Hierarchy Process Mining from Multi-source Logs

TELKOMNIKA, Vol.15, No.4, December 2017, pp. 1953~1968
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v15i4.6326  1953
Received August 5, 2017; Revised October 18, 2017; Accepted November 20, 2017
Hierarchy Process Mining from Multi-source Logs
Riyanarto Sarno*, Yutika Amelia Effendi
Jurusan Teknik Informatika, Fakultas Teknologi Informasi, Institut Teknologi Sepuluh Nopember
Kampus ITS Sukolilo, Jalan Raya ITS, Surabaya, Jawa Timur 60111, (031) 5994251
*e-mail: riyanarto@if.its.ac.id
Abstract
Nowadays, large-scale business processes is growing rapidly; in this regards process mining is
required to discover and enhance business processes in different departments of an organization. A
process mining algorithm can generally discover the process model of an organization without considering
the detailed process models of the departments, and the relationship among departments. The exchange
of messages among departments can produce asynchronous activities among department process
models. The event logs from departments can be considered as multi-source logs, which cause difficulties
in mining the process model. Discovering process models from multi-source logs is still in the state of the
art, therefore this paper proposes a hierarchy high-to-low process mining approach to discover the process
model from a complex multi-source and heterogeneous event logs collected from distributed departments.
The proposed method involves three steps; i.e. firstly a high level process model is developed; secondly a
separate low level process model is discovered from multi-source logs; finally the Petri net refinement
operation is used to integrate the discovered process models. The refinement operation replaced the
abctract transitions of a high level process model with the corresponding low level process models. Multi-
source event logs from several departments of a yarn manufacturing were used in the computational
study, and the results showed that the proposed method combined with the modified time-based heuristics
miner could discover a correct parallel process business model containing XOR, AND, and OR relations.
Keywords: Process Mining, Process Discovery, Multi Source Log, Petri Net, Refinement Operation, Time-
based Interval, Time-Based Heuristics Miner, Double Timestamp Event Log
Copyright © 2017 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
In case of business process, optimized business processes is important to reduce
costs. A business process modeling is required in analyzing the varieties of business
process [1]. Several large-scale information systems such as Enterprise Resource
Planning (ERP), Customer Relationship Management (CRM), and Workflow Management
System (WFMS), store information of business processes in the event log which are used for
decision making in the workflow of business process [2]. Event logs contain the information for
all executed activities of a workflow and one of data which can be analyzed in order to get a
complete process model [3]. They give the complete information about when and who is actor
which performed which activity, this matter contains very important information in terms of
execution of business processes [4]. To analyze the business processes based on real
executions from event log data, process mining technique is generally used [5].
Currently, the world of industry begins to give interest in the development of mining process
in regulating the flow of its business processes. Enterprise information systems are constructed
from many components so that they are increasingly complex [6]. For example ERP system,
such as SAP and Odoo, there are dozens of event logs in different department of organizations
for process mining [7]. Therefore the mining process is appropriate to be used for analyzing
cross-organizational workflows and to obtain the process model from event logs from several
departments in an organization. A process mining algorithm can discover the process model of
an organization without considering the detailed process models of the departments and the
relationship among departments. The exchange of messages among departments can produce
asynchronous activities among department process models. The event logs from departments
can be considered as multi-source logs, which cause difficulties in mining the process model.
Discovering process models from multi-source logs is still in the state of the art, therefore this
research proposes a hierarchy high-to-low process mining approach to discover the process

 ISSN: 1693-6930
TELKOMNIKA Vol. 15, No. 4, December 2017 : 1953 – 1968
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model from a complex multi-source and heterogeneous event logs collected from distributed
departments. The proposed method contains three steps: firstly a high level process model is
developed; secondly a separate low level process model is discovered from multi-source logs;
then the Petri net refinement operation is used to integrate the discovered process models.
We explore the distributed process mining from heterogeneous logs using a low-to-high
process mining approach in [8]. This work first separately obtain the process models of each
organization, and then integrate these models using four coordination patterns to obtain the
business process model. This work assumed that those distributed servers are the same, i.e.
they are functionally equal with each other [9]. After we obtain the integrated process model, we
use modified heuristics miner algorithm to discover process model. In this paper, we use
Modified Time-Based Heuristics Miner (MTBHM) algorithm [10]. This modified algorithm is
similar to the original Heuristics Miner; whereas the difference is in how to mine the parallel
activities; the use of direct and indirect activities. Heuristics miner uses direct activities, but
MTBHM algorithm uses both of them, direct and indirect activities [11]. Our experiment results
show that the MTBHM algorithm can discover parallel relation XOR, OR and AND, so that we
can produce complete business process model. Next, we present related work in section II. We
introduce high-to-low process mining and modified time-based heuristics miner in section III. In
section IV introduces a yarn manufacturing business process as a typical case to illustrate our
high-to-low process mining and modified time-based heuristics miner approaches. Finally, we
concludes the paper in section V.
2. Related Works
In the related works, we review works that relate to our proposed method in business
process mining.
2.1. Business Process Model
A set of linked activities which is produced for specific service is the definition of the
business process [10]. Business process has information about where and when the activities
are executed, input and output of activity, initial condition before activity is executed and final
condition after activity is executed [12]. The characteristics of the business process itself are as
follows:
1. Have a specific purpose
2. Have a specific input
3. Have a specific output
4. Utilize resource
5. Have an activity that can be executed in a certain order
6. It can involve more than one organization
Business process model can represents business process correctly. There are a lot of
ways to represent business process model, such as UML, Causal Net, BPEL, BPMN, EPC,
PNML, etc. Each type of model has different characteristic, such as Petri Net uses token to
connect the activity in the business process model, while in Causal Net, the activity can be
connected directly.
2.2. Event Log
In the case of process discovery, there is no prior process model. To discover the
process model, we use an event log as the beginning point of business process model analysis.
Event log is a basic resource that helps provide information about business process activities.
Event log will contain many information, it depends on each organizational information [10].
Generally, event log is divided into three main parts i.e. Case, Trace, and Activity.
a. Case and Trace
A case is a record of events related to a single executed process instance. Case can be
described as the production process of one stuff. Whereas trace records sequence of events
that belong to the same case [10]. For example, there is an event log N:
𝐿 = [
〈𝑎𝑝𝑝𝑙𝑒, 𝑏𝑎𝑙𝑙, 𝑐𝑢𝑝〉45
, 〈𝑑𝑜𝑙𝑙, 𝑏𝑎𝑙𝑙, 𝑐𝑢𝑝〉42
,
〈𝑎𝑝𝑝𝑙𝑒, 𝑏𝑎𝑙𝑙, 𝑑𝑜𝑙𝑙〉38
, 〈𝑑𝑜𝑙𝑙, 𝑎𝑝𝑝𝑙𝑒, 𝑐𝑢𝑝〉22]

TELKOMNIKA ISSN: 1693-6930 
Hierarchy Process Mining from Multi-source Logs (Riyanarto Sarno)
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We get the data about traces and cases in the event log L:
1. Contains 4 traces .i.e. (apple, ball, cup), (doll, ball, cup), (apple, ball, doll), (doll,
apple, cup)
2. Contains 147 cases .i.e. (apple, ball, cup) is executed 45 time, (doll, ball, cup) is
executed 42 time, (apple, ball, doll) is executed 38 time, and (doll, apple, cup) is
executed 22 time.
b. Activity
Activity is part of event log which presents sub of production process of a product.
For example, there are four activities in the event log L= {apple, ball, cup, doll}.
2.3. Mining Parallel Activity using Modified Time-based Heuristics Miner Algorithm
The MTBHM algorithm uses double timestamp event log and involves the direct and
indirect activities contained in the event log. This algorithm can also discover the process
models which contain parallel relations XOR, AND, and OR [10].
2.4.Parallel Relation XOR
XOR is one of types of parallel relation. XOR is divided into XOR-split and XOR-join. If
there are three activities in the event log and only one of them will be executed at the same
time, so this relation is categorized as XOR [10]. All of discovery algorithms can model the
parallel relation XOR [3].
2.5.Parallel Relation AND
AND is one of types of parallel relation. AND is divided into AND-split and AND-join. If
there are three activities in the event log and three of them will be executed all at the same time,
so this relation is categorized as AND [10]. All of discovery algorithms can model the parallel
relation AND [3].
2.6. Parallel Relation OR
OR is one of types of parallel relation. OR is divided into OR-split and OR-join. If there
are three activities in the event log and two of them will be executed all at the same time, so this
relation is categorized as OR [10]. Some discovery algorithms are not able to discover the OR
correctly. Some of them discover this parallel relation as AND-split and the others discover it as
XOR-split [8].
3. Research Method
In this section, we explain about the proposed method, including framework for high-to-
low process mining, an introduction example for the event log, and formal definition of the event
logs.
3.1. Framework for High-to-Low Process Mining
a. Recording Event Logs. While a workflow system runs on several distributed servers, each
server can record the event logs for each activity and store them into a database of event
logs. Such event logs collected from multi-source servers are used for our high-to-low
process mining. An example of event logs will be presented in the following subsection.
b. Developing High Level Process Model. Using the collected event logs, our proposed method
can discover the high level process model of the workflow. The results of this step are in
extended form of Petri nets with abstract transitions.
c. Discovering Low Level Process Model from Event Logs. Using the collected event logs, our
low level process mining method aims to discover the detailed process model for each
abstract procedure in the high level. The obtained low level process models are in the
standard form of Petri nets without any abstract transitions.
d. Integrating Process Model based on Petri Net Refinement Operation. After obtaining both the
high level process model and the low level process model from the distributed event logs, the
Petri net refinement operation is used to refine the abstract transitions with its corresponding
low level models to obtain the integrated model of the whole workflow system.

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3.2. An Introduction Example for the Event Log
During the execution of business process, information of each activity and abstract
procedure are recorded. We have the following explanations for the example event log:
(1) There are two events in the segment which records information about one activity A3 and
one abstract procedure PA1 (recorded as T1 in the event log); (2) The event log of one activity
records the case ID, activity, time stamp, operator, input message and output message. For
example, the operator of A3 is the Consigner, the start time of activity A3 is 09:13 April 14, and
the end time is 09:44 April 14. The input message record of A3 is empty, which means that the
execution of A3 does not need any message from other partners, and its output message is
pm1; (3) there are some differences between the event log of one activity and that of an
abstract procedure. Obviously, the log of an abstract procedure also records the case ID,
activity, time stamp, operator, input message, and output message. In addition, the messages
read and written during its execution are also recorded. For example, the messages read of PA1
are pm3, pm6, and pm7, and its write messages are pm2, pm5, pm8, which means that during its
execution PA1 receives messages pm3, pm6, and pm7 from other partners and sends messages
pm2, pm5, and pm8 to others.
3.3. Formal Definition of the Event Logs
We present the formal definitions of the event logs used in this proposed method:
a. Event log of an activity
Alog=(CaseID, Ai, ts, te, operator, Input Message, Output Message), where (1) CaseID
indicates the case which Ai runs in; (2) Ai is the name of activity; (3) ts is the start running
time of activity Ai; (4) te is the end running time of activity Ai; (5) operator is the operator ID
of Ai; (6) InputMessage is the input message set to execute Ai; (7) OutputMessage is the
output message set when finishing Ai.
b. Event log of an abstract procedure
Plog=(CaseID, PAi, ts, te, operator, InputMessage, Output Message, Read Message, Write
Message), where (1) CaseID indicates the case which PAi runs in; (2) PAi is the name of
abstract procedure; (3) ts is the start running time of activity PAi; (4) te is the end running
time of activity PAi; (5) operator is the operator ID of PAi; (6) InputMessage is the input
message set to execute PAi; (7) Output Message is the output message set when finishing
PAi; (8) Read Message is the read message set during the execution of PAi; and (9) Write
Message is the write message set during the execution of PAi.
In the following, both activity and abstract procedure are called by a joint name as the
assignment, which is formalized as ASLog=(CaseID, ASi, ts, te, Operator, Required Message,
Sent Message). It is noting that (1) for an activity, the Required Message and the SentMessage
are same as its Input Message and Output Message; and (2) for an abstract procedure, we
have Required Message=Input Message ∪ Read Message and Sent Message=Output Message
∪ Write Message. For the rest of this paper, we use the term assignment synonymously with
activity and abstract procedure.
In order to obtain complete and correct process models for business process of the
organization, the followings are the steps to be performed:
3.3.1. Step 1. Develop High Level Process Model
High level process model is mainly composed of two functional components. First, to
obtain assignment dependency relations and second, to take these relations as inputs to
construct the final high level process model.
High Level Process Model: ∑ 𝐻𝑃𝑀 is a kind of Petri nets extended with abstract
transitions, i.e. there are two kinds of transitions; to represent the normal activities and to
represent the abstract procedures. To differ from the normal transitions, a double rectangle is
used to represent an abstract transition. For example, a high level process model in Petri net
form is presented in Figure 1, sub 1 means an abstract transition.

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Figure 1. An Example of High level Process Model
3.3.2. Step 2. Discover Low Level Process Model from Event Logs
To refine abstract procedures in a high level process model, we need the complete low
level process models. This step is to mine the low level process model from its corresponding
event logs.
Low Level Process Model: ∑ 𝐿𝑃𝑀 defined is different from a ∑ 𝐻𝑃𝑀 as it does not
contain any abstract transition. Therefore, its firing rule is the same as a standard form of Petri
net. For example, a low level process model in Petri net form is shown in Figure 2.
Figure 2. An Example of Low level Process Model
3.3.3. Step 3. Integrate Process Model based on Petri Net Refinement Operation
Process mining technology is used to separately discover the high level models and low
level models. With the refinement operation, one abstract transition in the high level process
model can be refined by its corresponding low level model.
Refinement Operation: The refinement operation aims to refine the abstract transition by a
∑ 𝐿𝑃𝑀 . The structure of a ∑ 𝐿𝑃𝑀 will replace the abstract transition and other parts in the
original ∑ 𝐻𝑃𝑀. The ∑ 𝐻𝑃𝑀 after refinement is shown in Figure 3. Obviously, the
∑ 𝐻𝑃𝑀 becomes a standard form after refining sub1 with the ∑ 𝐿𝑃𝑀 .
Figure 3. An Example Model after Refinement

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3.3.4. Step 4. Mine using Modified Time-based Heuristics Miner Algorithm
There are three main steps to get a process model from an event log using MTBHM
algorithm [10].
a. Mining Dependency Graph
Mining Dependency Graph will produce matrix dependency measure which is used to
make dependency graph [13]. In Equation (1), we can determine the mining dependency graph:
𝐴 => 𝑤 𝐵 = (
|𝐴> 𝑤 𝐵|−|𝐵> 𝑤 𝐴|
|𝐴> 𝑤 𝐵|+|𝐵> 𝑤 𝐴|+ 2|𝐴||𝑤𝐵|+1
) (1)
where the symbols mean:
𝐴 => 𝑤 𝐵 : dependency from activity A to B
|𝐴 > 𝑤 𝐵| : frequency of activity A and B which follow each other directly
|𝐵 > 𝑤 𝐴| : frequency of activity B and A which follow each other directly
From Equation 1, we get the dependency measure matrix which will be used to make
the dependency graph. However, there are three thresholds which relate to the dependency
measure according to Weijters [14]-[15] and Cnudde [3]:
1. RBT (Relative to Best Threshold)
We can obtain the value of RBT using Equation (2).
𝑅𝐵𝑇 = 𝐴𝑣𝑔 𝑃𝐷𝑀 − (
𝑆𝐷 𝑃𝐷𝑀
2
) (2)
2. POT (Positive Observations Threshold)
This threshold aims to obtain the minimum dependency of all activities in the event log.
3. DT (Dependency Measure)
This threshold aims to consider the edge which will be chosen and put into the process
model. To determine the dependency threshold, we use the formula in Equation (3):
𝑅𝐵𝑇 = 𝐴𝑣𝑔 𝑃𝐷𝑀 − 𝑆𝐷 𝑃𝐷𝑀 (3)
b. Checking Short Loops
In process mining, there is a condition that one activity is executed multiple times in the
event log. This condition is well known as a loop. Short loop is divided into two types; LOL
(length of one loop) and LTL (length of two loop). The formula which is used to calculate the
LOL is in Equation (4).
𝐴 => 𝑤 𝐴 = (
|𝐴> 𝑤 𝐴|
max{|𝐴> 𝑤 𝑋|| 𝑋∈𝑒}
) (4)
𝐴 => 𝑤 𝐴 : dependency of LOL
|𝐴 > 𝑤 𝐴| : frequency of activity A and A which follow each other directly
max{|𝐴 > 𝑤 𝑋|| 𝑋 ∈ 𝑒} : frequency of activity A and X which follow each other directly, where A
is activity in the event log
Meanwhile, using Equation (5) we can calculate the LTL.
𝐴 =>2𝑤 𝐵 = (
|𝐴≫ 𝑤 𝐵|+|𝐵≫ 𝑤 𝐴|
|𝐴≫ 𝑤 𝐵|+|𝐵≫ 𝑤 𝐴|+1
) (5)
𝐴 =>2𝑤 𝐵 : dependency of LTL
|𝐴 ≫ 𝑤 𝐵| : frequency of activity ABA
|𝐵 ≫ 𝑤 𝐴| : frequency of activity BAB
c. Mining Parallel Activities
Mining Parallel aims to calculate the parallel relations in the event log. This method
uses a double timestamp event log and formula in Equation (6).

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𝐴 => 𝑤 (𝐵 ∧ 𝐶) = (
|𝐵 ⪖ 𝑤 𝐶|+|𝐶⪖ 𝑤 𝐵|+2|𝐵||𝑤𝐶|
|𝐴⪖ 𝑤 𝐵|+|𝐴⪖ 𝑤 𝐶|+|𝐵≫>𝑛𝑜𝑡 𝑤 𝐶|+|𝐶≫>𝑛𝑜𝑡 𝑤 𝐵|+1
) (6)
where the symbols refer to:
𝐴 => 𝑤 𝐵 ∧ 𝐶 : parallel measure of activity B and C, where the split is in activity A
|𝐴 ⪖ 𝑤 𝐵| : frequency of activity A and B which follow each other directly
|𝐶 ⪖ 𝑤 𝐵| : frequency of activity C and B which follow each other directly
|𝐴 ⪖ 𝑤 𝐵| : frequency of activity A and B which follow each other directly
|𝐴 ⪖ 𝑤 𝐶| : frequency of activity A and C which follow each other directly
|𝐵||𝑤𝐶| : parallel relation of activity B and C in the event log (counted per case ID)
|𝐵 >>> 𝑛𝑜𝑡 𝑤 𝐶| : frequency of activity B and C which do not follow each other directly
|𝐶 >>> 𝑛𝑜𝑡 𝑤 𝐵| : frequency of activity C and B which do not follow each other directly
After we apply the formula in Equation (6), we get the all relations both sequences and
parallel, then we group the parallel relations into AND, OR or XOR.
𝐴𝑣𝑔 𝑃𝐷𝑀 =
∑ 𝑒 𝑖
𝑛 𝑒
𝑖=1
𝑛 𝑒
(7)
𝐴𝑣𝑔 𝑃𝑀 =
∑ 𝑃𝑀 𝑖
𝑛 𝑃𝑀
𝑖=1
𝑛 𝑃𝑀
(8)
The classification of XOR, OR, and AND are:
a. XOR
𝐼𝑓 𝐴𝑣𝑔 𝑃𝑀 ≤ 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝐷𝑀 𝑡ℎ𝑒𝑛 𝑋𝑂𝑅 (9)
b. OR
𝐼𝑓 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝐷𝑀 ≤ 𝐴𝑣𝑔 𝑃𝑀 ≤ 𝐴𝑣𝑔 𝑃𝐷𝑀 𝑡ℎ𝑒𝑛 𝑂𝑅 (10)
c. AND
𝐼𝑓 𝐴𝑣𝑔 𝑃𝐷𝑀 ≤ 𝐴𝑣𝑔 𝑃𝑀 𝑡ℎ𝑒𝑛 𝐴𝑁𝐷 (11)
𝑃𝐷𝑀 : positive dependency measure
𝐴𝑣𝑔 𝑃𝐷𝑀 : average of PDM value
𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝐷𝑀 : minimum value of PDM value
𝑒𝑖 : arc weight from dependency measure
𝑛 𝑒 : total number of all edges
𝑃𝑀 : parallel measure
𝐴𝑣𝑔 𝑃𝑀 : average of PM value
𝑛 𝑃𝑀 : total number of PM value
4. Results and Analysis
A yarn manufacturing business process is used as a case to illustrate our high-to-low
process mining approaches. Figure 4 shows high level process model of yarn manufacturing
business process.
Step 1. Table 1 shows part of running logs of the high level architecture that involves
one running case, Case1. According to Table I, RequiredMessages and SentMessages of each
assignment can be obtained directly. Taking these running logs as input, the Pre-Set, Post-set,
ReceivedMessage and SentMessage of each assignment are shown in Table 2. After executing
Table 2 as input, the high level process model of yarn manufacturing business process is shown
in Figure 5. The result of high level mining is a high level process model with abstract transitions
that are represented by transition Ai (i = 1, 2, …, 9) and abstract transitions Tj (j = 1,2,3). The
detailed process about these three abstract procedures cannot be obtained at this stage. The
meanings of message places are explained in Table 4.

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Figure 4. High-Level Process Model of Yarn Manufacturing
Table 1. Part of the Running Logs of the High Level Process Model
Step 2. Part of the running logs of the purchase department, the blowing department
and the framing department are shown in Tables 5-7.
a. First, we consider Table 8, the Pre-Set, Post-set, ReceivedMessage and SentMessage
of each assignment, shown in Table 8. Then, by executing Table 8, we can obtain the
low level process model for the purchase department (T1), shown in Figure 6.
b. Second, we consider Table 9, the Pre-Set, Post-set, ReceivedMessage and
SentMessage of each assignment, shown in Table 9. Then, by executing Table 9, we
can obtain the low level process model for the blowing department (T2), shown in
Figure 7.
c. Third, we consider Table 10, the Pre-Set, Post-set, ReceivedMessage and
SentMessage of each assignment, shown in Table 10. Then, by executing Table 10, we
can obtain the low level process model for the framing department (T3), shown in
Figure 8.
Step 3. The low level process models in Figure 6, Figure 7 and Figure 8 are correspond
with the three abstract procedures in Figure 5. Then the abstract transitions T1, T2 and T3 can
be refined by the models in Figure 6, Figure 7 and Figure 8. The refined yarn manufacturing
business process model is shown in Figure 9.
Step 4. Process Mining using Modified Time-based Heuristics Miner Algorithm. We use
the event log in Table 3 for our experiments. The information of the event log consist of the case
ID, the activities, start time and end time and the organisator.
Assignment Activity Pre-Set Post-Set Required Message Sent Message
T1 Purchase {} {t1} {Pm1,Pm2} {Pm3,Pm4}
t1 J {T1} {t2} {Pm3} {Pm2}
t2 K {t1} {t3} {} {}
t3 L {t2} {t4} {} {}
t4 M {t3} {T2} {} {Pm5}
T2 Blowing {t4} {t5} {Pm5} {Pm6,Pm7}
t5 T {T2} {T3} {Pm7} {Pm8}
T3 Framing {t5} {t6} {Pm6,Pm8,Pm11} {Pm9,Pm10}
t6 AA {T3} {t7} {Pm10,Pm9} {}
t7 AB {t6} {t8} (} {Pm11}
t8 AC {t7} {} {} {}

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Table 2. Pre-Set and Post-Set of Each Assignment in the High Level Process Model
Figure 5. High-Level Model Mined for Yarn Manufacturing Business Process
Case ID Activity Time Stamp End Time Organisator Operator
Required
Message
Sent
Message
PP1 T1
20/06/2014
08.32
20/06/2014
13.42
Purchase
Dept
Operator
2
{Pm1,Pm2} {Pm3,Pm4}
PP1 t1
20/06/2014
13.42
20/06/2014
23.41
Spinning
Dept
Operator
1
{Pm3} {Pm2}
PP1 t2
20/06/2014
23.41
21/06/2014
08.16
Spinning
Dept
Operator
1
{} {}
PP1 t3
21/06/2014
08.16
21/06/2014
10.46
Spinning
Dept
Operator
1
{} {}
PP1 t4
21/06/2014
10.46
21/06/2014
16.57
Spinning
Dept
Operator
1
{} {Pm5}
PP1 T2
21/06/2014
16.57
6/21/2014
19:15:56
Blowing Dept
Operator
3
{Pm5} {Pm6,Pm7}
PP1 t5
21/06/2014
19.15
22/06/2014
10.51
Spinning
Dept
Operator
1
{Pm7} {Pm8}
PP1 T3
22/06/2014
10.51
22/06/2014
23.42
Framing Dept
Operator
4
{Pm6,Pm8,Pm1
1}
{Pm9,Pm10}
PP1 t6
22/06/2014
23.42
23/06/2014
04.48
Spinning
Dept
Operator
1
{Pm10,Pm9} {}
PP1 t7
23/06/2014
04.48
23/06/2014
16.44
Spinning
Dept
Operator
1
(} {Pm11}
PP1 t8
23/06/2014
16.44
23/06/2014
23.26
Spinning
Dept
Operator
1
{} {}
Pm1
T1
Pm4
t1
P1
t2
Pm5
T2
Pm7
t5
Pm8
T3
Pm10
P2
t3
P3
t4
Pm3
Pm2
Pm9
Pm6
Pm11
t6
P4 P5 P6
t7
t8

 ISSN: 1693-6930
1962
Table 3. Double Timestamp Event Log
Table 4. Meaning of Each Message
Message Meaning Message Meaning
Pm1 Accept Booking Pm3 Good Preparation notice
Pm2 Goods Arrival Notice Pm4 Deliver Goods
Pm5 Deliver Clumps of Cotton Fiber Pm9 Complete Lap Former for Spinning
Process Notice
Pm6 Processed Rolls Lap Notice
Pm7 Deliver Web Silver Pm10 Deliver Bobbin Roving
Pm8 Deliver Sliver Can Pm11 Bobbin Roving Verification notice
a. Mining Dependency Graph
The event log in Table X generates the matrix in Table XI. We use Equation 1 to obtain
the dependency measure. In Table XII, we obtain the dependency measure matrix. Next, we
need to determine the thresholds using Equation (2) and (3). We get the value of RBT is 0.6645,
POT is 3 and DT is 0.578 with average of PDM is 0.751 and SD PDM is 0.173.
Figure 6. Process Model Mined for the Purchase Department
Pm1
A1.
1
P1.
1
P1.
2
A1.2
P1.3 A1.5
A1.3 P1.8
A1.
9
A1.4
Pm
2
P1.4 A1.6
A1.7 P1.9
Pm4
Pm3
A1.8
P1.10
P1.7
P1.6
P1.5

1963
Table 5. Part of Running Logs of the Purchase Department
Case ID Activity Operator
Required
Message
Sent
Message
PP1 A1.1 Operator 2 {Pm1} {}
PP1 A1.2 Operator 2 {} {}
PP1 A1.3 Operator 2 {} {Pm3}
Table 6. Part of Running Logs of the Blowing Department
Required
Message
Sent
Message
Table 7. Part of Running Logs of the Framing Department
Required
Message
Sent
Message
PP1 A3.3 Operator 4 {Pm6} {Pm9}
PP1 A3.6 Operator 4 {Pm11} {Pm10}
b. Checking Short Loop
Equation 4 and Equation 5 use to calculate matrix of short loops. However, this model
does not have short loop because all of value in frequency short loop are zero.
Figure 7. Process Model Mined for the Blowing Department
t4
Pm5
A2.1
2.3
P1.11
P1.12
A2.2
A2.4
A2.5
P1.13
Pm7
Pm6
P1.15
P1.14 A2.6

 ISSN: 1693-6930
1964
Figure 8. Process Model Mined for the Framing Department
Table 8. Pre-Set and Post-Set of Each Assignment in the Purchase Department
Assignmen
t
Meaning Pre-Set Post-Set
Required
Message
Sent
Message
A2.1 Opposing Spike {} {A2.2} {Pm5} {}
A2.2 Air Current Blowing {A2.1} {A2.3} {} {}
A2.3 Open Clumps of Paper {A2.2} {A2.4} {} {}
A2.4 Cleaning Fiber with Dirt {A2.3} {A2.5} {} {}
A2.5
Cleaning/ Separation Fibers with Dirt and
Material to Make Rolls of Cloth
{A2.4} {A2.6} {} {Pm6}
A2.6 Striking Cotton {A2.5} {} {} {Pm7}
Table 9. Pre-Set and Post-Set of Each Assignment in the Blowing Department
Assignment Meaning
Pre-
Set
Post-
Set
Required
Message
Sent
Message
A3.1
Drawing
Breaker
{} {A3.2} {Pm8} {}
A3.2
Drawing
Finisher
{A3.1} {A3.3} {} {}
A3.3 Lap Former {A3.2} {A3.4} {Pm6} {Pm9}
A3.4 Drafting {A3.3} {A3.5} {} {}
A3.5 Twisting {A3.4} {A3.6} {} {}
A3.6 Winding {A3.5} {} {Pm11} {Pm10}
c. Mining Parallel Activity
Causal matrix is the first thing to be done in this step. The causal matrix is shown in
Table14. We obtain the parallel activities, which are 𝑎 → 𝑤 𝑏 ∧ 𝑑, ℎ → 𝑤 𝑐 ∧ 𝑔, 𝑑 → 𝑤 𝑒 ∧ 𝑓,
𝑔 → 𝑤 𝑒 ∧ 𝑓, 𝑚 → 𝑤 𝑝 ∧ 𝑛, 𝑠 → 𝑤 𝑜 ∧ 𝑟, 𝑡 → 𝑤 𝑢 ∧ 𝑥, 𝑎𝑎 → 𝑤 𝑥 ∧ 𝑧.
The parallel measure is calculated using Equation 6. 𝑎 → 𝑤 𝑏 ∧ 𝑑 = 0.714, ℎ → 𝑤 𝑐 ∧ 𝑔 =
0.5882, 𝑑 → 𝑤 𝑒 ∧ 𝑓 = 0.833, 𝑔 → 𝑤 𝑒 ∧ 𝑓 = 0.73846, 𝑚 → 𝑤 𝑝 ∧ 𝑛 = 0.1333, 𝑠 → 𝑤 𝑜 ∧ 𝑟 =
0.1333, 𝑡 → 𝑤 𝑢 ∧ 𝑥 = 0.5833, 𝑎𝑎 → 𝑤 𝑥 ∧ 𝑧 = 0.53846.
Then, we need to check if the parallel measurement can be averaged using
Equation 8 and 9. Then, we determine parallel relation XOR, OR, and AND using Equation 10,
11, 12. Using Equation 8 and 9, we obtain the average dependency measure is 0.751 and the
minimum dependency measure is 0.37.
a. The average parallel measure 𝑎 → 𝑤 𝑏 ∧ 𝑑 (0.714) and ℎ → 𝑤 𝑐 ∧ 𝑔 (0.5882) is 0.651. This
model uses OR.
b. The average parallel measure 𝑑 → 𝑤 𝑒 ∧ 𝑓 (0.833) and 𝑔 → 𝑤 𝑒 ∧ 𝑓 (0.73846) is 0.786. This
model uses AND.
c. The average parallel measure 𝑚 → 𝑤 𝑝 ∧ 𝑛 (0.1333) and 𝑠 → 𝑤 𝑜 ∧ 𝑟 (0.1333) is 0.133. This
model uses XOR.
d. The average parallel measure 𝑡 → 𝑤 𝑢 ∧ 𝑥 (0.5833) and 𝑎𝑎 → 𝑤 𝑥 ∧ 𝑧 (0.53846) is 0.561.
This model uses OR.
Hence, we can get the final model from Modified Time-based Heuristics Miner in
Figure 10. The meanings of each activity code are: A= Sending PO Number, B= Producing
t5
Pm8
A3.4
P1.17 A3.5 P1.19
A3.1 P1.16
Pm9
A3.2
Pm10
t6
A3.3
Pm11
P1.20
A3.6

1965
Good Orders Sup1, C= Packaging Good Orders, D= Determining PPh and Giving Permission,
E= Paying PPh, F= Producing Good Orders Sup2, G= Packaging Good Orders and Getting PPh
Confirm, H= Sending Good Orders, I= Receiving Good Receive, J= Getting Good Receive,
K= Bale Opening, L= Conditioning of MMP Fiber, M= Blending, N= Opposing Spike,
O= Cleaning Fiber with Dirt, P= Air Current Blowing, Q= Open Clumps of Paper, R= Cleaning/
Separation Fibers with Dirt and Material to Make Rolls of Cloth, S= Striking cotton, T= Carding,
U= Drawing Breaker, V= Drawing Finisher, W= Lap Former, X= Drafting, Y= Twisting,
Z= Winding, AA= Combing, AB= Ring framing, AC= Cone winding.
Table 10. Pre-Set and Post-Set of Each Assignment in the Framing Department
Assignment Meaning Pre-Set Post-Set
Required
Message
Sent
Message
A1.1 Sending PO Number {} {A1.2} {Pm1} {}
A1.2 Producing Good Orders Sup1 {A1.1} {A1.3} {} {}
A1.3 Determining PPh and Giving Permission {A1.2} {A1.4} {} {Pm3}
A1.4 Paying PPh {A1.3} {A1.5} {} {}
A1.5 Producing Good Orders Sup2 {A1.4} {A1.6} {} {}
A1.6 Packaging Good Orders {A1.5} {A1.7} {} {}
A1.7
Packaging Good Orders and Getting
PPh Confirm
{A1.6} {A1.8} {} {}
A1.8 Sending Good Orders {A1.7} {A1.9} {Pm2} {}
A1.9 Receiving Good Receive {A1.8} {} {} {Pm4}
Table 11. Direct Successor of Frequency Matrix
No Value of DM from
activity 1 to activity 2
Value of DM No Value of DM from
activity 1 to activity 2
Value of DM
1 𝐴 => 𝑤 𝐵 0.75 21 𝑀 => 𝑤 𝑁 0.75
2 𝐴 => 𝑤 𝐷 0.8 22 𝑀 => 𝑤 𝑃 0.8
3 𝐵 => 𝑤 𝐶 0.83 23 𝑁 => 𝑤 𝑂 0.75
4 𝐶 => 𝑤 𝐷 0.66 24 𝑂 => 𝑤 𝑆 0.75
5 𝐶 => 𝑤 𝐸 0.5 25 𝑃 => 𝑤 𝑄 0.8
6 𝐶 => 𝑤 𝐻 0.66 26 𝑄 => 𝑤 𝑅 0.8
7 𝐷 => 𝑤 𝐵 0.5 27 𝑅 => 𝑤 𝑆 0.8
8 𝐷 => 𝑤 𝐸 0.75 28 𝑆 => 𝑤 𝑇 0.875
9 𝐷 => 𝑤 𝐹 0.66 29 𝑇 => 𝑤 𝑈 0.8
10 𝐸 => 𝑤 𝐹 0.37 30 𝑇 => 𝑤 𝑋 0.75
11 𝐸 => 𝑤 𝐺 0.66 31 𝑈 => 𝑤 𝑉 0.83
12 𝐹 => 𝑤 𝐸 -0.37 32 𝑉 => 𝑤 𝑊 0.83
13 𝐹 => 𝑤 𝐺 0.8 33 𝑊 => 𝑤 𝑋 0.66
14 𝐺 => 𝑤 𝐵 0.5 34 𝑊 => 𝑤 𝐴𝐴 0.75
15 𝐺 => 𝑤 𝐼 0.83 35 𝑋 => 𝑤 𝑌 0.83
16 𝐻 => 𝑤 𝐼 0.875 36 𝑌 => 𝑤 𝑍 0.83
17 𝐼 => 𝑤 𝐽 0.875 37 𝑍 => 𝑤 𝑈 0.5
18 𝐽 => 𝑤 𝐾 0.875 38 𝑍 => 𝑤 𝐴𝐴 0.8
19 𝐾 => 𝑤 𝐿 0.875 39 𝐴𝐴 => 𝑤 𝐴𝐵 0.875
20 𝐿 => 𝑤 𝑀 0.875 40 𝐴𝐵 => 𝑤 𝐴𝐶 0.875
Table 13. Causal Matrix
INPUT ACTIVITY OUTPUT INPUT ACTIVITY OUTPUT
{} A B, D N O S
A B C P Q R
A D E, F Q R S
B C H S T U, X
D E, F G T U V
E, F G H U V W
H I J T X Y
I J K X Y Z
J K L V W AA
K L M Y Z AA
L M N, P AA AB AC
M N O AB AC {}
M P Q

 ISSN: 1693-6930
1966
Table 12. Dependency Measure Matrix
No Frequency of activity 1
directly followed by activity 2
Frequency
number
No Frequency of activity 1
directly followed by activity 2
Frequency
number
1 |𝐴 > 𝑤 𝐵| 3 21 |𝑀 > 𝑤 𝑁| 3
2 |𝐴 > 𝑤 𝐷| 4 22 |𝑀 > 𝑤 𝑃| 4
3 |𝐵 > 𝑤 𝐶| 5 23 |𝑁 > 𝑤 𝑂| 3
4 |𝐶 > 𝑤 𝐷| 2 24 |𝑂 > 𝑤 𝑆| 3
5 |𝐶 > 𝑤 𝐸| 1 25 |𝑃 > 𝑤 𝑄| 4
6 |𝐶 > 𝑤 𝐻| 2 26 |𝑄 > 𝑤 𝑅| 4
7 |𝐷 > 𝑤 𝐵| 1 27 |𝑅 > 𝑤 𝑆| 4
8 |𝐷 > 𝑤 𝐸| 3 28 |𝑆 > 𝑤 𝑇| 7
9 |𝐷 > 𝑤 𝐹| 2 29 |𝑇 > 𝑤 𝑈| 4
10 |𝐸 > 𝑤 𝐹| 5 30 |𝑇 > 𝑤 𝑋| 3
11 |𝐸 > 𝑤 𝐺| 2 31 |𝑈 > 𝑤 𝑉| 5
12 |𝐹 > 𝑤 𝐸| 2 32 |𝑉 > 𝑤 𝑊| 5
13 |𝐹 > 𝑤 𝐺| 4 33 |𝑊 > 𝑤 𝑋| 2
14 |𝐺 > 𝑤 𝐵| 1 34 |𝑊 > 𝑤 𝐴𝐴| 3
15 |𝐺 > 𝑤 𝐼| 5 35 |𝑋 > 𝑤 𝑌| 5
16 |𝐻 > 𝑤 𝐼| 7 36 |𝑌 > 𝑤 𝑍| 5
17 |𝐼 > 𝑤 𝐽| 7 37 |𝑍 > 𝑤 𝑈| 1
18 |𝐽 > 𝑤 𝐾| 7 38 |𝑍 > 𝑤 𝐴𝐴| 4
19 |𝐾 > 𝑤 𝐿| 7 39 |𝐴𝐴 > 𝑤 𝐴𝐵| 7
20 |𝐿 > 𝑤 𝑀| 7 40 |𝐴𝐵 > 𝑤 𝐴𝐶| 7
Figure 9. Refinement Model for the Yarn Manufacturing Business Process

1967
Figure 10. Final Model from Modified time-based Heuristics Miner
4. Conclusion
We have proposed a hierarchy process mining to discover the process model from a
complex multi-source and heterogeneous event logs collected from distributed departments of a
yarn manufacturing. The method developed a high level process model from multi-source logs,
then discovered separately the low level process models from the event logs of the
corresponding departments. The Modified Time-based Heuristics Miner was employed to
discover the process model containing sequence relations and parallel relations (XOR, AND,
and OR). Further the Petri net refinement operation was used to integrate the high level process
model with the corresponding low level process models. The refinement operation replaced the
abstract transitions of a high level process model with the corresponding low level process
models. Finally, a correct process model in the form of Petri net without any abstract transitions
was discovered.
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