Accelerated test models with the inverse Gaussian distribution

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Abstract A general family of three-parameter inverse Gaussian-type distributions is formulated which includes several models for the strength of general systems based on cumulative damage arguments. The models incorporate system size (or the “size effect”) as a known “acceleration” variable, so the family can be considered as inverse Gaussian accelerated test distributions. Some asymptotic inferential results for this family are developed and several special cases are considered. The results are illustrated and five specific models are compared based on their fits to carbon fiber tensile strength data.