Information Technology Reference
In-Depth Information
The purpose of the paper is to describe basic reliability structures that can
be put into use in the practical complex systems such as different machines
and mechanisms. The idea of using the reliability structures in human-machine
interface will be develop to obtain better diagnostics, monitoring and control of
various industrial equipment and devices.
2 Reliability Structure - Mathematical Model
A mathematical model of the system reliability is represented by the ordered
pair L N [8], where the
L N is a set of natural numbers assigned to individual
elements of the system, and
is a structural system function that specifies the
system state, depending on the state of its elements. This function takes a value
of 1 when the system is fit for use and 0 when the system is unfit [8].
If
˕
)] is the binary vector of the elements state
describing the reliability condition for all elements, such that
X
(
t
)=[
X 1 (
t
)
,X 2 (
t
)
, ...X n (
t
)takesthe
value 1 when the i-th element is fit, and 0 when the i-th element is unfit at
the time
X
(
t
describes the set of all the vectors state elements, structural
function can be represented as:
t
,and
S
˕
X
t
˕
X 1 (
t
,X 2 (
t
, ...X n (
t
S →{
,
}
[
(
)] =
[
)
)
)] :
0
1
(1)
Function presented in Eq. 1 is defined in literature as structural system
function [11].
The structure of the system can be also represented as a negative structural
system function (analysis-oriented on system failure). Such a function specify
the state of the system depending on the condition of its components, and takes
the value 0 when the system is fit, and 1 when the system is unfit [11].
[ ¯
[ ¯
¯
¯
)] : ¯
˕
¯
X
(
t
)] = ¯
˕
X 1 (
t
)
,
X 2 (
t
)
, ...
X n (
t
S →{
0
,
1
}
(2)
In the section the positive (Eq. 1) and the negative Eq. 2 structural system
functions were described.
3 Reliability Block Diagrams, Path-Sets and Cut-Sets of
the System
The most common way of the reliability structure graphical representation is
a reliability block diagram (RBD). RBD is used to model the reliability struc-
ture of the system by means of lines (connecting links) defining the reliability
relationships between system elements.
In analysis in the assumed decomposition level the individual elements can
be modelled by reliability blocks. In systems modelling some ancillary elements
are used. During complex reliability structures formation the nodes can be used.
In computer reliability analysis systems (by RBD) the use of marginal nodes is
required (start and end node). Basis symbols used in this method are presented
in Tab. 1.
 
Search WWH ::




Custom Search