Page 256 - DMTH404_STATISTICS

Statistics

Notes The availability of system at time t, A(t), is given by

A(t) r(A (t), ,A (t))

n
i
 μ λ )t 

 r   e (  λ μ . 
 μ  λ μ  λ 
The limiting availability A is given by

 μ 

A  limA(t) r  . 
t  μ  λ 

Example 1: The Series System
The availability of system at time t, A(t), is given by

n    
A(t)    i  i e (  i   i )t 
i 1    i    i 
 
i
i
and
n 
A   i .
i 1    i
i

Example 2: The Parallel System

The availability of system at time t, A(t), is given by
n   
A(t) 1    i (1 e (  i   i )t ) 


i 1    i 
 
i
and
n 
A    i .
1
i 1    i

i
The average uptime U and downtime D are given respectively by
 μ 
r  
λ
U   μ  
n     μ   μ  
 i i   i   r 0 , i  
r 1 ,

λ
λ
i 1    i   μ    μ  
i

  μ  

 1 r    U
λ
  μ  
D  .
 μ 
r  
λ
 μ  
248 LOVELY PROFESSIONAL UNIVERSITY