Chapter 14 Monte Carlo Simulation
14.1 Introduction
• Find several parameters
• Parameter follow the specific probability distribution
• Generate parameter following the probability distribution
14.2 Generation of random number
14.3 generation of random numbers following standard uniform
distribution
• The pseudo random number following standard uniform distribution:
mind by the limitation of computer used.
14.2.2 Random variables with nonuniform distribution
• Distribution function:
)(1 uFx x
Niux ii ..,,.........2,1;ln
14.2.3 Generation of discrete random variable
• X can take n+1 distinct values with mass function pX(xi), the cumulative distribution function is given by:
The discrete random number Xi and Xi+1 can be determined by:
i
jjXiX xpxF
0
)()(
14.3 Generation of jointly distributed random variable
14.3.1 independent variable
Density and distribution function
14.3.3 generation of correlated normal random variables
Vector of mean value
Covariance matrix
Express Xi as:
The mean values and standard deviation:
The mean values of Wj can be determined as
XaW 1
Example 14.9 the torque transmitted by a plate clutch with a single pair of friction surfaces, shown in Fig. 14.6, can be expressed as:
pressureuniformfordD
dDFfT
and
wearuniformfordDFf
T
)(4
)(4
22
33
14.4 computation of reliability
14.4.1 Sampling size and error in simulation
14.4.2 Example: reliability analysis of a straight line mechanism