Joe Padgett and Meredith Tomlinson

Department of Statistics

University of South Carolina

Inference for Accelerated Test Models Based on Gaussian Degradation Processes

Failure of a system under an environmental stress can often be described by an accelerated test model that incorporates the stress variable (or covariate), L. System failure under environmental stress level L can be modeled in general as the first passage of accumulated damage to a critical level. Using a discrete additive damage model leads to accelerated Birnbaum-Saunders-type distributions which can be approximated closely by inverse Gaussian-type models. However, assuming damage is represented continuously as a Gaussian process with positive drift parameter nL (depending on L), directly gives a family of failure time distributions that are inverse Gaussian-type accelerated test models. This approach allows inference about the failure time distribution at environmental stress L based on either observed failures or observed levels of degradation of such systems (before failure), or both. Simulated failure/degradation data from Gaussian processes, as well as real data, are used to illustrate the approach.

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