The Hybrid Warranty for Heterogeneous Population Subject to Dependent Competing Failure Processes

This paper studies the reliability and the hybrid warranty for the products from the heterogeneous population subject to dependent competing risks namely degradation process and environmental shocks. The heterogeneous population is composed of two stochastically ordered subpopulations and the subpopulation degradation process is modeled by the inverse Gaussian process, and the products can fail due to competition between soft failure and hard failure processes. Firstly, we give the reliability function of the product under two different competing failure processes. Secondly, we propose a hybrid warranty that combines free replacement and minimal repair, and the corresponding cost model is established to determine the optimal replacement period. Finally, the detailed illustrative examples are presented.