# Monte Carlo Simulation

Use a Monte Carlo Simulation to account for risk in quantitative analysis and decision making.

The simulation uses a mathematical model of the system, which allows you to explore the behavior of the system faster, cheaper, and possibly even safer than if you experimented on the real system.

The simulation provides expected values based on equations that define the relationship between the inputs (X) and outputs (Y). These may be known equations, or they may be based on a model that you created from a designed experiment (DOE) or regression analysis in Minitab.

Upon completion of the initial simulation, Engage displays a histogram and summary statistics, including expected output values and an estimate of their variability. If you provide specification limits, the results also include process performance metrics.

Engage provides the following analysis methods to help you further improve the results of the initial simulation.
• Parameter Optimization: Identifies optimal settings for the inputs that you can control. Engage searches a range of values for each input to find settings that meet the defined objective and lead to better performance of the system.
• Sensitivity Analysis: Identifies the inputs whose variation have the most impact on your key outputs. Use this method along with your process knowledge to identify the inputs that can be adjusted to make improvements.
A Monte Carlo Simulation answers the following questions.
• What distribution best fits my input data? What values can I expect for my outputs?
• How capable is my process or product, given uncertainty in the input parameters?
• What are the optimal settings to achieve my goal?
• How does the variation in the inputs affect the variation in the response?

## How-to

1. Identify the equations, y=f(x), that explain the relationship between the inputs and outputs. Equations can come from process knowledge or from a statistical analysis.
2. Define the distribution of each input variable. If you do not know which distribution to use, Engage can examine historical data in a CSV file and recommend a possible distribution.
3. Run a Monte Carlo simulation.
4. Perform a parameter optimization.
5. Perform a sensitivity analysis.