An improved model for dependent competing risks considering continuous degradation and random shocks

•An age- and state-dependent competing risks model is proposed.•The natural degradation process and the health state are considered continuous and dependent.•The closed-form reliability function is derived for a special case of the model. Many products and systems are subject to multiple degradation processes, such as ageing, wear, and so on, as well as random shocks induced by the external environment. Some models have been proposed to represent the degradation processes concerning random shocks. However, most reported models have only focused on degradation due to the effects of age. In different health states, the influence of shocks acting on the degradation processes may vary, owing to the current state of the system or component. In this study, an age- and state-dependent competing risks model that considers random shocks is proposed. The impact of the current degradation state on the overall degradation process, including the effect of shocks accelerating the degradation rate and increasing the degradation increment, is incorporated. As a special case, when the degradation path is linear, the closed-form reliability function is derived for continuous case. Comparison studies show that reported models that do not consider the effect of the current degradation state overestimate the reliability.