The paper considers linear degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Estimators of traumatic event cumulative intensities, and of various reliability characteristics are proposed. Prediction of residual reliability characteristics given a degradation value at a given moment is discussed. Non-parametric, semiparametric and parametric estimation methods are given. Theorems on simultaneous asymptotic distribution of random functions characterising degradation and intensities of traumatic events are proposed. Asymptotic properties of unconditional and residual reliability characteristics estimators are given. Real tire wear and failure time data are analysed.
We present a model and semiparametric estimation procedures for analysis of survival data with cross-effects (CE) of survival functions. Finite sample properties of the estimators are analyzed by simulation. A goodness-of-fit test for the proportional hazards model against the CE model is proposed. The well known data concerning effects of chemotherapy and radiotherapy on the survival times of gastric cancer patients is analyzed as an example.
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