Page 247 - DMTH404_STATISTICS

Unit 17: System Reliability

3. The k-out-of-n System. If p = p for all i = 1, …, n, then Notes
i
r( ) P{ ( ) 1}
x


p

n
 P{  x  k}
i
i 1

n  n 
i

    p (1 p) n i  .
i
i k  

The Bridge Structure
Assume that all components have the same reliability p.
p r(p)
0.8 0.91136
0.9 0.97848 1 4

0.95 0.99478 3
2 5
0.99 0.99980

System Reliability

Theorem 1. If r(p) is the reliability function of a system of independent components, then r(p) is
an increasing function of p.

Example: Communications System

Suppose we are concerned about the reliability of the controller, server and transformer. Assume
that these components are independent, and that
p = .95
controller
p = .96
server
p = .99
transformer

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