Monte Carlo is an efficient tool to simulate complex physical and mathematical systems.  Large sample sizes are usually required to obtain acceptable accuracy.  This obviously exaggerates the slowness and expensiveness problem inherent part of the method.  The motivation to this research is to tackle such disadvantage and identify a proper alternative to this method. The aim of this work is to conduct a comparative study of tolerance analysis of mechanical assemblies using two different techniques, namely Monte Carlo method (MC) and Orthogonal Arrays (OAs).  In particular, standard and small orthogonal experiments are utilized to replace the huge sample sizes needed in case of Monte Carlo method.  The mean and variance of design functional requirements are determined using both methods.  Then, a comparison between the results, that were obtained from both methods, were assessed to evaluate the performance of the Orthogonal Array (OA) method as an alternative of Monte Carlo simulation (MCS) tool. In this paper, disk-drive assembly, knuckle joint with three arms assembly, one-way clutch assembly, and helical spring have been used as case studies of mechanical assemblies to highlight the strength of the alternative method. Based on the achievable results one can argue that Monte Carlo method can be replaced by Orthogonal Arrays gives acceptable results in a shorter time.  The first and second moments of examples revealed that both methods give close results. However, the second moment not completely matched that obtained using Monte Carlo method at 3-levels; it matched that obtained using Monte Carlo method at 2-levels. These discrepancies are challenging issues for further investigation in future work. Apart from this imperfection, it is recommended to play a significant role, particularly to simulate a wide range of engineering applications.