# Use a Monte Carlo Analysis to Predict Compliance

January 19th, 2023 05:03 AM / by Dan Ridolfi, PE

### OVERVIEW:

A Monte Carlo analysis is a powerful way to predict future performance based on past results. Many rock products like base, asphalt, and concrete are comprised of a blend of aggregate materials. The aggregate blend often must comply with a specification. A Monte Carlo simulation is a way to model blend performance against a specification by analysis applying past variability to each product and randomly estimating a property, like gradation, for each aggregate. Then the aggregates are mathematically combined according to the relative percentages to calculate a random blended value. This is done 1,000's or 10's of thousands of times to get a random distribution of probable results. The pool of results is statistically compared to the specification to assess risks or find opportunities.

In this Leveraging LASTRADA video, you will see:

Two common uses of a Monte Carlo simulation are provided, and analysis can be duplicated using Microsoft Excel and LASTRADA™.

If you would like to discuss how to use your aggregate gradation test results to optimize aggregate blends for compliance with specifications, request a consultation with one of our engineers.

EXPECTED OUTCOMES:

After this video, you’ll be able to:
1. Evaluate if an aggregate blend will likely comply with a specification.
2. Determine an aggregate's maximum allowable standard deviation to ensure asphalt, concrete, or base blends with that aggregate comply with specifications.

VIDEO TRANSCRIPT:

How can we use past production data to predict future performance? You might want to predict if a blend of aggregates that could include RAP will comfortably meet gradation requirements in production, or you might want to provide guidance on gradation targets to prevent a past issue. The Monte Carlo analysis is a powerful way to model future performance using past data. You calculate a result using previous information, then you apply the measured variability to each property, randomly determine new properties, and then recalculate the result. You do this thousands or tens of thousands of times to create a frequency distribution of answers from which you apply simple probability calculations to measure success. In this Leveraging LASTRADA video, I will show you how to use a Monte Carlo analysis to predict the odds of success of producing an aggregate blend within specification. LASTRADA users will find the file used in this video with an applied XML schema in the Customer Resource Center. Non-LASTRADA users can download a simple Excel version of the same report on our website. I'm going to use the Monte Carlo analysis to solve two example problems. The first example is that I have two sand sources available, and I want to understand which sand is in the specification. The second example is to understand how consistent an aggregate needs to be so that when I re-screen my plant to produce specialty aggregates like chip seal aggregates, I keep my asphalt combined blend within specification.

To create a summary report that shows all the results of all the trials, first, change the trial number from one to two to three, or whatever's appropriate, and then press copy trial to report. When you do that, you can flip to the report page, and each trial will be copied over here you can then print this page or convert it to a PDF to look at the results side by side with the second use of a Monte Carlo simulation would be a specialty aggregate product, and what I mean by that is let's say we produce this half inch by quarter inch chip and it on average runs at 81.2 percent as its percent passing the 3 8. but we at least once a season rescreen the plant to make a chip seal aggregate, and we take that fine material that 81 percent passing and we take 10 percent out of there and we use it to make a slurry aggregate so this number goes from 81 to 71.

As an example, now the standard deviation on the three-eighth sieve is 8.9 percent which is actually quite high. We also saw in the previous calculations that the percent within specification was still near 100, even though the variability was high at 8.9 percent. So the question is, can we adjust that gradation to the same targets? What we just see right here is the 95, 86, and 62 percent, and maintain that high percent within limit. Let's go ahead and do that. So if I change this to 71 and then run the results again, looking at this percent within the specification of the three-eighth. We went from 99, which we saw earlier, down to 96.4. Now, this is on that border that we discussed earlier at the 95 percent, and this also assumes you don't adjust the plant, so if we can readjust these percentages up here, then we should be pretty confident that we should be able to be within specification again and this 8.9 percent is not a bad result. So just for discussion purposes, what if it wasn't 8.9 percent? What if it was 11 percent? We could rerun this evaluation again, and we see that the numbers drop even lower, so 9.5 and now 11 appear to be really high standard deviations, but because there's only 18 percent in this mix and it's being blended with other products that are fairly consistent, it's not a big deal, and that's the power of the Monte Carlo simulation.

It's hard to look at how each product's variability influences the final result. The Monte Carlo simulator allows us to see that. I hope you found this video helpful and that you can use it in your daily work.

Thank you for watching; for more tips like this one, check out our other Leveraging LASTRADA videos at www.lastradapartners.com/resources. LASTRADA Partners employs registered professional engineers and industry veterans that can help you solve problems such as this one. You can schedule a free consultation with one of our engineers by going to our contact page. Thank you.

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