Characteristics of Birnbaum and Saunders model

Fatigue failure occurs when some dominant crack or cracks in a component extend to a critical level under the application of cyclic loading. By using the theory of stochastic processes Birnbaum and Saunders proposed a probability model to characterize the time (i.e., the number of cycles) required to propagate a fatigue crack past a critical value. The model is phenomenologically quite sound and provides a probabilistic interpretation of Miner's rule. In statistical literature a thorough treatment of the model is missing. For example, no work has been reported about the renewal and related functions of this model. This paper presents: (i) a summary of some known characteristics of the model; (ii) parameter estimation methods, and K-S test statistics for the model validation; (iii) the nature of hazard function in terms of the coefficient of life variation; (iv) the renewal function, renewal rate function and variance of number of renewals in graphical form; and (v) a comparison of a typical set of various functions.