Enabling timing analysis for caches has been pursued by the critical real-time embedded systems (CRTES) community for years due to their potential to reduce worstcase execution times (WCET). Measurement-based protabilistic timing analysis (MBPTA) techniques have emerged as a solution to time-analyze complex hardware including caches, as long as they implement some random policies. Existing random placement and replacement policies have been proven efficient to some extent for single-level caches. However, they may lead to some probabilistic pathological eviction scenarios. In this work we propose new random placement and replacement policies specifically tailored for multi-level caches and for avoiding any type of pathological case.