A Study On The Warranty Policy For Heterogeneous Populations Subject To The Shock Process

In practice,almost all products are heterogeneous,and homogeneous products are very rare.The performance of products is usually affected by external shocks during operation due to the complexity of its own structure.This thesis studies the warranty policy for the heterogeneous populations based on the performance degradation process and the environmental shocks,where the heterogeneous populations are composed of two stochastically ordered subpopulations.Firstly,we consider that the performance degradation process of heterogeneous products is modeled by the general degradation path.The instantaneous shock is used as the burn-in method to improve the performance of the heterogeneous populations.The lifetime of the heterogeneous populations before and after the shock has been compared in the sense of stochastic orders.Only the products from the heterogeneous populations that have survived the shock will be provided with a renewable free-replacement warranty,and the corresponding cost model is established to determine the optimal shock magnitude.Besides,the corresponding profit model is established based on a new sales volume function,and the optimal warranty policy is determined by maximizing the profit.Finally,the numerical example is given.Secondly,we consider that the performance degradation process of heterogeneous products is modeled by the Inverse Gaussian process,and establish a reliability model for heterogeneous products subject to competing failure which is affected by environmental shocks,where the external shock has two effects: the product fails immediately if the shock magnitude exceeds its own strength;otherwise,shock damage occurs due to the shock and accelerates the degradation failure process of the product.Besides,we propose a hybrid warranty that combines replacement and minimal repair.The renewable free-replacement warranty is provided in the first stage of the warranty period,and the non-renewable free minimal repair warranty is provided in the second stage.Then,we establish the corresponding warranty cost model to determine the optimal replacement period.Finally,the detailed illustrative example is presented.