Page 249 - DMTH404_STATISTICS

Unit 17: System Reliability

Notes
1 4
3
2 5

If each component has reliability p, then


4
r( ) 1 P {all components i C are not functioning} 



p
 j 
 j 1 

4

 1   P{all components i C are not functioning}
j

j 1
2
 1 2(1 p)  2(1 p) 3



p r(p) lower bound
0.8 0.91136 0.90400
0.9 0.97848 0.97800 1 4
3
0.95 0.99478 0.99475
0.99 0.99980 0.99980 2 5

Example:
1. Calculate a lower bound on the reliability of this system. Assume that all components
have the same reliability p.

4

2
5
1
3 7

2
3
2. The m inim al cut sets are {1}, {2, 3}, {3, 4, 5}, and {7}. H ence r  1 – 2(1 – p) – (1 – p) – (1 – p) .
4

2
5
1
3 6

17.5 System Life in Systems Without Repair

th
Suppose that the i component in an n-component system functions for a random lifetime
having distribution function F and then fails.
i

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