Optimal warranty period design for new products subject to degradation and environmental shocks considering imperfect maintenance

For new products, manufacturers usually aim to set a reasonable warranty period before market launch to maximize future profits. However, the lack of historical warranty claim records makes it challenging to optimize the warranty period effectively. This paper proposes a new framework to optimize the warranty period for new products based on laboratory data, considering degradation-shock competing failures and imperfect maintenance. First, a degradation-shock competing failure model for the new products is established based on laboratory accelerated degradation data. Next, the impact of imperfect maintenance on warranty costs is quantified using the maintenance improvement factor model. Then, an optimization model for the warranty period is established with the aim of maximizing the manufacturer's profit. Finally, a case study is carried out to verify the validity and applicability of the proposed model. The numerical results clearly indicate that the frequency and magnitude of shock failures significantly impact the optimal warranty period for the product. Moreover, as the mean value of the imperfect maintenance factor increases from 0.5 to 0.9, the manufacturer’s profit first rises from 6.49 to 7.79, then drops to 7.42, which means strategically relaxing maintenance requirements can lead to higher profit margins for manufacturers.