Costs model for two-dimensional lifetime warranty policies based on combined repairs

In recent years, lifetime warranty has attracted broad attention from both manufacturers and customers as these types of warranties offer assurance for a longer reliable useful life and the potential higher cost of failure. In this paper, two-dimensional free rectification lifetime warranty taking into account the age and usage of product have been developed to estimate the corresponding costs. Manufacture have a duty to provide free services to the sold product with the defection of design and manufacturing process during the scope of lifetime warranty, which is determined by age and usage of common. To make the model more realistic complete repair Combined with Minimal Repair (CMR) is taken into account during the calculation of the warranty cost and the developed models capture the uncertainties of lifetime warranty coverage period. Numerical examples are given to illustrate the presented model, which shows the expected lifetime warranty costs to the manufacturer increases as the lifetime increase and costs with the product failure rate both on age and usage for different combinations of the limitation of lifetime.