Some Useful Models for Failure Time Under Stochastic Monotonicity : Model Specification and Inference

We propose some useful models for hitting time under stochastic monotonicity assumption. Depending on whether the underlying shock process is governed by a Poisson process or a Brownian motion, on whether each shock has a deterministic impact size or a random impact size, and on whether failure is defined by a threshold crossing or by a hazard rate, we develop various “failure” time models. We then explain how to utilize information contained in the failure time to make inferences on the underlying model parameters which characterizes shock processes and the impact sizes. Real life applications are briefly mentioned.