Reliability is an important issue related to the modular multilevel converter (MMC)-based medium voltage (MV) drives. The design for reliability (DFR) approach has been discussed in many power electronic systems in recent years. MMC-based MV drives power losses and thermal cycling are strongly affected by start-up and low-speed operation, since zero-sequence current injection must be applied. In order to implement fast thermal simulations, the traditional DFR approach does not consider the heat sink thermal capacitance, which can significantly affect the MMC lifetime prediction. This article discusses how the heat sink realisations (material, thickness) affect the MMC-predicted lifetime and evaluates how the drive start-up time affects the damage in the power converter. The case study is based on a 1.4 MW slurry pump system driven by a three-phase induction motor. The lifetime evaluation of the MMC is realised through the Monte-Carlo simulation. The results show that the traditional approach results in an underestimation of up to 42.5% of the converter lifetime. In addition, long start-up times lead to a longer lifetime when compared to the shorter start-up times, due to the reduced thermal stresses in the semiconductors.