Aggressive technology scaling has resulted in an increase in process variations and statistical diversity in manufacturing. Process variations result in variations in path length, and thus a possibly different set of critical paths for different process corners, requiring consideration of process variation in delay test methods. Furthermore, the process variation adds some near-critical paths to the set of critical/longest paths [4]. Therefore, to maintain circuit reliability, testing methodologies need to be improved. As technologies become smaller, the effect of process variation becomes more significant. Process variation causes circuit performance to deviate from initial design expectations. Therefore, this could lead to reducing time margins and, therefore, increasing the probability of time violations. Consequently, by reducing the size of transistors, the importance of delay testing has become increasingly greater [10]. Process variation is a combination of systematic effects and random effects (e.g. the number of dopant atoms implanted in a transistor) that cause frequency variations [9]. It should be noted that random variations, in particular RDF (Random Dopant Fluctuation), are dominant [14]. To handle timing defects, two fault models, path delay fault and transition delay fault, were used. Small Delay Defects (SDD) are a type of delay defects that are affected by variations such as process variations, crosstalk, and power supply noise effects. SDDs introduce a small additional design delay [10] at new technology scales. The delay introduced by SDD is small, but the overall impact can impact the performance of the target circuit if the sensitized path is critical. To capture the cumulative effect of a small delay... half of the document... the proposed method, considering the shared ports between the paths, eliminates the candidate critical path set U. All paths in the U have the potential to violate the predefined time constraint (TC). Pruning the previously set path allows us to use optimal methods with an acceptable execution time. Therefore, after this step, we propose to use an Integer Linear Programming (ILP) method to find the best set of paths from the reduced set. For ILP selection, we propose an objective function that considers both the correlation between paths and the criticality of each path. The remainder of this paper is organized as follows. Work in the field of path selection on the presence of process variation is addressed in Section II. Section III describes the proposed heuristic method. The experimental results are described in Section IV and the paper concludes in Section V.