
• Doganaksoy , N. 1995 . “ Likelihood ratio confidence intervals in life-data analysis ” . In Chapter 20 of Recent Advances in Life-Testing and Reliability Edited by: Balakrishnan , N. Boca Raton : CRC Press .
   Google Scholar
• Doganaksoy , N. and Schmee , J. 1993 . Comparisons of approximate confidence intervals for distributions used in life-data analysis . Technometrics , 35 : 175 – 184 .
   Google Scholar
• Efron , B. 1982 . The Jackknife, the Bootstrap and Other Resampling Plans . Philadelphia: Society for Industrial and Applied Mathematical ,
   Google Scholar
• Efron , B. 1987 . Better bootstrap confidence intervals (with discussion) . Journal of the American Statistical Association , 82 : 171 – 200 .
   Google Scholar
• Efron , B. and Tibshirani , R. J. 1993 . An Introduction to the Bootstrap New York : Chapman & Hall. .
   Google Scholar
• Engelhardt , M. , Bain , L. J. and Wright , F. T. 1981 . Inference on the parameters of the Birnbaum–Saunders fatigue life distribution based on maximum likelihood estimation . Technometrics , 23 ( 3 ) : 251 – 256 .
   Google Scholar
• Hall , P. 1992 . The Bootstrap and Edgeworth Expansion New York : Springer-Verlag .
   Google Scholar
• Jeng , S. L. and Meeker , W. Q. 2000 . Comparisons of approximate confidence intervals for Type I censored data . Technometrics , 42 ( 2 ) : 135 – 148 .
   Google Scholar
• Jeng , S. L. and Meeker , W. Q. 2002 . Bootstrap Likelihood Ratio Statistics Department of Statistics Iowa State University . Preprint
   Google Scholar
• McCarter , K. C. 1999 . “ Estimation and prediction for the Birnbaum–Saunders distribution using Type-II censored samples, with a comparison to the inverse Gaussian distribution ” . Kansas State University . Ph.D. dissertation
   Google Scholar
• Meeker , W. Q. and Escobar , L. A. 1998 . Statistical Methods for Reliability Data New York : John Wiley and Sons Inc. .
   Google Scholar
• Nelson , W. 1982 . Applied Life Data Analysis New York : John Wiley & Sons .
   Google Scholar
• Ostrouchov , G. and Meeker , W. Q. Jr. 1988 . Accuracy of approximate confidence bounds computed from interval censored Weibull and lognormal data . Journal of Statistical Computation and Simulation , 29 : 43 – 76 .
   Google Scholar
• Owen , W. J. and Padgett , W. J. 1999 . Accelerated test models for system strength based on Birnbaum–Saunders distributions . Lifetime Data Analysis , 5 : 133 – 147 .
   Google Scholar
• Owen , W. J. and Padgett , W. J. 2000 . A Birnbaum–Saunders accelerated life model . IEEE Transactions on Reliability , 49 ( 2 ) : 224 – 229 .
   Google Scholar
• Piegorsch , W. W. 1987 . Performance of likelihood-based interval estimates for two-parameter exponential samples subject to Type I censoring . Technometrics , 29 : 41 – 49 .
   Google Scholar
• Raaijmakers , F.J. M. 1980 . The life time of standby system of units having the Birnbaum–Saunders distribution . Journal of Applied Statistics , 17 : 490 – 497 .
   Google Scholar
• Rieck , J. R. and Nedelman , J. R. 1991 . A log-linear model for the Birnbaum–Saunders distribution . Technometrics , 33 ( 1 ) : 51 – 60 .
   Google Scholar
• Serfling , R. J. 1980 . Approximation Theorems of Mathematical Statistics New York : John Wiley & Sons. .
   Google Scholar
• Shao , J. and Tu , D. 1995 . The Jackknife and Bootstrap New York : Springer-Verlag .
   Google Scholar
• Smith , R. L. 1991 . Weibull regression models for reliability data . Reliability Engineering and System Safety , 34 : 55 – 77 .
   Google Scholar
• Vander Wiel , S. A. and Meeker , W. Q. 1990 . Accuracy of approximate confidence bounds using censored Weibull regression data from accelerated life tests . IEEE Transactions on Reliability , R-39 : 346 – 351 .
   Google Scholar
• Volodin , I. N. and Dzhungurova , O. A. 2000 . On limit distribution emerging in the generalized Birnbaum–Saunders model . Journal of Mathematical Sciences , 99 ( 3 ) : 1348 – 1366 .
   Google Scholar