Reliability modeling and warranty optimization for products with self-healing under a dynamic shock environment

As modern products evolve in intelligence, self-healing mechanisms have been gaining prominence in the field of reliability. In actual operation, the performance of a product is inevitably influenced by external environments and user interactions. However, existing warranty studies often overlook these factors, leading to oversimplifications in product reliability modeling. This paper offers a comprehensive and realistic view of the product failure process by integrating the dynamic shock environment, inherent self-healing property, and post-sale consumer utilization. The constructed reliability evaluation model accounts for fatal and non-fatal shocks with a dynamic time-varying failure threshold. We introduce the concept of self-healing trigger/delay time, considering a generalized self-healing process. The approximate product reliability is derived, and its accuracy is validated using Monte Carlo simulations. Then, derived from real-world practices, we propose a novel two-stage warranty policy which combines lemon law principles with preventive maintenance. By minimizing the expected cost rate throughout the warranty service period, a preventive maintenance schedule optimization model is developed from the manufacturer's perspective. Finally, a numerical case is presented to reveal the influences of different factors on product reliability and demonstrate the existence of the optimal solution.