The failure intensity improvement of two-stage warranty under lemon laws conditions for repairable products

The bathtub-shaped failure intensity, in which the intensity function initially decreases, followed by a long period of constant or near-constant intensity until wear-out finally occurs, characterizes the change in failure intensity throughout the entire life cycle. Under the lemon laws, the two-dimensional warranty period is always divided into the refund period and preventive maintenance period. This paper considers the failure intensity functions within two adjacent warranty periods, respectively. Within the refund period, the PAR-S-LLP failure intensity model is adopted since the manufacturing defects are not screened out completely during the burn-in process. Within the preventive period, a convex failure intensity is introduced to characterise the conditional failure intensity function after maintenance. Simultaneously, the related costs within these two warranty period are considered.