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.