Monte Carlo simulation can be used for tolerance analysis (Monte Carlo tolerance analysis) to determine the rejection rate of assemblies. In this application we will look at an example assembly where parts A and B must fit inside part C with a clearance fit. For performance reasons we want to minimize the total clearance so A and B fit as snug as possible without interference. Part B is a spacer that can have its width changed to reach the desired objective.
We are willing to accept a 1.5% rejection rate that the assembly will not fit together. Let's assume that we have performed a test run to produce the parts using the production equipment that will be used in final production. From this data we assume that part dimensions are normally distributed and we can determine the standard deviation of each dimension. We will also assume that mean dimensions are equal to the nominal dimension for each part.
With the data in hand, a spreadsheet model can be constructed to simulate. The model is shown below with the random variable cells in green.
Note that the two A parts are "identical" in terms of nominal dimension, but their widths are modeled as separate parts. These parts will not necessarily be the same exact width and therefore are treated as separate random variables.
After simulating for 25,000 iterations, we find that 1.64% of the time the assembly will not fit together. This is close to the 1.64% rejection target. We can stop and go with the design as is, or we can decrease the nominal width of B and run another simulation. This can be repeated until the 1.5% target has been reached.
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