Accelerated test models using the inverse Gaussian distribution

In this dissertation, a general family of three-parameter inverse Gaussian-type distributions is formulated. These include several models for the strength of general systems based on discrete cumulative damage arguments. The models incorporate system size as a known "acceleration" variable, so the family can be considered as inverse Gaussian accelerated test distributions. Some asymptotic inferential results for the general three-parameter family of distributions 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.;The important problem of choosing levels of the acceleration variable for performing accelerated testing is investigated for the models mentioned above. Motivated by the power-law exponential model, a "locally penalized" D-optimal design criterion is proposed as an approach to determine "nearly-optimal" levels of the acceleration variable for future experimental testing. Illustrations of the approach are presented once again by using carbon fiber tensile strength data where the fiber length is the "acceleration variable.";Some Bayesian inferential results are also obtained through the marginal posterior distributions of the acceleration parameters and the model parameters, where different types of non-informative priors are considered. The necessary integrals for these marginal posterior distributions, which are intractable, are approximated using the Laplace approximation procedure. The same carbon fiber data was used for illustrations.;Finally, some preliminary results are obtained using a continuous cumulative damage model, which lead to several additional three-parameter inverse Gaussian-type models that incorporate the "size" of the system as the acceleration variable. Several different parametric acceleration models are considered and compared in terms of their fits to the carbon fiber data.