Monte Carlo Simulation Example

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A variation of this example appears in the Weibull++/ALTA Help file.

Monte Carlo Simulation: A Hinge Length Example

A hinge is made up of four components A, B, C, D, as shown next. Seven units of each component were taken from the assembly line and the following measurements (in cm) were recorded:

[math]\displaystyle{ \begin{matrix} \text{Dimensions for A} & \text{Dimensions for B} & \text{Dimensions for C} & \text{Dimensions for D} \\ \text{2}\text{.0187} & \text{1}\text{.9795} & \text{30}\text{.4216} & \text{33}\text{.6573} \\ \text{1}\text{.9996} & \text{2}\text{.0288} & \text{29}\text{.9818} & \text{34}\text{.5432} \\ \text{2}\text{.0167} & \text{1}\text{.9883} & \text{29}\text{.9724} & \text{34}\text{.6218} \\ \text{2}\text{.0329} & \text{2}\text{.0327} & \text{30}\text{.192} & \text{34}\text{.7538} \\ \text{2}\text{.0233} & \text{2}\text{.0119} & \text{29}\text{.9421} & \text{35}\text{.1508} \\ \text{2}\text{.0273} & \text{2}\text{.0354} & \text{30}\text{.1343} & \text{35}\text{.2666} \\ \text{1}\text{.984} & \text{1}\text{.9908} & \text{30}\text{.0423} & \text{35}\text{.7111} \\ \end{matrix} }[/math]

Determine the probability that the stress of the A, B and C components will result to the value of D falling out of specification.

Solution

In a Weibull++ standard folio, enter the parts dimensions measurements of each component into a separate data sheets. Analyze each data sheet using the normal distribution and the RRX analysis method. The parameters are:

[math]\displaystyle{ \begin{matrix} \text{A} & \text{B} & \text{C} & \text{D} \\ \hat{\mu }=2.0146 & \hat{\mu }=2.0096 & \hat{\mu }=30.0981 & \hat{\mu }=34.8149 \\ \hat{\sigma }=0.0181 & \hat{\sigma }=0.0249 & \hat{\sigma }=0.1762 & \hat{\sigma }=0.7121 \\ \end{matrix} }[/math]

Next, perform a Monte Carlo simulation to estimate the probability that (A+B+C) will be greater than D. To do this, choose the User Defined distribution and enter its equation as follows. (Click the Insert Data Source button to insert the data sheets that contain the measurements for the components.)

On the Setting tab, set the number of data points to 100, as shown next.

Click Generate to create a data sheet that contains the generated data points. Rename the new data sheet to "Simulated (A+B+C)."

Follow the same procedure to generate 100 data points to represent the D measurements. Rename the new data sheet to "Simulated D."

Analyze the two data sets, "Simulated (A+B+C)" and "Simulated D," using the normal distribution and the RRX analysis method.

Next, open the Life Comparison tool and choose to compare the two data sheets. The following picture shows the pdf curves of the two data sets.

The following report shows that the probability that (A+B+C) will be greater than D is 16.033%. (Note that the results may vary because of the randomness in the simulation.)