Failure rate estimation in a dynamic environment

We present a method to assess the reliability of a material operating in a dynamic environment. The dynamic environment is represented as a sequence of shocks governed by a self-exciting point process. The time-to-failure of the material is assumed to have a piecewise exponential distribution. A Cox model is integrated to take into account the effect of the stress. Maximum likelihood estimates of the model parameters are obtained and their properties are studied through simulated data. An application on field data is displayed. Hypothesis testing procedures for environment effect are suggested.