A general discrete degradation model with fatal shocks and age- and state-dependent nonfatal shocks

A general discrete competing risks model with age- and state-dependent random shocks is developed in this research. This model allows for a more generalized structure of dependence by considering the current degradation state. Random shocks are classified into fatal shocks and nonfatal shocks with corresponding probability. Fatal shocks can bring immediate failure, and nonfatal shocks will affect the degradation process. In this sense, the dependent relationships have two folds: a) the dependence between nonfatal shocks and the natural degradation process, reflected by a time-scaled accelerated factor, and b) the dependence between the current state and nonfatal shocks, which is modulated by three functions of the current state representing the effects on degradation increments and degradation rate acceleration of nonfatal shocks. The extended Kalman filter (EKF) is used together with measured data to estimate the distribution of the current state. Based on the degradation state equation and measurement function, a closed-form reliability function is derived, and the reliability can be updated given new measured data. An illustrative example is provided to demonstrate the advantages of the proposed model. The result shows that the reliability evaluation is more realistic when the impact of the current state on random shocks is considered.