Accelerated Event Times with Multiple Thresholds

Abstract

In some systems lowering any one of several stress variables limits the extent to which the others are able to accelerate random event times. That is, each stress variable can cap acceleration of the time to failure distribution, independent of the others. For example, repeated electrostatic shocks will set off a high-explosive detonator within the first few attempts only if voltage and energy are both sufficiently large. This article presents a class of time-to-event models with soft thresholds on multiple stressors. These models are fit to data obtained from an experiment performed at Los Alamos National Laboratory to estimate probabilities that detonators will fire from accidental electrostatic discharge. The models include a limited failure component to account for the possibility that a fraction of units is completely unable to produce the event of interest regardless of how long one waits or how many trials are attempted.

Keywords:

• Accelerated stress model
• Limited failure population
• Sensitivity testing
• Tail quantiles

Supplementary Materials

We have provided supplementary material that gives details on the reparameterization of the extended generalized gamma family of distributions, the relationships between the natural and stable parameters, the detonator test dataset, and code for replicating much of our analysis.

Acknowledgments

We thank Michael Hamada for helpful comments and C.C. Essix for her encouragement and support.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

This work was funded by the Enhanced Surveillance Campaign (C8) at Los Alamos National Laboratory.