1. A method for predicting a remaining useful life (RUL) for a component in a set of components within a computer system, wherein the set of components includes a monitored component, the method comprising, in at least one computer, performing operations for: collecting values of at least one degradation-related parameter associated with the operation of the monitored component within the computer system, wherein the degradation-related parameter is a direct measurement of a degree of degradation of the monitored component; collecting values of at least one stress-based parameter from the computer system, wherein the stress-based parameter measures an accumulative stress in the operating environment of the set of components which can cause degradation of the set of components; and predicting an RUL for a component in the set of components using at least a predicted first RUL for the monitored component and a predicted second RUL for the set of components, wherein the first RUL is predicted based at least on the values of the at least one degradation-related parameter and the second RUL is predicted based at least on the values of the at least one stress-based parameter; wherein predicting the RUL for the component in the set of components using at least the first RUL and the second RUL involves: determining if the first RUL indicates that the monitored component is not close to failure and if the second RUL indicates that the set of components is close to failure; and if so, predicting the RUL for the monitored component based on the first RUL when the first RUL is associated with a first confidence level; and otherwise, predicting the RUL for the monitored component based on the second RUL when the first RUL is associated with a second confidence level that is lower than the first confidence level.