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Making the World a Little Brighter with Monte Carlo Simulation

If you have a process that isn’t meeting specifications, using the Monte Carlo simulation and optimization tool in Companion by Minitab can help. Here’s how you, as a chemical technician for a paper products company, could use Companion to optimize a chemical process and ensure it consistently delivers a paper product that meets brightness standards.

paperThe brightness of Perfect Papyrus Company’s new copier paper needs to be at least 84 on the TAPPI brightness scale. The important process inputs are the bleach concentration of the solution used to treat the pulp, and the processing temperature. The relationship is explained by this equation:

Brightness = 70.37 + 44.4 Bleach + 0.04767 Temp – 64.3 Bleach*Bleach

Bleach concentration follows a normal distribution with a mean of 0.25 and a standard deviation of 0.0095 percent. Temperature also follows a normal distribution, with a mean of 145 and a standard deviation of 15.3 degrees C.

Building your process model

To assess the process capability, you can enter the parameter information, transfer function, and specification limit into Companion's straightforward interface, and instantly run 50,000 simulations.

paper brightness monte carlo simulation

Understanding your results

monte carlo simulation output

The process performance measurement (Cpk) is 0.162, far short of the minimum standard of 1.33. Companion also indicates that under current conditions, you can expect the paper’s brightness to fall below standards about 31.5% of the time.

Finding optimal input settings

Quality Companion's smart workflow guides you to the next step for improving your process: optimizing your inputs.

paramater optimzation

You set the goal—in this case, maximizing the brightness of the paper—and enter the high and low values for your inputs.

optimization dialog

Simulating the new process

After finding the optimal input settings in the ranges you specified, Companion presents the simulated results for the recommended process changes.

optimized process output

The results indicate that if the bleach amount was set to approximately 0.3 percent and the temperature to 160 degrees, the % outside of specification would be reduced to about 2% with a Cpk of 0.687. Much better, but not good enough.

Understanding variability

To further improve the paper brightness, Companion’s smart workflow suggests that you next perform a sensitivity analysis.

sensitivity analysis

Companion’s unique graphic presentation of the sensitivity analysis gives you more insight into how the variation of your inputs influences the percentage of your output that doesn’t meet specifications.

sensitivity analysis of paper brightness

The blue line representing temperature indicates that variation in this factor has a greater impact on your process than variation in bleach concentration, so you run another simulation to visualize the brightness using the 50% variation reduction in temperature.

final paper brightness model simulation

The simulation shows that reducing the variability will result in 0.000 percent of the paper falling out of spec, with a Cpk of 1.34. Thanks to you, the outlook for the Perfect Papyrus Company’s new copier paper is looking very bright.

Getting great results

Figuring out how to improve a process is easier when you have the right tool to do it. With Monte Carlo simulation to assess process capability, Parameter Optimization to identify optimal settings, and Sensitivity Analysis to pinpoint exactly where to reduce variation, Companion can help you get there.

To try the Monte Carlo simulation tool, as well as Companion's more than 100 other tools for executing and reporting quality projects, learn more and get the free 30-day trial version for you and your team at companionbyminitab,com.

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