Optimal burn-in and warranty design for heterogeneous population subject to stochastic degradation

In practice, product heterogeneity is commonplace. Burn-in processes are extensively utilized to screen out weak products from heterogeneous batches before delivery to customers, proving to be an effective strategy for enhancing product reliabilit y and reducing warranty costs. This study introduces a model that integrates burn-in procedures with warranty policies for a heterogeneous product population, where the degradation processes are modeled using a general degradation path. We propose utilizing shock as a method of burn-in and offer a renewable warranty for products that survive this process upon delivery to customers. Initially, a novel shock-based burn-in model is developed, and the effects of shock are analyzed concerning population characteristics. Subsequently, a cost model is formulated to determine the optimal magnitude of shock that minimizes the total expected cost. The optimal sale price, warranty period, shock magnitude, and replacement threshold level are calculated to maximize expected profit. An illustrative example is provided to demonstrate the application of the model.