An object is manufactured on some date. There are two things which contribute to the risk of failure: time passed since the date of manufacture and the amount of cumulative usage. Assuming there is data on multiple objects at different time points, a parametric PH model can be used ( $t$ = time since manufacture, $U(t)$ = cumulative usage up to time $t$ ): $$h(t \mid U) = \lambda \gamma t^{\gamma-1}\,\exp\!\big(\beta_1 U(t)\big)$$ Is it possible to define a model where two hazard functions are added for the hazard from time and hazard from cumulative usage? $$h(t) = \lambda_1\gamma_1 t^{\gamma_1-1} + \lambda_2\gamma_2\, U(t)^{\gamma_2-1}$$ Typically, I have seen additive hazard models that are additive in terms of covariates (Aalen additive hazards model): $$\lambda(t \mid X) = \beta_0(t) + \beta_1(t) X_1 + \beta_2(t) X_2 + \cdots + \beta_p(t) X_p$$ But is it possible to have a model that is additive in the hazard contributions of two time scales? $$h(t) = \lambda_1\gamma_1 t^{\gamma_1-1} + \lambda_2\gamma_2\, U(t)^{\gamma_2-1}$$

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