Page 243 - DMTH404_STATISTICS

Unit 17: System Reliability

Introduction Notes

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

17.1 State Vectors

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
17.1.1 Structure Functions

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 (x) is called the structure function of the system.

17.1.2 The Series Structure

A series system functions if and only if all of its n components are functioning:

...
1 2 3 n
Its structure function is given by
n
x
 ( )   x .
i

i 1
17.1.3 The Parallel Structure
A parallel system functions if and only if at least one of its n components are functioning:

1
.
.
.
n

LOVELY PROFESSIONAL UNIVERSITY 235