Non-parametric estimation from simultaneous renewal–failure–degradation data with competing risks

A new joint model for linear degradation and competing failure data with partial renewals is proposed. Non-parametric statistical estimation procedures for failure intensities and failure probabilities as functions of degradation level are given

Testing proportional hazards for specified covariates

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data may be right censored. The limit distribution of the test statistic is derived. Power of the test against approaching alternatives is given. Real data examples are considered