Chapter 14 Monte Carlo Simulation

1. Chapter 14 Monte Carlo Simulation

2. 14.1 Introduction • Find several parameters • Parameter follow the specific probability distribution • Generate parameter following the probability distribution

3. 14.2 Generation of random number

5. 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.

7. 14.2.2 Random variables with nonuniform distribution • Distribution function:

14. 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:

18. 14.3 Generation of jointly distributed random variable 14.3.1 independent variable Density and distribution function

25. 14.3.3 generation of correlated normal random variables Vector of mean value Covariance matrix

26. Express Xi as: The mean values and standard deviation:

27. The mean values of Wj can be determined as

29. Example 14.9 the torque transmitted by a plate clutch with a single pair of friction surfaces, shown in Fig. 14.6, can be expressedas:

32. 14.4 computation of reliability

34. 14.4.1 Sampling size and error in simulation 14.4.2 Example: reliability analysis of a straight line mechanism