Page 246 - DMTH404_STATISTICS

Statistics

Notes For example, the system will work if 1 and 2 are not working, but it can work if either 1 or 2 are
working.
Its structure function is given by

 ( ) max{x ,x }max{x ,x ,x }max{x ,x }max{x ,x ,x }.
x

1 2 1 3 5 4 5 2 3 4
Example:

4

2
5
1
3 7

What are the minimal path sets for this system?
What are the minimal cut sets?

System Reliability

Component Reliability:
p = P{x = 1}.
i i
System Reliability:
r = P{(x) = 1}=E[(x)].
When the components are independent, then r can be expressed as a function of the component
reliabilities:
r = r(p), where p = (p , …, p ).
1 n
The function r(p) is called the reliability function.

Example:
1. The Series System

r( ) P{ ( ) 1}
x

p


 P{x  1 for all i  1, n}
i
n
  p . i

i 1
2. The Parallel System

x
r( ) P{ ( ) 1}
p


 P{x  1 for some i  1, n}
i
n

 1   (1 p ).
i
i 1

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