Some reliability issues for incomplete two-dimensional warranty claims data

Bivariate reliability and vector bivariate hazard rate or hazard gradient functions are expected to have a role for meaningful assessment of the field performance for items under two-dimensional warranty coverage. In this paper a usage rate based simple class of bivariate reliability function is proposed and various bivariate reliability characteristics are studied for warranty claims data. The utilities of such study are explored with the help of a real life synthetic data. •Independence between age and usage rate is established.•Conditional reliability and hazard gradient along age and usage are determined.•The change point of the hazard gradients is estimated.•The concepts of layered renewal process and NHPP are introduced.•Expected number of renewals and failures at different age-usage cut-offs are obtained.