Monte Carlo Simulation Online: Uncertainty Propagation Analysis
What Is Monte Carlo Simulation?
Monte Carlo simulation propagates uncertainty by drawing a large number of random samples: each input variable is assigned a probability distribution (normal, uniform, triangular and so on), random values are substituted into the calculation formula, and the process is repeated thousands of times to obtain the probability distribution of the output. Because it does not rely on the linear approximation of error-propagation formulas, it handles complex nonlinear relationships and arbitrary combinations of distributions, making it the standard method for tolerance stacking, capacity prediction and risk assessment. Presenting results as distributions and probabilities is closer to engineering reality.
How to Set Input Distributions
Choose a distribution based on the nature of each variable: use a fitted normal distribution (mean +- standard deviation) for process data, a uniform or triangular distribution when only a range is known (a triangular distribution with a most-likely value is more realistic), Poisson or binomial for counts and defects, and Weibull for lifetime data. The tool lets you set the distribution type and parameters for each input and displays the input distributions for verification. The input settings directly determine the realism of the simulation, and biased inputs propagate into the output conclusions.
How to Interpret Results
The tool outputs the result histogram, cumulative distribution curve, mean/standard deviation/quantiles (P5, P50, P95) and confidence intervals, plus the probability of exceeding specification limits. A tolerance-stacking simulation, for example, can directly give the assembly out-of-tolerance rate, yield and worst-case interval. More iterations make the distribution more stable; the tool defaults to tens of thousands of runs and supports Latin hypercube sampling for efficiency, with quantile estimates converging as iterations increase. The histogram can be exported directly into reports.
How to Use It (Step by Step)
Log in, define the calculation formula (arithmetic operations and common functions are supported), assign a distribution and parameters to each input, set the number of iterations, run the simulation, and review the result distribution, quantiles and out-of-spec probability before exporting the data. Start with a small number of iterations to debug the formula, then run the full simulation. Combine extreme values with business judgment to see whether they are truly reachable, and use sensitivity analysis to identify the inputs that matter most. Save the settings and results for reproducibility and traceability.