# 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.

LASTRADA users will start by exporting a mix design and importing the data from The Mix Design into the Monte Carlo sheet. Be sure that you have a blend with all of your aggregate products loaded into it, so you don't have to retype any information. To export, we go ahead, and we hit this export button here, and save the file to a location that we know. The next thing we're going to do is import the exported data from LASTRADA into this Monte Carlo simulation spreadsheet. So I'm going to go here and press import. I'm going to go find the file that we created, and then we'll hit import. Okay, I've added all the standard deviations for the products in this table, and then I've added the plus or minus tolerances in our specifications to this section of this table here. The next thing we want to do is we want to go ahead and run the analysis and when we hit run, what the spreadsheet is going to do is it's going to estimate based on these standard deviations a gradation for each product, and then it's going to calculate a combined gradation using these percentages, here based on the number of repetitions it's going to do it that many times. In this case, I've got it set to a thousand, and then it's going to give us the average of the results for each sieve size and the standard deviation of each sieve size. So I'm going to go ahead and hit run, and we'll let it run a thousand iterations, and you can see the numbers are changing the standard deviations and the averages. So as this is running, the question is, how many iterations should you do? I would suggest you run it as many times as you need so that the mean and the standard deviation begin to settle down to a number. We found in practice with real production data that 10,000 iterations seem to be about the right number for the projects that we're working on. So, what do the results mean, or what is this telling us? You know, based on the variability of the aggregates that we produce or use at these percentages in the mixed design. We should expect the percent within limits or percent within the specification of this gradation to be what is shown in this column here, and again that's if you don't adjust the plant at all. It's really not a real-world scenario that we don't adjust the plant, so think of this column not as an absolute percent within spec but call it risk tolerance. So at a hundred percent, your risk is low to zero, and anything below eighty percent, the risk would be considered very high. Then based on your experience in using a tool like this or using this tool specifically and your own production experience, you can set appropriate numbers here for what is an acceptable percent within spec or risk tolerance anything between 90 and 95 would be a good starting place as being sort of borderline risk. If you don't have that experience, anything above 95 should be pretty comfortable to be produced in the specification in production. So maybe start with those numbers, and as you use the tool and you get your own experience together. With that tool, you can find appropriate numbers for your plant. So what we were trying to evaluate was using this natural sand number four versus this natural sand number five and to see which one is going to be more likely to be within specification than the other. So what we want to do is we want to evaluate this percentage within the specification column from one gradation to the next. So what you do is you come over here, and you copy the trial to the report, and the results will be copied over for us, and then we're going to go ahead and clear the results. So that the percent within spec is cleared and all the iterations are cleared and then what we're going to do is I'm going to go back into LASTRADA, and I'm going to switch these sand sources and then copy over the new plant settings. So I'm going to go ahead and do that now. We're back in LASTRADA let's go ahead and calculate a blend targeting the same gradation but using the alternate sand source. I'm going to go ahead and change this to 20.7, and then I'm going to change this to 0, and I'm going to tell LASTRADA you cannot change this off 0, and then I'm going to tell it to optimize, and now I've got new plant settings that achieve the same gradation as before, but using this alternate sand source. So now I'm going to go ahead and copy these values over to that same spreadsheet that we were working on before. I copy those new percentages into this column here, and now I'm going to go ahead and hit run again. Let's look at the results we can see switching sand sources from this natural sand here to this sand here didn't affect the three-quarter, half, three-eighth, and number 200 sieves in terms of gradation risk, but the number eight sieve was affected substantially, as it dropped another eight percent on its percent within spec. That makes sense because when we look at the standard deviation of the second sand source compared to the first sand source, we see that the standard deviation is almost double.

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.

Start a discussion with one of our engineers to learn more about how LASTRADA Partners can help you streamline your workflows, improve quality and reduce costs.

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