Warranty claims forecasting based on a general imperfect repair model considering usage rate

• We propose GRP-based models considering usage rate to forecast warranty claims.
• We use the AFT model to study the effect of usage rate on the system reliability.
• We use a nonlinear constrained programming method to estimate the parameters.
• A case study with real data is performed.
• The choice of GRP model is important when solving practical problems.

Because manufacturers of products sold with any type of warranty incur additional costs from servicing customer warranty claims, accurately forecasting the number of warranty claims has become increasingly important to manufacturers. Under the assumption of Weibull distributed time to failure, we propose two models based on a generalised renewal process that consider product usage rate to forecast the number of failures of products sold with a two-dimensional warranty policy. The accelerated failure time model is used to investigate the effects of the product usage rate on system reliability. The maximum likelihood estimation combined with a nonlinear constrained programming method is used to estimate the parameters of the proposed models. We conduct data experiments based on both simulation and real data collected from an excavator manufacturer in China to test the performance of the proposed models. The results indicate that the models incorporating a variable usage rate more accurately forecast the number of failures than those models based on a nominal usage rate.