This paper proposes two new importance measures: one new importance measure for systems with -independent degrading components, and another one for systems with -correlated degrading components. Importance measures in previous research are inadequate for systems with degrading components because they are only applicable to steady-state cases and problems with discrete states without considering the continuously changing status of the degrading components. Our new importance measures are proposed as functions of time that can provide timely feedback on the critical components prior to failure based on the measured or observed degradation. Furthermore, the correlation between components is considered for developing these importance measures through a multivariate distribution. To evaluate the criticality of components, we analysed reliability models for multi-component systems with degrading components, which can also be utilized for studying maintenance models. Numerical examples show that the proposed importance measures can be used as an effective tool to assess component criticality for systems with degrading components.