Statistical analysis and reliability prediction with short fatigue crack data

This paper proposes a probability model to describe the growth of short fat igue cracks. The model defines the length of each crack in a specimen as a random quantity, which is a function of randomly varying local properties o f the material microstructure. Once the model has been described, the paper addresses two questions: first, statistical inference, i.e. the fitting of the model parameters to data on crack lengths; and secondly, predicting th e future behaviour of observed cracks or cracks in a new specimen. By defin ing failure of a specimen to be the time at which the largest crack exceeds a certain length, the solution to the prediction problem can be used to ca lculate a probability that the specimen has failed at any future time. The probability model for crack lengths is called a population model, and t he statistical inference uses the ideas of Bayesian statistics. Both these concepts are described. With a population model, the solution to statistica l inference and prediction requires quite complicated Monte Carlo simulatio n techniques, which are also described.