In the Business Process Management domain, business process modeling is the key technique used to bridge the gap between Information Technology and Management domains, by introducing graphical diagrams understandable by both technical and business stakeholders. Nowadays BPMN (Business Process Model and Notation) models are the most widely-used workflow mapping diagrams, used to document, analyze, improve, and automate organizational activities. Therefore, business process models must be of high quality as ones of the most valuable artifacts for organizational and information systems design and development. This study considers the application of intelligence theory by introducing and using predicates to assess the business process modeling rules fulfillment by BPMN elements. The proposed intelligent information technology assumes BPMN model processing, detection of incorrect elements that violate modeling rules, impact assessment of different element types, quality and error volume measurement, as well as the textual explanations generation for the detected incorrect BPMN elements. The experiments with the large set of business process models are performed, obtained results are analyzed and discussed, conclusions are drawn and the further research is formulated.
way. Such an important BPM technique is used for graphical description of business processes, their analysis and improvement [6].
Business Process Model and Notation (BPMN) offers a set of graphical elements used to describe various workflow aspects, such as events, activities, gateways (i.e. AND, OR, and XOR connectors determining decisions within business process scenarios and the corresponding execution logic), and flows. These BPMN elements were created to bridge the gap between IT and management domains, understandable by both technical and business users [6]. BPMN models assume workflows triggered by start events, finished by end events. Other activities and events, occurring within the workflow, are represented by tasks (or sub-processes) and intermediate events respectively [6].
Hence, business process modeling is a key BPM technique, which is used to graphically describe organizational workflows as interrelated models and, therefore, simplify business and IT providers’ communication for the enhancement of the IT systems design, development, and maintenance [7].
Thus, this study aims to improve the quality and reduce the volume of errors, which may occur in business process models, by introducing the corresponding intelligent information technology.
The research object of this study, is the procedure of business process models’ quality and error volume assessment. While the research subject is the intelligent information technology for business process models’ quality and error volume assessment.
In [8] Panayiotou et al., while studying modeling architecture development for Industry 4.0, stressed on the importance of business process modeling for BPM, since it assumes visual description of the organizational activities, events, and decisions via graphical models.
Avila et al. in their study on the modeling guidelines to create high-quality business process models [9] summarized, that such visual representation helps stakeholders to understand, capture, analyze, and improve enterprise business processes.
Business process modeling also allows to improve events monitoring, information control, and assess organizational efficiency [10].
In [11] Haj Ayech et al. discuss the critical importance of business process modeling techniques for the success of any BPM project or its particular goals. Authors of [11] proposed to extend the BPM lifecycle to improve the maintainability of BPMN models, by introducing structural measures based on activities, gateways, network and control-flow features:
NOAJS – Number of Activities, Joins, and Splits; CNC – Coefficient of Network Connectivity;
CFC – Control Flow Complexity.
Moreover, the authors of [11] suggested the use of modeling guidelines (rules), understandability and maintainability measures, as well as validation tools and their own measures. These measures were also applied by Fotoglou [12] et al. in their study on complexity clustering of BPMN models. NOAJS and CFC were considered by Kbaier et al. in [13] to determine respective threshold values for these measures using data mining techniques.
Threshold values for BPMN modeling measures were considered in [14] by Augusto et al. Also in [15] Corradini et al., through the study on consistent BPMN modeling, suggested the use of size and complexity measures to get insights on business process models quality from the architectural perspective.
The use of quality criteria for business process model assessment is considered in [16], authors Dai et al. suggested expert judgement and software engineering measures usage within the study on business process models refactoring and redundancy elimination. In [17] Pavlicek et al. considered the use of modeling rules and best practices to measure business process model quality.
Authors of [18] suggested the gathering structural measures of BPMN models to assess modeling rules conformance and the overall model quality.
Let us consider the rules for consistent business process modeling proposed in [19] and further elaborated in [20]:
Start events should have one outgoing flow.
Intermediate events should have one incoming and one outgoing flow.
Boundary events should have one outgoing flow.
End events should have one incoming flow.
Activities (i.e. task or sub-process) should have one incoming and one outgoing flow. Gateways should have either one incoming and two outgoing flows (i.e. for splits), or two incoming and one outgoing flow (i.e. for joins).
As the artificial intelligence research trend is growing and our basic goal is to formalize the
humancentric analysis of BPMN models and their certain elements, let us apply the intelligence theory’s
method of comparator identification [21]. This indirect identification method is based on predicate
logic, taking any data (signals) as input and providing binary value (0 or 1) on output [21]:
Ρ( , , … , ) = Κ
= ( ),
= ( ), … ,
= ( ) = ,
(
Let us formally describe the set of business process element types as (i.e. start events, end events, intermediate events, boundary events, tasks, sub-processes, AND-gateways, OR-gateways, and XORgateways) [23], | | = 9 (see Table 1). process elements; process elements. is the set of nodes that represents various business process elements, such as events, activities (i.e. tasks or sub-processes), and gateways, ∈ , ∈ [1, | |]; is the set of pools, each of which may contain nodes to define business process boundaries within a model, = ⊆ ∩ ∩ … ∩
= ∅, ∈ [1, | |] ; ⊆
× is the binary relationship that represents sequence flows between business ⊆ × is the binary relationship that represents message flows between business Above, the definition of assumes the set of pools, which elements (i.e. single pools) are subsets of another set of nodes and that these subsets do not intersect – ∩ … ∩ = ∅.
Let us introduce the tuple of business process model elements given in Table 1: ∩ , = 〈 , , , , , ,
〉, , ∈ is the set of start events, is the set of parallel (AND) gateways, ∈ , ∈ [1, | |]; is the set of inclusive (OR) gateways, is the set of exclusive (XOR, as well as complex and event-based) gateways, ∈ ,
Let us apply the intelligence theory [22] and formulate the following predicates to assess business process elements’ correspondence to the modeling rules [20]: ∈ [1, | |].
4. Boundary events:
In 6. Sub-processes: is the number of outgoing sequence flows of the start event ∈ is the number of incoming sequence flows of the end event ∈ is the number of incoming sequence flows of the intermediate event is the number of incoming outgoing flows of the intermediate event ∈ ∈ ; is the number of outgoing sequence flows of the boundary event ∈ . , , , , , ,
= 1, = 1, 1, In 0, = 1 ∧ Out = 1, is the number of incoming sequence flows of the task is the number of incoming outgoing flows of the task ∈ ; ∈ . = 1, In 0, = 1 ∧ Out = 1, is the number of incoming sequence flows of the sub-process is the number of incoming outgoing flows of the sub-process ∈ ; ∈ .
,
In
= 1 ∧ Out
= 2 ∨ In
= 2 ∧ Out
= 1 ,
(
Therefore, by processing BPMN files of business process models as XML documents [23], we may obtain In and Out
numbers of incoming and outgoing sequence flows for each business process model element
∈ , as it is shown in Fig. 2.
Having the collection of business process models , the sets of business process elements are obtained for each processed BPMN model: ∀ ∈ [1, | |]:
= , , .
(
is the sub-set of business process elements ( ) of a certain type ∈ [1, | |] is the particular business process element of a certain type ∈ [1, | |] ⊆ ∈
Hence, by processing the collection of business process models , the following summarized measures can be found: ∀ ∈ : = 1 −
, ∈ [1, | |], ∈ [1, | |]. ∀ ∈ [1, | |]: =
, ∀ ∈ [1, | |]: | | ∈
, is the any sub-set of business process elements of a certain type ∈ [1, | |], extracted from -th BPMN model,
∈ [1, | |].
Let us introduce the definition of a business process modeling error as the violation of a certain
modeling rule (
is the fault rate of business process elements of a certain type ∈ [1, | |].
Let us apply Saaty’s pairwise comparison method [25] to calculate weights of business process Obtained weights may describe the impact of each business process element type on the overall Thus, the following steps should be completed to calculate the weights of BPMN elements’ impact 1. For each pair ( , ), , ∈ [1, | |] of business process element types calculate the ratio based ′ =
Order business process element types by the corresponding fault rates in reverse order and map obtained fault rate ratios ′ onto 1–9 scale [25] using logarithmic Min-Max scaling and round down transformation to obtain the elements placed above the main diagonal of the judgment matrix : = + ln ′ − ln , ∈[ ,| |]
min ′ ln , ∈[ ,| |] max ′ − ln , ∈[ ,| |]
min ′ where = 1 and = 9 according to Saaty’s 1–9 scale. ∙ ( − ) , , ∈ [1, | |], > .
(16) ∀ ∈ [1, | |]:
= ∀ ∈ [1, | |]: = | | | | | | |
∙ | ∙ ∈ ∈ . .
Let us define the business process model quality as the degree to which business process elements
of different types fulfill the modeling rules (
Hence, it becomes possible to assess the “volume” of business process modeling errors or, in other words, “errability” of a business process model: = | | ∏| |
∑| | | | ∏| |
, ∈ [1, | |].
Level of business process modeling rules Level of business process modeling
Calculate the elements placed below the main diagonal of the judgment matrix : = 1
Diagonal elements of the judgment matrix are equal to 1: = 1, , ∈ [1, | |], = .
Calculate weights of each business process element type ∈ [1, | |] using the formula [25]: (17) (18) (19) (20) (21) (22)
Let us apply the Harrington’s scale and desirability function [27] to introduce business process models’ quality and errability levels (see Table 2). Assessment levels for business process models’ quality and errability
Function value The following linguistic variables can be obtained based on quality measures , ∈ [1, | |]: The following linguistic variables can be obtained based on errability measures , ∈ [1, | |]: ∀ ∈ [1, | |]:
= ∀ ∈ [1, | |]: = ⎧ ⎪ ⎨ ⎪ ⎩ ⎧ ⎪ ⎨ ⎪ ⎩ , , , ℎ, , ,
0.2 ≤ , 0.37 ≤ 0.63 ≤ < 0.2, < 0.37, < 0.63, < 0.8, 0.8 ≤
.
< 0.2, 0.2 ≤ , 0.37 ≤ 0.63 ≤ < 0.37, < 0.63, < 0.8, ℎ ℎ
Finally, the proposed procedure of BPMN models’ analysis (Fig. 3) includes the following steps:
1. Extract business process elements and their properties from BPMN files by processing each
model as the XML document (Fig. 2).
2. Assess extracted business process elements’ correspondence to modeling rules (
For each analyzed business process model ∈ [1, | |], the information about elements that do not fulfill the modeling requirements (i.e. that introduce errors) is provided as the set of explanations for various types of BPMN elements Θ: ∃ ∈ : ( ) = 0 having “ with Out( ) outgoing flows found” for ; ∃ ∈ : ( ) = 0 having “ with In( ) incoming flows found” for ; ∃ ∈ : ( ) = 0 having “ with In( ) incoming, Out( ) outgoing flows found” for ; ∃ ∈ : ( ) = 0 having “ with Out( ) outgoing flows found” for ; ∃ ∈ ∪ : ( ) = 0 having “ with In( ) incoming and Out( ) outgoing flows found” for ; ∃ ∈ : ( ) = 0, ∈ { , , } having “ with In( ) incoming and Out( ) outgoing flows found” for .
Therefore, each business process model ∈ [1, | |] containing incorrect elements is provided with the sub-set of respective explanations Θ ⊆ Θ.
The software implementation of the proposed approach is developed using Python programming language. Its activity diagram is demonstrated in Fig. 4.
Gray components on the activity diagram (see Fig. 4) demonstrate used Python modules:
“os” [28] is used to walk over the catalog of BPMN models;
“xmltodict” [29] is used to process BPMN model files as XML documents;
“csv” [30] is used to prepare output results as CSV (Comma-Separated Values) documents.
Others are developed components used to implement particular method’s steps (see Fig. 4):
“rules” is used to detect incorrect business process elements using (
Experiments below are performed using the Camunda’s repository of 3729 BPMN files [31], out of which 3722 were successfully processed and 7 remained with processing errors.
Fig. 5 demonstrates the distribution of extracted BPMN elements by different types.
Using fault rate measures and the Saaty’s pairwise comparison method (15) – (18), the following judgement matrix was obtained:
And the following weights were calculated (Fig. 8) to assume the impact of BPMN element types on the models’ quality.
The Consistency Rate (CR) is less than 0.1 (10%), hence, the judgment matrix (23) is considered to be consistent: (23) (24) (25) =
− | | | | − 1
= 0.01 < 0.1, where
= 1.45 is the Random Consistency Index (RI) suggested by Saaty for | | = 9 [25].
Having the maximum eigenvalue of
= 9.13, the Consistency Index (CI) is found [25]:
The exploratory analysis results of quality and errability measures are demonstrated in Table 3.
Quality Errability Min 0,49 0,00 Q1 (25 percentile) 0,94 0,01
0,96 0,04
Fig. 11 demonstrates the distribution of analyzed BPMN models using Harrington scale linguistic values for quality (21) and errability (22) measures.
Let us summarize the obtained results of BPMN models’ processing and analysis: “Task” is the most widely-used element occurred 32278 times (Fig. 5) in the processed BPMN models; “Task” and “XOR-Gateway” are the most error-prone elements (Fig. 6) – faulty tasks occurred in the dataset 2844 times, while faulty XOR-Gateways occurred 2679 times; however, “Sub-Process” and “Boundary Event” are the most critical elements according to the fault rate measures, followed by gateways of all types – “AND-Gateway”, “OR-Gateway”, and “XOR-Gateway” (Fig. 7); much less critical BPMN elements according to the fault rate measures are “Intermediate Event”, “Task”, “End Event” (Fig. 7); much smaller impact on business process model quality show “Start Event” elements (Fig. 7); in general, sub-processes, boundary events, and gateways of all types (AND, OR, XOR) make over 85% impact of BPMN models’ quality according to the weights (Fig. 8) calculated using Saaty’s pairwise comparison method; the distribution by quality measure ranges demonstrates the most of BPMN models (3309 or 89%) have > 0.9, ∈ [1, | |] (Fig. 9); while the distribution by errability (i.e. error volume) measure ranges demonstrates the same amount of BPMN models (3309 or 89%) have < 0.1, ∈ [1, | |] (Fig. 10); the exploratory analysis results demonstrate minimum quality value of 0.49 and maximum errability values of 0.50 (Table 3); the other interesting exploratory analysis results demonstrate (Table 3): a. 25% of BPMN models have < 0.94 and < 0.01, ∈ [1, | |]; b. 50% of BPMN models have < 0.96 and < 0.04, ∈ [1, | |]; c. 75% of BPMN models have < 0.99 and < 0.06, ∈ [1, | |]; Harrington scale-based estimates of business process models’ quality and errability (Fig. 11) demonstrate: a. 3613 (97.07%) BPMN models are of “Very good” quality – [0.8, 1) and, respectively, of “Very low” errability – [0, 0.2); b. 106 (2.85%) BPMN models are of “Good” quality – [0.63, 0.8) and, respectively, of “Low” errability – [0.2, 0.37); c. and only 3 (0.08%) BPMN models are of “Satisfactory” quality – [0.37, 0.63) and, respectively, of “Moderate” errability – [0.37, 0.63).
Finally, let us consider the example BPMN model from the Camunda’s repository [31]. The one of BPMN models’ version “warenversand_-_english_00f5b29d34c8482d9ec476f554c6dad0.bpmn” of the goods dispatch business process is shown in Fig. 12.
Moreover, the BPMN model in Fig. 12 demonstrates inconsistent use of lanes and pools, e.g. the “Logistic Company” is modeled using lane, while the counterparties are expected to be modeled as pools, communicated via message flows [23].
Table 4 below outlines the following measures of the goods dispatch BPMN model (see Fig. 12). , and IER is the incorrect elements rate: = . (27)
Due to the introduced weights that differentiate the impact of various BPMN element types on the business process models’ correctness, the sample model’s (Fig. 12) quality and errability measures are estimated at 0.77 and 0.23 respectively, while the more straightforward measures CER and ERR are demonstrating values of 0.64 and 0.36.
This paper addressed the problem of business process model quality improvement and error volume reducing using intelligent information technology. In particular, the intelligence theory’s method of comparator identification based on predicate logic was applied to assess business process modeling rules fulfillment by different BPMN elements. The BPMN notation is considered as the standard for organization and information system workflow design, essential for BPM and IT domains due to its powerful capabilities of business process documenting, analyzing, improving, and automating.
The proposed approach and intelligent software, implemented as the Python tool, allow to: extract BPMN elements and detect incorrect ones that violate modeling rules; assess impact of different BPMN element types on business process model correctness; assess business process model quality and errability (i.e. error volume) as numeric measures and linguistic variables that correspond to different levels; provide textual explanations for the detected incorrect BPMN elements to assist responsible for business process modeling users. (26)
The results of experiments with 3729 Camunda’s BPMN models [31], generated and summarized by the developed intelligent tool, were analyzed and discussed. Therefore, it is possible to assume the ability of considered intelligent information technology to efficiently handle large enterprise business process model repositories, and further apply it to the analysis of real-world BPMN models.
Future work in this field includes the use of advanced intelligent techniques, such as fuzzy logic and comparator networks, to improve “thinking mechanisms” of the proposed technology. Deeper analysis of BPMN elements (e.g. various events’ behavior, data stores, pools and lanes, message flows), as well as of business process semantics, should be conducted in the future work.
The authors have not employed any Generative AI tools.