Page 258 - DMTH404_STATISTICS

Statistics

Notes Let

 the state of the system be the number of failed components
  = the failure rate of each component
  = the repair rate

 

j+1 j j 1

(s j) (s j+1)

This looks like an M/M/s/s queue (Erlang Loss system).

 1
 s 1   j 

1 

A  1 P         .
s

 j 0 j!   

 
j+1 j j 1

(n j) (n j+1)

17.10 Summary

 The ability of a system or component to perform its required functions under stated
conditions for a specified period of time

System reliability is a function of:
 the reliability of the components
 the interdependence of the components
 the topology of the components

 Consider a system comprised on n components, where each component is either functioning
or has failed. Define
th
  1, if the i component isfunctioning
x  
i th
  0, if the i componenthasfailed
The vector x = {x , …, x } is called the state vector.
1 n
 Assume that whether the system as a whole is functioning is completely determined by
the state vector x. Define

 1, if the system isfunctioning when the state vector is x
 x
( )  
 0, if the system has failed when the state vector is x
The function f(x) is called the structure function of the system.

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