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.