Simulation-Assisted Estimation of Failure Models with Stochastic Hazard Rates

Failure models with stochastic hazard rates provide more realistic and accurate characterization of systems failure behavior under dynamic and heterogeneous working environments. However, incorporation of stochastic hazard rates results in compound distribution involving integration over random variables, which generally does not have closed form solutions. Using Weibull models with gamma-distributed shape parameters as an example, this paper proposes a simulation-assisted method for estimation of failure models with stochastic hazard rates. A simulated log-likelihood function is constructed by approximating the compound failure distribution with statistical sampling. An algorithm based on differential evolution is subsequently developed to implement maximum likelihood estimation through optimization via simulation. The proposed simulation-assisted method has been tested to be accurate in model estimation based on numerical experiments using simulated data.