Prof. Ahmed Farouk Abdul Moneim
Components are existing in ONE of TWO STATES:
1 WORKING STATE with probability R
0 FAILURE STATE with probability F
R+F = 1
R
RELIABLE
F
FAILURE
Selecting a random number 0<= X<= 1
X lies in the green zone, the component is in State 1 (Working)
Otherwise, the component in State 0 (Failure)
Prof. Ahmed Farouk Abdul Moneim
How to Generate a Sample of Time To Failure (TTF) of a Components
By Monte Carlo Simulation Experiment
Failure Probability
Selecting a Random Number 0<= X <= 1
Put X= Failure Probability anf find TTF
CONSTANT FAILURE RATE
X  1  e   TTF 
e  TTF   1  X
e  TTF  
1
1 X
TTF
1
 1 
TTF    Ln 


1

X
 


X  1 e
Weibull Distribution
e
 TTF
 
 



 TTF

 





 TTF 


  
 1 X

 1
TTF    Ln 
1 X

e
1
 




1
1 X
MINIMUM CUT SETS
1,2 and 3,4
1
3
2
4
1,2 and 3,4 and 1,4 and 2,3
1
3
2
4
1
1,2,3 and 1,2,4 and 1,3,4
2,3,4
2/4
2222
3
4
Prof. Ahmed Farouk Abdul Moneim