knowledge is the only knowledge that helps Marcus
as efficiently as possible. An informal network
identifies which person needs informal help from
another. These two visions are complementary but
the level of granularity in an interdependencies
system is the person while it is the role in the
business process. Thus, it is necessary to map
persons and tasks in order to map the informal
network and the business process. Let’s note
Execute (p,t), where p
∈
Persons and t
∈
Tasks be
the relation denoting this information (p executes
task t). This relation, instanciated thanks to the
interviews, intrinsically maps interdependancies
system and business process.
For our application case, we identified several
executors: Henry (project manager), Earl
(administrative assistant), Wu (administrator) and
Wilhelmina (project co-manager), with Execute
(Henry,Inventory); Execute (Henry,Order), Execute
(Earl, Order), Execute (Wu, Order), and Execute
(Wilhelmina, Order) meaning that Henry, Wu, Earl
and Wilhelmina are co-executors of the task;
Execute
(Henry,Edition); Execute (Henry,Ending validation)
and Execute (Wilhelmina, Ending validation);
Execute (Henry,Reversibilty validation).
One has to note the fundamental distinction
between an executor and a contributor. An executor
appears in the official procedure associated to the
task. For example, according to the official
procedure, Henry is an executor of the Ending
validation task. The official procedure also stipulates
that Henry must ask for Wilhelmina’s validation for
the execution of this task. In this context,
Wilhelmina is also an executor of the task.
Contributors are Steven and Karen (see Figure 3)
who are persons that an executor (Henry) informally
ask for help to. Wilhelmina does not appear in
Figure 3 this shows that she does not ask for help to
anyone. Steven and Karen are the only contributors
for this task.
5.1 Definition and Measurement of
Metrics for Robustness Evaluation
We present here some metrics, at the task level.
Definition (Metric “Global Sensitivity of a
Task”). For a task, this metric counts the number of
persons implied in the task: executors plus
contributors (that appear in the interdependencies
system). The higher is the measure, the riskier is the
task. For a task t, this metric, noted
global_sensitivity(t) is defined by Cardinality(I),
where I is the set defined by
{p’
∈
Persons | Execute(p’,t) or there is p
∈
Persons
such that (Execute(p,t) and Needs(S,p,p’,t))}.
For instance, for the Ending Validation task (see
Figure 3 and the instanciation of the Execute
relation), one has I={Henry, Wilhelmina, Karen,
Steven}, so global_sensitivity(Ending validation) =4.
For the Inventory task (see Figure 2 and the
instanciation of the Execute relation), one has
global_sensitivity(Inventory)=13.
Definition (Metric “Sensitivity by Depth of a
Task”). For a task, this metric measures the
maximal size of a path going from an executor to a
contributor. Intuitively, the larger is the path, the
riskier it is to go from an executor to a contributor (if
a person is missing then the path is “broken”). In the
following, Max(s), where s is a set of integers,
returns the higher element of s (and returns 0 if s is
empty); and Max_path(executor,contributor,S’), where
{executor, contributor}
⊆ Persons and S’ is an
interdependencies system, returns the size of the
larger path from executor to contributor in S’. For a
task t, the sensitivity by depth metric, noted
sensitivity_by_depth(t) is defined by Max(depth_paths)
where depth_paths is the following set:
For instance, for the Ending validation task (see
Figure 3), sensitivity_by_depth(Ending validation)=1.
For the Inventory task (see Figure 2),
sensitivity_by_depth(Inventory)=2.
Now, let’s consider a metric measuring the
density of the informal network underlying a task t.
The density is a well-known metric used in the
social network analysis community. It measures the
number of non oriented connections devided by the
number of possible non oriented connections
(number of non oriented connexion in the
corresponding strongly connected graph). The
highter is the measure, the denser is the network and
so the more tolerant is the network to the absence of
a person, as persons are very connected (they “know
each other”). Contrary to previous metrics,
performing the measurement with the graph
restricted to the considering task would be limitative
because, if persons know each other, that is not
necessary via this specific task execution. We then
define the density for the whole informal network S
limited to the persons (but not the relations) implied
in the task. We decide to measure a dispersion (1-
density) for uniformization with the other metrics
preserving the highter
is riskier convention for
results interpretation.
USING INFORMATION OF AN INFORMAL NETWORK TO EVALUATE BUSINESS PROCESS ROBUSTNESS
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