About the Convergence Check

Rather than calculating all statistics just during the postprocessing analysis, Optimization Process Composer updates the mean and standard deviation for each response at specified convergence check intervals (the default is after every 25 sample points). If during the current convergence check, the mean and standard deviation of all responses have not changed from the associated values at the previous convergence check (within a user-set convergence tolerance), Optimization Process Composer terminates the Monte Carlo simulation. The remaining statistics are then calculated using the existing data set. Because the Monte Carlo Simulation points are independent, these points can be run, for efficiency, in parallel rather than sequentially.

The error in an estimate obtained using simple random sampling decreases (i.e., converges) at the rate of $1/N$ , where $N$ is the number of points; the error with descriptive sampling decreases at the rate ${(\mathrm{I}\mathrm{n}N)}^q/N$ , where $q$ is a problem-specific number that is close to the best possible rate of $1/N$ for a full factorial sample. Because the discretization of the sample space changes with a change in $N$ , it is impossible to achieve the best convergence rate for descriptive sampling by adding points incrementally. Although the error in the estimate obtained using Sobol sampling is slightly higher than that of descriptive sampling, estimates obtained using Sobol sampling converge faster than descriptive sampling because the Sobol sequence is independent of the number of samples.