We present an evaluation method for estimating the lower bound number of Monte Carlo STA trials required to obtain at least one sample which falls within top-k % of its parent population. The sample can be used to ensure that target designs are timing-error free with a predefined probability using the minimum computational cost. The lower bound number is represented as a closed-form formula which is general enough to be applied to other verifications. For validation, Monte Carlo STA was carried out on various benchmark data including ISCAS circuits. The minimum number of Monte Carlo runs determined using the proposed method successfully extracted one or more top-k % delay instances.