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**Statistical Thinking for Industrial Problem Solving**

In this video, we show how to do a Monte Carlo simulation in JMP using the Prediction Profiler.

We use the file Anodize.jmp. This file contains the results of a 12-run custom design with five factors and four continuous responses. The experimental objective was to find settings of the factors to optimize the four responses: Thickness, L*, a* and b*.

The data have been analyzed and optimal settings have been saved as a script in the data table. To see these results, we run the Profiler 1 script in the data table.

The profiler provides the optimal settings for the five factors to achieve target values for the four responses.

However, there is likely to be some random variation in the factors, and also some random variation in the responses.

What if we want to estimate the range of response values that we might expect if we implement the optimal settings?

We can use a simulation. Or, more formally, we can perform a Monte Carlo simulation.

To do this, we select Simulator from the red triangle for the Prediction Profiler.

For each factor, you can add random variation following a specified distribution. For example, at a fixed value of 69.49, the distribution of Anodize Temp might be normally distributed with an estimated standard deviation of 1.5.

You can also add random variation in the responses. This is variation in the responses not explained by the factors in your experiment.

We'll run a script in which we've entered estimated standard deviations for both the factors and the responses.

Here, four of the factors will vary slightly, but Anodize Time is fixed, with no random variation.

For each of the responses, we've entered spec limits as a column property in the data table. You see dashed lines in the simulate panel for each of the responses representing these spec limits.

To simulate responses, we'll click the Simulate button. You see simulated distributions for each of the responses and a summary table for the simulation.

Each time you click this button, the results change slightly.

Let's add the ppm, or parts per million, to these results. To do this, we right-click on the table of simulated values, and select Columns and then PPM.

As we click the Simulate button repeatedly, you can see that the predicted defect rate is between 0.4% and 0.9%. You can also see that all of the defects are for the response L*.

You can use this simulator to explore "what if" scenarios. For example, what if we can cut the variation in Anodize Temp in half? That is, what if the actual standard deviation could be cut from 1.54 to 0.75? How would the defect rate change?

To see this, we enter 0.75 as the standard deviation for Anodize Temp, and click Simulate again. You can see that there are still some defects for L*, but the defect rate is much lower than before.

Note that you can also simulate data to a data table. You can do this to estimate the capability at the optimal settings.

Let's take a quick look at this.

By default, the number of simulated values is 5000. We'll click Make Table. This produces a new table, with 5000 simulated values for each response and each of the factors.

A distribution script has been saved to the data table. Instead, we'll use Distribution from the Analyze menu to analyze these data.

We select Thickness, L*, a* and b* as the Y, Columns, and click OK.

Because the specification limits have been saved as column properties, capability analyses are automatically reported for each response.

Let's look at the estimated capability for L*.

You can see that the distribution is slightly off target, shifted toward the lower spec limit. Some parts will fall below the lower specification limit for this response.