Abstract
Joint cumulative hazard functions were previously used to simultaneously determine two survival times in the presence of censoring, and a weak convergence result was derived. However, a bivariate history up to a failure point or a censored point on a two-dimensional time scale (i.e., a "sample path") is possible to use for failure data analysis of industrial products. A bivariate estimator based on the Nelson-Aalen estimator is now proposed for estimating a cumulative hazard function under the assumption that a sample path can be modeled as a straight line. Application of the proposed estimator to actual data demonstrated that it enables estimation of the usage-frequency-dependent failure probability.
