[en] Multi-state single-plant risk models are developed and the impacts of various failure and repair characteristics associated with safe shutdown and multiple accident conditions are analyzed. Comparisons of models are presented and recommendations are made for selecting a model. Fundamental recursive equations are then derived for the probabilistic characteristics of components in general. These equations are new results for multi-state components, allow replacement components to be new or old, and allow general failure and repair time distributions to be used. The equations are solved for the time dependent state probabilities and conditional and unconditional failure and repair rates