The appeal of Monte Carlo Simulation lies in its applicability under very general settings and the unlimited precision that can be achieved. In particular, Monte Carlo can be used in all situations where other techniques (Linear and non linear propagation, and Numerical Integration) can be used but can yield more precise estimates. For this reason, Monte Carlo is easily the most popular tool used in tolerance problems.
Until recently the caveat was in the amount of processing power and time it took to complete a simulation. Now @RISK from Palisade Corporation can utilize the full processing power and dual cores of today’s personal computers, so this is no longer an issue. The other issue, what was deemed as “Pseudo random number generators,” has been overcome by @RISK offering 8 tested and proven random number generators such as Mersenne Twister, RAN3I, MRG32k3a, MWC and KISS . . . to name a few. These are just a few of the reasons why @RISK is becoming the standard Monte Carlo Simulation package in DFSS Training and Six Sigma classes around the world.
Reference: Design for Tolerance of Electro-Mechanical Assemblies: An Integrated Approach by Narahari, Sudarsan, Lyons, Duffy and Sriram