Biomedical Engineering Reference
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(
A
)M
1
(M
2
M
3
)
(
B
)M
1
(M
2
M
3
)
(
C
)(M
1
M
2
,M
2
M
3
)
Fig. 6.1
Refinement charts
system. The diagrams use a visual notation loosely based on Statechart [
8
]. A mode
is represented by a box with a mode name; a mode transition is an arrow connecting
two modes. The direction of an arrow indicates the previous and next modes in a
transition. Refinement is expressed by nesting boxes. A refined diagram with an
outgoing arrow from an abstract mode is equivalent to outgoing arrows from each
of the concrete modes. It is also similar to ingoing arrow. In a refinement, nesting
box can be arranged hierarchically and can be represented by basic rules of our
refinement chart (see Fig.
6.2
). Basic rules of refinements are a parallel refinement
[
M
1
(M
2
M
3
...
M
n
−
1
M
n
)
]
, sequential refinement
[
M
1
(M
2
M
3
···
M
n
−
1
M
n
)
]
and nested refinement
[
(M
1
M
2
,M
2
M
3
, ..., M
n
−
1
M
n
)
. Furthermore, refinement charts, which appears in the hierarchical form can
be represented in the sequential or parallel or nesting, or in all sequential, parallel
and nesting ways. A complete system can be represented by using mixing of all
refinement chart notations, means each subsystem can be refined by any rule that is
given in Fig.
6.2
.
Figure
6.1
presents for only three modes (M1, M2 and M3) with different kinds
of refinements. The parallel relationship among several refinement boxes states that
a system operates simultaneously in all the subsystems. For instance, Fig.
6.1
(A)
represents the abstract mode
M
1 and two parallel refinements are represented by
nesting mode boxes
M
2 and
M
3. Transition between these two refinements
M
2
and
M
3 are not allowed. Entry into a parallel refined subsystem requires entry into
all of its immediate child refinement. A transition out of one refinement requires an
exit out of all the refined subsystems in parallel to it. The sequential relationship
among several refinement boxes states that the system operates in at most one of
these subsystems at any time. For example, Fig.
6.1
(B) represents an abstract mode
M
1 and two sequential refinements are presented by the nesting mode boxes
M
2
and
M
3 in two levels of hierarchy, where
M
2 and
M
3 are embedded in
M
1. The
transitions between
M
2 and
M
3 allows the system to go from one refinement to an-
]
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