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A Monte Carlo simulation is a quantitative analysis that accounts for the risk and uncertainty of a system by including the variability in the inputs. The system may be a new product, manufacturing line, finance and business activities, and so on. 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. Suppose you are investigating the time to complete similar construction projects. There are four phases: Proposal, Scoping, Execution and Delivery. The measurements are in business days. Here, the inputs are the number of business days it takes to complete each phase. The output is simply the total number of business days it takes to complete the project.
Project Time = Proposal + Scoping + Execution + Delivery
Here's how the simulation works:
Companion 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.
|When to Use||Purpose|
|Early-project||Use simulation to predict how long a project will take.|
|Mid-project||Given y=f(x), use simulation to estimate values for a response of interest.|
This form has no data requirements because Companion simulates the data based on the model assumptions. However, if you're unsure which distribution to choose when defining the model inputs, Companion can evaluate historical data that is stored in a CSV file and recommend a distribution.
A Monte Carlo simulation relies on the assumptions you make. First, you must obtain the equation (y= f(x)) that explains the relationship between the inputs and outputs. This equation may come from process knowledge (the length of a project is just the sum of each phase), or from a statistical analysis where you fit a predictive model such as a designed experiment (DOE) or regression analysis on the historical data in Minitab.
A Monte Carlo simulation also depends on a reasonable specification of the distribution for each input, which defines the variation. If you do not know which distribution to use, Companion can examine historical data in a CSV file and recommend a possible distribution.
Each iteration of the simulation draws a random sample of possible values from the distributions for each input, enters these values into the equation, and then calculates the outputs. The number of iterations should adequately cover the range of possible input and output values, and provide accurate results. The maximum number is 1,000,000. However, the default of 50,000 is sufficient for most models.
There is no limit to the number of inputs and outputs in the model. Your simulation can be as large as necessary.
For more information, go to Add a Monte Carlo simulation.