Appendix B
Monte Carlo Calculations
I. MONTE CARLO SIMULATIONS
The simulation procedure can be broken down into seven steps:
1. Fit failure criterion data (usually yield strength or tensile strength)
to an appropriate distribution function. Goodness-of-fit statistics
are useful in the determination of an acceptable model.
2. Define the applied stress on the part to be designed.
3. Assign a distribution function to each variable in the stress
equation and assume a starting value for each, variables are
typically load and dimensions.
4. Generate random variates from the failure criterion distribution
and from each of the variable distributions.
5. Calculate the stress using the random variate for each variable and
compare that stress with the random variate from the failure criterion distribution.
Whenever the stress exceeds the failure
variate, a failure has occurred.
6. Repeat the last two steps n times, where 1/n=probability of
failure; e.g., a probability of failure of 10 -6 requires 10
6
calculations.
7. If only one failure has occurred in the n calculations, the design is
valid for a probability failure of 1/n. If no failure occurred, or
more than one occurred, adjust the assumed design variables (step
4) and repeat last three steps until only one failure occurs in
simulations.
225
Monte Carlo Calculations
I. MONTE CARLO SIMULATIONS
The simulation procedure can be broken down into seven steps:
1. Fit failure criterion data (usually yield strength or tensile strength)
to an appropriate distribution function. Goodness-of-fit statistics
are useful in the determination of an acceptable model.
2. Define the applied stress on the part to be designed.
3. Assign a distribution function to each variable in the stress
equation and assume a starting value for each, variables are
typically load and dimensions.
4. Generate random variates from the failure criterion distribution
and from each of the variable distributions.
5. Calculate the stress using the random variate for each variable and
compare that stress with the random variate from the failure criterion distribution.
Whenever the stress exceeds the failure
variate, a failure has occurred.
6. Repeat the last two steps n times, where 1/n=probability of
failure; e.g., a probability of failure of 10 -6 requires 10
6
calculations.
7. If only one failure has occurred in the n calculations, the design is
valid for a probability failure of 1/n. If no failure occurred, or
more than one occurred, adjust the assumed design variables (step
4) and repeat last three steps until only one failure occurs in
simulations.
225