A New Three-Parameter Extension to the Birnbaum-Saunders Distribution

The Binrbaum-Saunders (B-S) distribution was derived in 1969 as a lifetime model for a specimen subjected to cyclic patterns of stresses and strains, and the ultimate failure of the specimen is assumed to be due to the growth of a dominant crack in the material. The derivation of this model will be revisited, and because the assumption of independence of crack extensions from cycle to cycle can be quite unrealistic, one new model will be derived by relaxing this independence assumption. Here, the sequence of crack extensions is modeled as a long memory process, and characteristics of this development introduces a new third parameter. The model is investigated in detail, and interestingly the original B-S distribution is included as a special case. Inference procedures are also discussed, and an example dataset is used for model comparison

[1]  A. F. Desmond,et al.  On the Relationship between Two Fatigue-Life Models , 1986, IEEE Transactions on Reliability.

[2]  William J. Padgett,et al.  A Birnbaum-Saunders accelerated life model , 2000, IEEE Trans. Reliab..

[3]  Sam C. Saunders,et al.  Estimation for a family of life distributions with applications to fatigue , 1969, Journal of Applied Probability.

[4]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[5]  W. J. Padgett,et al.  Accelerated Test Models for System Strength Based on Birnbaum-Saunders Distributions , 1999, Lifetime data analysis.

[6]  Lee J. Bain,et al.  Inferences on the Parameters of the Birnbaum-Saunders Fatigue Life Distribution Based on Maximum Likelihood Estimation , 1981 .

[7]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[8]  Jorge Alberto Achcar.  Inferences for the Birnbaum-Saunders fatigue life model using Bayesian methods , 1993 .

[9]  Z. Birnbaum,et al.  A new family of life distributions , 1969 .

[10]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[11]  R. Brook,et al.  Cumulative Damage in Fatigue: A Step towards Its Understanding , 1969 .

[12]  Sam C. Saunders.  A Family of Random Variables Closed Under Reciprocation , 1974 .

[13]  D. Dupuis,et al.  Robust estimation of the Birnbaum-Saunders distribution , 1998 .

[14]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[15]  E. Stacy.  A Generalization of the Gamma Distribution , 1962 .

[16]  James R. Rieck,et al.  A log-linear model for the Birnbaum-Saunders distribution , 1991 .

[17]  Arthur Fries,et al.  Fatigue Failure Models ߝ Birnbaum-Saunders vs. Inverse Gaussian , 1982, IEEE Transactions on Reliability.

[18]  A. Desmond.  Stochastic models of failure in random environments , 1985 .