Monte Carlo Simulation

A second method for estimating performance variability, often considered the most accurate method, is through Monte Carlo simulation. Monte Carlo simulation techniques are implemented by randomly simulating a population of designs, given the stochastic properties of one or more random variables, with a focus on characterizing the statistical nature (mean, standard deviation, variance, range, distribution type, etc.) of the performance responses (outputs) of interest. Several sampling techniques exist for simulating a population. Two techniques are currently implemented within Isight as plug-ins: Simple Random Sampling and Descriptive Sampling (Saliby, 1990).

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For more information on these sampling techniques and the basic Monte Carlo approach, see About the Sampling Techniques.

To implement Monte Carlo simulation for variability estimation, uncertain parameters (random variables) must be characterized by specific distribution functions that they follow and the associated properties of the distributions (mean and standard deviation, or distribution-specific properties). If no distribution is known and only a range of possible values is given, the uniform distribution can be used to allow random sampling across the defined range. Given the statistical definition of random variables, the statistical estimates of performance derived from Monte Carlo simulation, using either sampling technique, can then be used to determine sigma level quality, percent variation within specification limits, probability of meeting specification limits, or defects per million parts based on defined specification limits.

The computational cost of Monte Carlo simulation for variability estimation is generally very high, often requiring hundreds or thousands of sample points for accurate estimation. However, Monte Carlo simulation is also the most accurate. Monte Carlo simulation is recommended when specific distributions and their properties are known and should be followed closely.