Fatigue is likely the leading cause of failure of military hardware in the field. Thus it is extremely important for DoD to develop a better understanding of the sources of fatigue, to control the rate of fatigue, and to measure and predict fatigue in deployed hardware. Therefore, a high priority at the workshop was a session on the evolution and current status of statistical work in fatigue modeling.

The field of fatigue modeling lies at the interface of the disciplines of statistics and materials science, and success stories in this field invariably involve close collaboration between both disciplines. Materials scientists understand the structure and properties of the relevant materials while statisticians can model the behavior of these materials and analyze experimental or observational data that help refine these models. The products of this collaboration form the basis for replacement and repair policies for fatigue-prone systems and for the general management of hardware subject to fatigue. It is important to pursue efforts to enhance the statistics/materials science collaboration.

The Saunders Paper

Sam Saunders provided a historical perspective on fatigue modeling. Attention to this problem stems from analysis of the Comet, a post–World War II commercial jet aircraft. In the mid-1960s, around two dozen separate deterministic fatigue decision rules had been published, but none of them was very successful. The most accurate on average was found to be Miner’s rule: that the damage after n service cycles at a stress level that produces an expected lifetime of N cycles is proportional to n/N. Subsequently, it was proven that Miner’s rule made use of (apparently unknowingly) the expected value for fatigue life assuming that damage increments were generated from a specific class of distribution functions. However, the distribution of fatigue life about its expectation was either not considered or ignored.

A useful stochastic approach to the problem of fatigue modeling was provided by the development and application of the inverse Gaussian distribution (see, e.g., Folks and Chhikara, 1989). (The Birnbaum-Saunders distribution was developed first, but it is a close approximation to the inverse Gaussian distribution, which is easier to work with analytically.) Some

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