Download Chapter 14 Monte Carlo Simulation

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:
x  Fx1 (u )
xi   ln ui ;
i  1,2,..........., N
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:
i
FX ( xi )   p X ( x j )
j 0
The discrete random number Xi and Xi+1 can be
determined by:
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
W  a  X
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:
T
Ff
(D  d )
4
for
uniform wear
and
Ff D 3  d 3
T
( 2
)
2
4 D d
for uniform
pressure
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