Electrolytic capacitor with a DC-side inductor is a typical DC-link filtering configuration in grid-connected diode rectified Adjustable Speed Drives (ASDs). The criteria to size the DC-link filter are mainly from the aspects of stability and power quality. Nevertheless, the reliability of the DC-link filter is also an essential performance factor to be considered, which depends on both the component inherent capability and the operational conditions (e.g., electro-thermal stresses) in the field operation. Nowadays, unbalanced voltage has the most frequent occurrence in many distribution networks. It brings more electrical-thermal stress to the component, affecting the reliability of the capacitors. In order to study the reliability performance of the LC filter in an ASD system quantitatively, this paper proposes a mission profile based reliability evaluation method for capacitors. Different from the conventional lifetime estimation, a nonlinear accumulated damage model is proposed for the long-term estimation, considering the nonlinear process of ESR growth and capacitance reduction during the degradation. Based on the proposed lifetime estimation procedure, four case studies are investigated: 1) Lifetime benchmarking of capacitors in LC filtering and slim capacitor filtering configurations; 2) Scalability analysis for the lifetime of capacitors in terms of system power rating and grid-unbalanced levels; 3) Lifetime estimation of capacitors in DC-link filter with long-term mission profile, and 4) The impact of the capacitor sizing on the lifetime of DC-link capacitor under grid-balanced and grid-unbalanced conditions. The results serve as a guideline for proper selection of DC-link configurations and parameters to fulfill a specification in adjustable speed drives.