=Paper=
{{Paper
|id=Vol-247/paper-12
|storemode=property
|title=A weighted coupling metric for business process models
|pdfUrl=https://ceur-ws.org/Vol-247/FORUM_11.pdf
|volume=Vol-247
|dblpUrl=https://dblp.org/rec/conf/caise/VanderfeestenCR07
}}
==A weighted coupling metric for business process models==
https://ceur-ws.org/Vol-247/FORUM_11.pdf
41
A weighted coupling metric for
business process models
Irene Vanderfeesten1 , Jorge Cardoso2 , Hajo A. Reijers1
1
Technische Universiteit Eindhoven, Department of Technology Management,
PO Box 513, 5600 MB Eindhoven, The Netherlands
{i.t.p.vanderfeesten, h.a.reijers}@tm.tue.nl
2
University of Madeira, Department of Mathematics and Engineering,
9000-390 Funchal, Portugal
jcardoso@uma.pt
Abstract. Various efforts recently aimed at the development of quality
metrics for process models. In this paper, we propose a new notion of
coupling, which has been used successfully in software engineering for
many years. It extends other work by specifically incorporating the effects
of different types of connectors used on a process model’s coupling level.
1 Introduction
Quality metrics in software engineering have shown their potential as guidance
to improve software designs and make them more understandable and easier to
maintain. Since business process and software program designs have a lot in com-
mon [7,9], the adaptation of quality metrics to the business process design area
seems worthwhile. Several researchers already identified the potential for these
business process metrics [1,4,5]. We adopted a classification of quality metrics
into five categories from software engineering [2,8]: (i) coupling, (ii) cohesion,
(iii) complexity, (iv) modularity, and (v) size. Together with cohesion, coupling
is considered to be the most important metric [8]. In this paper we present a
coupling metric for business process models.
2 A weighted coupling metric
The definition we use for coupling is taken from the definitions found in the soft-
ware engineering area [2,3]: Coupling measures the number of interconnections
between the activities in a process model. The degree of coupling depends on
how complicated the connections are and also on the type of connections between
the activities.
So far, only a small number of researchers have developed coupling metrics for
business processes [6,7]. However, they have not considered the different types
of coupling in business processes, as perhaps seems logical on the basis of the
definition of coupling that is used in the software engineering field. The contri-
bution of this paper is a new coupling metric, based on the existing ones [6,7,9]
42
and inspired by software metrics, which weights different connections between
activities (e.g. AND, OR, XOR). Our coupling metric CP counts all pairs of
activities in a process model that are connected to each other:
t1 ,t2 ∈T connected(t1 , t2 )
CP =
|T | ∗ (|T | − 1)
where connected(t1 , t2 ) =
⎧
⎪ 1 , if (t1 → t2 ) ∧ (t1 = t2 )
⎪
⎪
⎪
⎨1 , if (t1 → AND → t2 ) ∧ (t1 = t2 )
m n
m
1
n
(2 −1)·(2 −1) + (2(2m−1)·(2 −1)−1 1
−1)·(2n −1) · m·n , if (t1 → OR → t2 ) ∧ (t1 = t2 )
⎪
⎪ 1
⎪
⎪ , if (t1 → XOR → t2 ) ∧ (t1 = t2 )
⎩ m·n
0 , if (t1 = t2 )
in which t1 and t2 are activities, m is the number of ingoing arcs to the connec-
tor, and n is the number of outgoing arcs from the connector.
Each branch between two activities receives a weight according to the type of
connection. This weight is based on the probability that the particular branch
is executed. Because we often do not know about the probabilities for execu-
tion of certain branches in a model at runtime, we assume they are uniformly
distributed. The weights for each branch can then be determined as follows:
– the AND is the strongest binder, because every branch of the AND con-
nector is followed in 100% of the cases. Thus, the probability of following a
particular branch is 1. Figure 1(a) presents a small process model with an
AND-constructor. After A has been executed, always B and C have to be
executed as well. Therefore, the branch from A to B and the branch from A
to C both have a probability of 1 to be followed (and thus a weight of 1).
– the XOR is the weakest binder, because in any case only one of the branches
1
is followed. Thus, the probability of following a particular branch is m·n ,
where m is the number of ingoing branches and n is the number of outgoing
branches. The process model in Figure 1(c) includes two alternatives: either
the branch of A to B is followed, or the branch from A to C. Both cannot be
followed at the same time. Because of our assumption that the two branches
1
have an equal likelihood of being followed, their probability is 1·2 = 12 . And
thus, the weight of each branch in the XOR case of Figure 1(c) is 12 .
– the OR must have a weight in between the AND and XOR, since one does
not know upfront how many of the branches will be followed. It could be that
they are all followed (cf. AND situation), that only one branch is followed (cf.
XOR situation), but it could also well be that several branches are followed.
The weight of an arc is therefore dependent on the probability that the arc is
followed. In case of an OR there are (2m −1)·(2n −1) combinations of arcs that
can be followed. One of them is the AND situation, for which the probability
1 (2m −1)(2n −1)−1
then is (2m −1)(2 n −1) ∗ 1. All the other combinations ( (2m −1)(2n −1) ) get the
1
weight of an XOR ( m·n ). Thus, in total, the weight of an arc going from one
43
activity to another activity via an OR connector can be calculated by:
1 (2m −1)·(2n −1)−1 1
(2m −1)·(2n −1) + (2m −1)·(2n −1) · m·n . Figure 1(b) shows an example. The
1 2
1 (2 −1)·(2 −1)−1 1 2
weight for each connection is: (21 −1)·(2 2 −1) + (21 −1)·(22 −1) · 1·2 = 3 .
A A A
AND OR XOR
B C B C B C
(a) cp = 0.333 (b) cp = 0.222 (c) cp = 0.167
Fig. 1. Some examples of business process model (fragments) and their value for the
coupling metric.
A B
ABCDEFG
A 0 0 23 0 0 0 0
\/
C B 0 0 23 0 0 0 0
C 0 0 0 12 21 0 0
X
D 0 0 0 0 0 0 0
D E E 0 0 0 0 0 1 1
/\ F 0 0 0 0 0 0 0
G 0 0 0 0 0 0 0
F G
Fig. 2. An example EPC process model and a table containing the weighted values of
the connections between the activities of the process model
Example - In Figure 2 an example process model is shown, represented in the
EPC modelling language. Next to the figure a table shows the weights of the
connections. The total coupling for this process model then is:
2
+ 23 + 12 + 12 + 1 + 1
CP = 3 = 0.103
7∗6
44
3 Conclusion
The development of business process metrics to evaluate business processes is
only a recently emerging area of research. In this paper we presented a coupling
metric that deals with the different types of connections that can exist between
the activities in a process model (e.g. AND, OR, XOR). We believe these business
process metrics can help to identify problems in a process model and design
process models that are easy to understand and maintain. Further empirical
work will be necessary to investigate these presumptions.
Acknowledgement
This research is partly supported by the Technology Foundation STW, applied
science division of NWO and the technology programme of the Dutch Ministry
of Economic Affairs.
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