=Paper=
{{Paper
|id=Vol-3736/paper6
|storemode=property
|title=Post-press product quality assessment models for the IIoT system
|pdfUrl=https://ceur-ws.org/Vol-3736/paper6.pdf
|volume=Vol-3736
|authors=Bohdan Durnyak,Petro Shepita,Lyubov Tupychak,Yurii Petriv,Julia Shepita
|dblpUrl=https://dblp.org/rec/conf/icyberphys/DurnyakSTPS24
}}
==Post-press product quality assessment models for the IIoT system==
https://ceur-ws.org/Vol-3736/paper6.pdf
Post-press product quality assessment models for the
IIoT system⋆
Bohdan Durnyak1,†, Petro Shepita1,∗,† Lyubov Tupychak 1,,† Yurii Petriv1,† Julia
Shepita1,†
1 Ukrainian Academy of Printing, Pid Goloskom str., 19, Lviv, 79020, Ukraine
Abstract
This study proposes a method for building a model of assembly quality factors by implementing a
factor ranking approach. The method considers the relationships between factors, their types, and
the expert weights assigned to each type. The reliability of the obtained models confirmed, supported
by the implementation of a universal set of values and corresponding linguistic terms for each
linguistic variable of the assembly stage. A model of logical derivation constructed, reflecting factor
classification and the process of forming forecasted quality indicators for small-volume editions
production at the VSHRA. The study also involves calculating membership functions of linguistic
variables and constructing graphs to illustrate the relationships between parameters of the linguistic
variables and values of the membership functions. Additionally, a fuzzy knowledge base designed,
and mathematical models for forecasting assembly quality were developed using expert evaluations
of fuzzy logical statements. Fuzzy logic equations derived to establish relationships between input
and output data membership functions. These findings provide a foundation for developing a module
to assess the production process quality within the industrial Internet of Things system of a printing
company.
Keywords
factor ranking, assembly quality, linguistic variables, fuzzy knowledge base, fuzzy logic, industrial
Internet of Things, printing company, printing machine.1
1. Introduction
Trends in the development of the printing industry indicate that the circulation of publications
is constantly decreasing with a simultaneous increase in their nomenclature. Production time
reduced, product quality requirements are increasing, thinner and lighter paper is used while
reducing its costs, and the finishing of printed products is becoming more complicated and
improved. Global manufacturers of post-press equipment, such as Muller Martini, Heidelberg,
Hohner, Osaka, Purlux and others, work in such realities, creating modern automated flow lines,
which include insert-sewing-cutting units (VSHRA). They satisfy the needs of the market by
ICyberPhyS-2024: 1st International Workshop on Intelligent & CyberPhysical Systems, June 28, 2024, Khmelnytskyi,
Ukraine
∗ Corresponding author.
† These authors contributed equally.
durnyak@uad.lviv.ua (B. Durnyak); pshepita@gmail.com (P. Shepita); ltupychak@gmail.com (L. Tupychak)
yuriy.petriv@gmail.com (Yu.Petriv) juliashepita@gmail.com (J. Shepita)
0000-0003-1526-9005 (B. Durnyak); 0000-0001-8134-8014 (P. Shepita); 0000-0002-0963-3360 (L. Tupychak); 0009-
0005-0547-9801 (Yu.Petriv);0009-0009-0325-0201 (J. Shepita)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
strictly performing the necessary operations and shortening the time intervals between them
as much as possible. The most effective is the application of VSHRA for the release of small-
volume editions complete with attachments.
The technological process of the production of small-volume publications (TPVMV) at
VSHRA is equipped with post-operational machines that perform systematic operations, and
the quality of production of small-volume publications (ML) depends on many heterogeneous
factors. The properties of the materials used, modes of operation, design features of post-
operative machines of the VSHRA and their individual elements determine them.
The integration of the entire complex of printing equipment into a single information system
of control and management allows for continuous production of orders and assessment of their
quality at all stages of the technological process.
Based on the above, there is a need to develop models for assessing the quality of the
insertion-sewing-cutting unit in IIoT, which will allow not only to ensure quality control, but
also to forecast the technological process when planning production tasks.
2. Researching the state of the problem and setting a task
To correctly solve the problem of quality prediction, it is necessary to study a large number of
factors and take into account the variety of their characteristics, since the factors can be
quantitative (block thickness, paper moisture, paper density), qualitative (type of wire material,
quality of notebook preparation, knife sharpness) and binary . Under such circumstances, the
relevance of the problem of building expert systems designed to solve informal problems arising
at various stages of scientific research and engineering and technical activity becomes obvious
[1-3]. Based on the analyzed literature [1, 2], it was established that quality control mainly takes
place visually without taking into account the human factor. In addition, apply the described
requirements to various types of printing products to a limited extent [4, 5].
The above data indicate the absence of research results focused on forecasting and quality
management of the production [6] of small-volume publications at the VSHRA, based on the
establishment of factors and prioritization of their influence on the studied processes, the design
of alternative options for their implementation, a priori calculation of the prognostic integral
quality indicator.
3. Theoretical information about the research object
The market offers VSHRA (Saddle-Stitch Binding Machines) with varying productivity and
configurations. Different models of VSHRA have different formats for incoming booklets,
finished product formats, and operating speeds [7, 8, 9].
The productivity of modern machines exceeds 20,000 copies of finished products per hour.
For example, Heidelberg offers several options. The Stitchmaster ST 300 operates at speeds up
to 13,000 cycles per hour with a maximum of 16 feeder sections. Another model, the
Stitchmaster ST 100, has slightly lower productivity (up to 9,000 cycles per hour) and can be
equipped with four double feeder sections. In 2000, a new model, the Stitchmaster ST 400, was
introduced. This VSHRA has six stitching heads that can stitch blocks up to 12 mm thick. The
machine features a high degree of automation, including a mechanism for automatic format
adjustment. The feeder sections are modular, and the operating speed has been increased to
14,000 cycles per hour. Additionally, when stackers (pile forming modules) and a packing
machine are connected to the VSHRA, the finished products can be immediately sent to the
warehouse or the customer. One drawback of VSHRA is that it is only used for assembling
blocks by insertion, so the volume of publications, even printed on thin paper, does not exceed
128 pages [10].
In addition to the main operations—automatic block assembly by insertion, cover folding,
wire stitching (2, 4, 6, 8 stitching heads), and three-side trimming of finished brochures—VSHRA
machines offer additional options such as central knife cutting of double brochures, card
pasting, CD insertion, and other products [11, 12].
Modern VSHRA machines can have up to 40 automatic booklet feeding sections (feeders), as
seen in models like Muller Martini Tempo 22 and Muller Martini Primera 160. However,
typically, lines consist of 4-8 automatic feeders. Feeders can supply pre-prepared booklets with
a positive (or negative) shingling—opened by hooks, and non-shingled booklets—opened by a
pair of vacuum suckers. When preparing for operation, feeders must be adjusted according to
the format and thickness of the booklets. Feeders can be horizontal or vertical in design, with
varying formats and speeds. Vertical feeders have a larger capacity and are much more
convenient for loading booklets. To increase productivity and ensure continuous operation,
they can be connected to continuous feeding devices, such as cascade feeders, for example,
Muller Martini 3736 and Muller Martini 3738 [13].
Horizontal feeders work more efficiently with single-fold booklets on thin paper (including
LWC). If a publication needs to include thin inserts (such as tracing paper or designer papers
with advertising modules), both horizontal and vertical feeding stations can be installed in the
line, in the sequence required by the brochure manufacturing technology.
It is not always justified to have a VSHRA with 8 feeders if 6 are sufficient for 98% of the
jobs. However, with a machine equipped with 4-6 feeders, it is sometimes necessary to add 1-2
booklets or folded sheets with advertising inserts made of plastic, cardboard, tracing paper, or
papyrus paper of a completely different format. For this, so-called manual feeding sections and
various auxiliary devices (such as a plastic card gluing device) are used, which have an
additional spot on the transport chain where the operator can insert the needed booklet [14].
These additional devices significantly expand the capabilities of VSHRA, which is very
important given the high market interest in various types of advertising inserts, discs, samples,
cards, and souvenirs [15, 16].
Many brochures, newspapers, magazines, and other printed products have a cover.
Typically, this is a sheet offset printed and cut to format from material thicker than the inner
pages of the future publication. The cover feeder separates a single sheet from the stack, folds
it (some models also feature pre-scoring for inner/outer creasing), giving it the shape of a cover.
It then places it onto the transporter, thereby reducing one technological operation—the folding
of the cover on a folding machine. Therefore, such feeders are also called "folding feeders."
When preparing for operation, feeders must be adjusted according to the format and thickness
of the cover.
Each manufacturer offers cover feeders in their product range. For instance, Muller Martini
has types 1528 and 1529, Heidelberg Stitchmaster has type UFA, Osako has model ORC-305, and
Purlux has ZYDY440E, etc.
After the block is assembled, it enters the stitching station. Here, the block is stitched with
wire using stitching heads (ranging from 2 to 8 heads). The heads can be standard (e.g., HK 75,
Hohner Universal 52/8, Deluxe G8) or designed for loop stitching. For binding blocks, printing
wire or low-carbon steel wire of general use is applied. Technological instructions recommend
using wire with a diameter of 0.4 to 0.7 mm for stitching blocks with a thickness of 0.5 to 5 mm
and a diameter of 0.8 mm for greater thickness. Stitching is done saddle-stitch style [9, 12].
The three-knife trimmer station performs the final operation in the VSHRA, giving the
brochure, magazine, or book its final appearance. Therefore, it is very important for this module
to operate as efficiently as possible without defects according to the required format of the
finished publication.
In addition to trimming the finished brochure on three sides, three-knife trimmer stations
can be equipped with additional knives for cutting double brochures [16] or perforation. Each
manufacturer has several models of three-knife trimmer stations with which they equip their
VSHRA. For Muller Martini, these include models 890, 1522, and more modern models 0304,
0449, 0459. For Heidelberg, these are the TR models (TR 100, TR 300, etc.).
New-generation VSHRA machines are equipped with automatic setup systems. For example,
Muller Martini equips the VSHRA BravoPlus with the AMRYS system. The AMRYS automatic
setup system controls the thickness of the book block and the feed speed. The parameters of the
adjusted three-side trimming module are stored in the computer memory. The system manages:
synchronization of book blocks, format parameters on the feeder, thickness, feed for trimming,
width, and length. For the feeder, this includes controlling the length, width, and offset for the
booklet opening device with air flow regulation, booklet stop, and synchronization [13, 14].
Depending on the manufacturer, model, and configuration, VSHRA machines are equipped
with sensors and control systems [8-9]: booklet feed/non-feed sensor; block passage sensor;
block completeness sensor; side block thickness gauge; block positioning/misalignment control;
staple presence sensor; automatic quality control system; multiprocessor integrated control
system over an optical network [15, 16].
All VSHRA machines are equipped with transport systems that ensure the passage of the
future publication block from module to module. Booklet transportation in VSHRA is carried
out by thin belts made of modern, completely smooth, anti-static materials with specially
treated edges, preventing the accumulation of paper dust and ink, protecting the product from
unwanted marks and mechanical damage [10].
Table 1 shows the technical characteristics of VSHRA machines popular in the Ukrainian
market from various manufacturers [17, 18, 19].
4. Presentation of the IIoT model of a printing enterprise.
The Industrial Internet of Things integrates information technologies, user data with equipment
data into production and allows machines to communicate with each other (Fig. 1) [20, 21]. As
a result of managing things, devices and machines, printing production becomes autonomous,
flexible, efficient and resource-saving [22].
The traditional model of "supplier-consumer" interaction of the new concept is radically
changing due to the following factors: automation of the process of monitoring and
management of the product life cycle; the organization of effective logical structures that self-
optimize from enterprises - suppliers to enterprises - end consumers, etc.
Thus, the Industrial Internet of Things allows for the organizational and technological
transformation of production, which in turn makes it possible to integrate material, transport,
human, engineering and other resources and to scale software-controlled virtual pools (shared
economy) almost without limits and to provide the user with more than the devices themselves
, and the results of their use (device functions) due to the implementation of cross-functional
production and business processes.
Therefore, the need to create models for assessing the quality of work of the insert-sewing-
cutting unit is one of the necessary factors for the implementation of end-to-end production
and business processes.
Table 1
Technical characteristics of VSHRA machines popular in the Ukrainian market from various
manufacturers
Format, mm
The maximum Number of
Quantity
Model thickness of the sewing machines, Speed, cycles/h.
Company, country outlays, max
max. min. brochure max (cycles/min.)
Hohner, HBS 7000 390×350 105×130 8 8 4 7000
Germany
HBS 10000 400×350 130×105 12 12 4 10000
Heidelberg, SТ 100 355×311 128×92 10 4 4 9000
Germany
SТ 300 480×320 128×92 15 6 6 13000
SТ 500 500×330 128×80 12 16 6 13000
Muller-Martini, Presto II 365×305 93×60 10 6 6 9000
Switzerland
Primera 480×320 90×80 13 16 8 14000
Primera 160 480×320 105×74 13 40 8 16000
Tempo E220 340×260 115×90 13 40 4 22000
Supra 340×260 115×90 13 30 4 30000
PURLUX, NOVA 10 450×311 158×100 8 6 14 10000
China
NOVA 12 480×320 153×108 10 6 14 12000
Figure 1: Basic IIoT model of a printing enterprise.
5. Factors influencing the quality of production of publications at
VSHRA
The technological process for manufacturing small-volume publications (TPMVP) on VSHRA
(Saddle-Stitch Binding Machines) is implemented using operational machines that perform
sequential operations, namely: block assembly 1, cover folding 2, block stitching with wire 3,
three-side trimming 4, which can be represented by a structural diagram (see Fig. 2). Thus,
TPMVP and operational machines are complex systems where the quality of small-volume
publications depends on many factors. These factors are determined by the properties of the
materials used, operating modes, the design features of the VSHRA operational machines, and
their individual elements, among others. The importance of each factor determines the weight
of the factor or the degree of its influence on the final result and allows for the prediction of
product quality.
Figure 2: Structural Diagram of the Main Operations for TPMVP on VSHRA.
The task of predicting the quality of TPMVP at the output of VSHRA is solved based on the
evaluation of defined factors and is considered as finding the mapping
𝑋𝑋 ∗ = (𝑥𝑥1∗ , 𝑥𝑥2∗ , … , 𝑥𝑥𝑛𝑛∗ ) → 𝑑𝑑𝑗𝑗 𝜖𝜖𝜖𝜖 = (𝑑𝑑1 , 𝑑𝑑2 , … , 𝑑𝑑𝑛𝑛 ), (1)
where X* - is the set of factors affecting the quality of small-volume publications (SVP), and
D is the set of predicted quality outcomes for SVP.
To correctly solve the quality prediction task, it is necessary to study a large number of
factors and consider the variety of their characteristics, as the factors can be quantitative (e.g.,
block thickness, paper humidity, paper density), qualitative (e.g., type of wire material, quality
of booklet preparation, knife sharpness), and binary.
Under these circumstances, the relevance of building expert systems to solve unstructured
problems that arise at various stages of scientific research and engineering activities becomes
evident [23, 24].
5.1. Calculation of the membership functions of the selection factors of small
volume editions.
The problem of any technological process remains the numerical prediction of the set values of
the parameters of the same process, which a priori would ensure the proper quality of the
investigated process. A well-argued answer to this task can be obtained by using the methods
and tools of the theory of fuzzy sets and linguistic variables [1, 9, 16] for its solution, the main
component of which are membership functions constructed using the term set meanings and
linguistic terms of factors. Among the many methods of determining membership functions,
Saati's method of pairwise comparisons has become the most popular [14, 24]. This method
involves certain difficulties, which are due to the need to find the eigenvector of the matrix of
pairwise comparisons, which is specified using a specially proposed scale. The more the
universal set on which the linguistic term is defined increases, the more difficult the research
becomes.
The method of constructing membership functions [10, 14], which is used in the work, also
uses the matrix of pairwise comparisons of the universal set. However, it differs in that it does
not require the calculation of the eigenvector of the matrix, unlike Saati's method [9].
A method of constructing the membership functions of the factorization factors [8] of fuzzy
sets is proposed. A method based on which linguistic evaluations are formalized not only of all
factors affecting the quality of the process of assembly of small-volume publications, but also
of factors influencing the subsequent stages of production of small-volume publications at the
VSHRA, such as the process of folding the cover, the process of sewing with wire and the
process of trimming with three sides [14]. The hierarchical set of the above stages corresponds
to the model [18] presented in fig. 3.
Figure 3: A model of logical deduction.
Let is a linguistic variable (LZ) that describes the quality of assembly of small-volume
editions at the VSHRA. The quality of the indicator depends on a number of linguistic variables,
which are presented in table 2.14 and can be written in the form of the following ratio:
𝐾𝐾 = 𝑓𝑓𝐾𝐾 (𝑘𝑘1 , 𝑘𝑘2 , 𝑘𝑘3 , 𝑘𝑘4 , 𝑘𝑘5 , 𝑘𝑘6 ), (2)
where k1 - LZ "number of loaded stations"; k2 - LZ "notebook format"; k3 - LZ "number of
complex notebooks in a block"; k4 - LZ "speed of operation of the VSHRA"; k5 - LZ "quality of
preparation of notebooks"; k6 - LZ "operator qualification".
6. Modeling of the technological process of assembly of small-
volume editions at VSHRA
The main goal of this section is to create mathematical models based on the theory of fuzzy
logic [55, 56, 68, 70], which allow predicting the level of quality of the assembly of small-volume
publications based on the known values of the influencing factors. Fuzzy logic equations of
different levels of input and output variables shown in fig. 3. Each fuzzy equation corresponds
to a knowledge base, which is an expert statement about the relationship between fuzzy terms
of input and output linguistic variables in relation (2).
Consider the relation (2). To evaluate the linguistic variables that combine the quality of the
assembly of small-volume editions on the VSHRA (K) with the number of loaded stations (k1),
the format of the notebooks (k2), the presence of complex notebooks in the block (k3), the speed
of the VSHRA work (k4), the quality of the preparation of notebooks (k5) and qualification of
the operator (k6), we suggest using the following system of term sets:
𝑇𝑇(𝐾𝐾) = 〈𝑙𝑙𝑙𝑙𝑙𝑙, 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏, 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎, 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎, 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 ℎ𝑖𝑖𝑖𝑖ℎ〉, (3)
T(𝑘𝑘1 ) = 〈minimum, average, maximum〉,
𝑇𝑇(𝑘𝑘2 ) = 〈small, medium, large〉,
𝑇𝑇(𝑘𝑘3 ) = 〈few, moderate, many〉,
𝑇𝑇(𝑘𝑘4 ) = 〈low, medium, high〉,
𝑇𝑇(𝑘𝑘5 ) = 〈low, medium, high〉,
𝑇𝑇(𝑘𝑘6 ) = 〈𝑙𝑙𝑙𝑙𝑙𝑙, 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎, 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎, 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎, ℎ𝑖𝑖𝑖𝑖ℎ〉,
The fuzzy knowledge base corresponding to relation (2) has the form:
𝐼𝐼𝐼𝐼 ( 𝑘𝑘1 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)𝐴𝐴𝐴𝐴𝐴𝐴 (4)
(𝑘𝑘4 = ℎ𝑖𝑖𝑖𝑖ℎ)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = 𝑙𝑙𝑙𝑙𝑙𝑙)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑙𝑙𝑙𝑙𝑙𝑙)
𝑂𝑂𝑂𝑂 (𝑘𝑘1 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) 𝐴𝐴𝐴𝐴𝐴𝐴
(𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = 𝑙𝑙𝑙𝑙𝑙𝑙) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝐾𝐾 = 𝑙𝑙𝑙𝑙𝑙𝑙),
𝐼𝐼𝐼𝐼 ( 𝑘𝑘1 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) (6)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)
(𝑘𝑘
𝐴𝐴𝐴𝐴𝐴𝐴 6 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝑂𝑂𝑂𝑂 (𝑘𝑘1 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = ℎ𝑖𝑖𝑖𝑖ℎ) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝐾𝐾 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎),
𝐼𝐼𝐼𝐼 ( 𝑘𝑘1 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)𝐴𝐴𝐴𝐴𝐴𝐴 (5)
(𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)
𝑂𝑂𝑂𝑂 (𝑘𝑘1 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) 𝐴𝐴𝐴𝐴𝐴𝐴
(𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = 𝑙𝑙𝑙𝑙𝑙𝑙)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)
𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝐾𝐾 = 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎),
𝐼𝐼𝐼𝐼 (𝑘𝑘1 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚) (7)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝑂𝑂𝑂𝑂 (𝑘𝑘1 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑓𝑓𝑓𝑓𝑓𝑓)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘4 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = ℎ𝑖𝑖𝑖𝑖ℎ) 𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝐾𝐾 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎),
𝐼𝐼𝐼𝐼 (𝑘𝑘1 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑓𝑓𝑓𝑓𝑓𝑓)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘4 = 𝑙𝑙𝑙𝑙𝑙𝑙) (8)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = ℎ𝑖𝑖𝑖𝑖ℎ)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎)𝑂𝑂𝑂𝑂 (𝑘𝑘1 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘2 = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘3 = 𝑓𝑓𝑓𝑓𝑓𝑓)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘4 = 𝑙𝑙𝑙𝑙𝑙𝑙)𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘5 = ℎ𝑖𝑖𝑖𝑖ℎ)
𝐴𝐴𝐴𝐴𝐴𝐴 (𝑘𝑘6 = ℎ𝑖𝑖𝑖𝑖ℎ) 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 (𝐾𝐾 = ℎ𝑖𝑖𝑖𝑖ℎ),
The logical expressions (4) - (8), which describe the fuzzy matrix of values of the assembly
process in table 2, correspond to the following fuzzy logical equations (9) - (13).
Table 2
Fuzzy matrix of knowledge of the assembly process
k1 k2 k3 k4 k5 k6 K
maximum big many high low low
low
maximum big many average low below average
maximum big many average average below average below
average many average low below average average
average
average average norm average average average
average
average small norm average high average
average small norm average average above average above
small few average high above average average
minimal
minimal small few low high above average
high
minimal small few low high high
𝜇𝜇low (𝐾𝐾) = 𝜇𝜇maximum (𝑘𝑘1 )ʌ𝜇𝜇 big (𝑘𝑘2 )ʌ𝜇𝜇 many (𝑘𝑘3 )ʌ𝜇𝜇 high (𝑘𝑘4 )ʌ𝜇𝜇low (𝑘𝑘5 )ʌ𝜇𝜇low (𝑘𝑘6 ) (9)
v𝜇𝜇maximum (𝑘𝑘1 )ʌ𝜇𝜇 big (𝑘𝑘2 )ʌ𝜇𝜇 many (𝑘𝑘3 )ʌ𝜇𝜇 high (𝑘𝑘4 )ʌ𝜇𝜇low (𝑘𝑘5 )ʌ𝜇𝜇 below average (𝑘𝑘6 )
𝜇𝜇 below average (𝐾𝐾) = 𝜇𝜇maximum (𝑘𝑘1 )ʌ𝜇𝜇 big (𝑘𝑘2 )ʌ𝜇𝜇 many (𝑘𝑘3 )ʌ𝜇𝜇 high (𝑘𝑘4 )ʌ𝜇𝜇low (𝑘𝑘5 )ʌ (10)
𝜇𝜇 below average (𝑘𝑘6 )v𝜇𝜇 average (𝑘𝑘1 )ʌ𝜇𝜇 average (𝑘𝑘2 )ʌ
𝜇𝜇 many (𝑘𝑘3 )ʌ𝜇𝜇 average (𝑘𝑘4 )ʌ𝜇𝜇low (𝑘𝑘5 )ʌ𝜇𝜇 below average (𝑘𝑘6 )
𝜇𝜇 average (𝐾𝐾) = 𝜇𝜇 average (𝑘𝑘1 )ʌ𝜇𝜇 average (𝑘𝑘2 )ʌ𝜇𝜇norm (𝑘𝑘3 )ʌ𝜇𝜇 average (𝑘𝑘4 )ʌ (11)
𝜇𝜇 average (𝑘𝑘5 )ʌ𝜇𝜇 average (𝑘𝑘6 )v𝜇𝜇 average (𝑘𝑘1 )ʌ𝜇𝜇small (𝑘𝑘2 )ʌ
𝜇𝜇norm (𝑘𝑘3 )ʌ𝜇𝜇 average (𝑘𝑘4 )ʌ𝜇𝜇 high (𝑘𝑘5 )ʌ𝜇𝜇 average (𝑘𝑘6 )
𝜇𝜇 above average (𝐾𝐾) = 𝜇𝜇 average (𝑘𝑘1 )ʌ𝜇𝜇small (𝑘𝑘2 )ʌ𝜇𝜇norm (𝑘𝑘3 )ʌ𝜇𝜇 average (𝑘𝑘4 )ʌ (12)
𝜇𝜇 average (𝑘𝑘5 )ʌ𝜇𝜇 above average (𝑘𝑘6 )v𝜇𝜇 average (𝑘𝑘1 )ʌ𝜇𝜇small (𝑘𝑘2 )ʌ
𝜇𝜇few (𝑘𝑘3 )ʌ𝜇𝜇 average (𝑘𝑘4 )ʌ𝜇𝜇 high (𝑘𝑘5 )ʌ𝜇𝜇 above average (𝑘𝑘6 )
𝜇𝜇 high (𝐾𝐾) = 𝜇𝜇 average (𝑘𝑘1 )ʌ𝜇𝜇small (𝑘𝑘2 )ʌ𝜇𝜇few (𝑘𝑘3 )ʌ𝜇𝜇low (𝑘𝑘4 )ʌ (13)
high (𝑘𝑘 )ʌ𝜇𝜇 above average (𝑘𝑘 )v𝜇𝜇 average (𝑘𝑘 )ʌ𝜇𝜇small (𝑘𝑘 )ʌ𝜇𝜇few (𝑘𝑘 )ʌ𝜇𝜇low (𝑘𝑘 )ʌ
𝜇𝜇 5 6 1 2 3 4
𝜇𝜇 high (𝑘𝑘5 )ʌ𝜇𝜇 high (𝑘𝑘6 )
To utilize logical equations (9) - (19), it is necessary to define the membership functions for
all fuzzy terms.
The membership functions cannot be used if the input variable varies continuously, meaning
it can take not only the values, but also intermediate ones between them.
To overcome this limitation, we will employ linear interpolation [15].
𝑓𝑓(𝑥𝑥1 ) − 𝑓𝑓(𝑥𝑥0 ) (14)
𝑓𝑓(𝑥𝑥) = 𝑓𝑓(𝑥𝑥0 ) + (𝑥𝑥1 − 𝑥𝑥0 ),
𝑥𝑥1 − 𝑥𝑥0
Thus, we obtain:
𝜇𝜇𝑖𝑖−1 − 𝜇𝜇𝑖𝑖 (15)
μ(𝑘𝑘1 ) = 𝜇𝜇𝑖𝑖 + (𝑘𝑘 − 𝑢𝑢𝑖𝑖 ),
𝑢𝑢𝑖𝑖−1 − 𝑢𝑢𝑖𝑖 1
The membership functions of the variables for the assembly stage are presented in Appendix B.
Based on the obtained term sets with normalized values of membership functions at five
division points of the universal set, we will form tables (3 - 8) of linguistic variables for the
defuzzification stage.
Table 3
Membership Functions of the Term Set T(k1) –Number of Loaded Stations
ui , pcs 4 8 16 24 40
𝜇𝜇𝑚𝑚𝑚𝑚𝑚𝑚 (𝑢𝑢𝑖𝑖 ) 1 0,78 0,56 0,33 0,11
𝜇𝜇 average (𝑢𝑢𝑖𝑖 ) 0,56 0,81 1 0,81 0,56
𝜇𝜇max (𝑢𝑢𝑖𝑖 ) 0,11 0,33 0,56 0,78 1
Table 4
Term-set membership functions T(k2) - notebook format
ui , m2 0,004 0,012 0,044 0,088 0,165
𝜇𝜇small (𝑢𝑢𝑖𝑖 ) 1 0,78 0,44 0,22 0,11
𝜇𝜇 average (𝑢𝑢𝑖𝑖 ) 0,14 0,36 1 0,36 0,14
𝜇𝜇 big (𝑢𝑢𝑖𝑖 ) 0,11 0,22 0,44 0,78 1
Table 5
The membership functions of the term set are the number of complex notebooks T(k3)
ui , pcs 1 3 5 8 10
𝜇𝜇few (𝑢𝑢𝑖𝑖 ) 1 0,89 0,67 0,33 0,11
𝜇𝜇norm (𝑢𝑢𝑖𝑖 ) 0,66 0,89 1 0,89 0,66
𝜇𝜇 many (𝑢𝑢𝑖𝑖 ) 0,11 0,33 0,67 0,89 1
Table 6
The membership functions of the term set are the operating speed of the VSHRA T(k4)
ui , cycle/hour 1000 5000 15000 25000 30000
𝜇𝜇low (𝑢𝑢𝑖𝑖 ) 1 0,83 0,54 0,23 0,1
𝜇𝜇 average (𝑢𝑢𝑖𝑖 ) 0,48 0,83 1 0,83 0,48
𝜇𝜇 high (𝑢𝑢𝑖𝑖 ) 0,27 0,48 0,72 0,92 1
Table 7
Membership functions of the term set T(k5) - the quality of the preparation of notebooks
ui , points 1 2 3 4 5
𝜇𝜇low (𝑢𝑢𝑖𝑖 ) 1 0,78 0,56 0,33 0,11
𝜇𝜇 average (𝑢𝑢𝑖𝑖 ) 0,56 0,81 1 0,81 0,56
𝜇𝜇 high (𝑢𝑢𝑖𝑖 ) 0,11 0,33 0,56 0,78 1
As a result of substituting degrees of membership into the system of fuzzy logic equations (9) –
(13), the equation of the membership functions is obtained:
𝜇𝜇low (𝐾𝐾) = 0,33ʌ0,22ʌ0,33ʌ0,72ʌ0,11ʌ0,33v (16)
0,33ʌ0,22ʌ0,33ʌ0,92ʌ0,11ʌ0,33 = 0,11v0,11 = 0,11,
𝜇𝜇 average (𝐾𝐾) = 0,81ʌ0,36ʌ0,89ʌ0,92ʌ0,56ʌ0,81v (17)
0,81ʌ0,22ʌ0,89ʌ0,92ʌ0,89ʌ0,80 = 0,36 v 0,22 = 0,36,
𝜇𝜇 high (𝐾𝐾) = 0,78ʌ0,78ʌ0,89ʌ0,54ʌ0,89ʌ0,78v (18)
0,78ʌ0,78ʌ0,89ʌ0,54ʌ0,90ʌ0,78 = 0,54v0,54 = 0,54.,
Table 8
Term-set membership functions T(k6) – operator qualification
ui , points 1 3 6 9 12
𝜇𝜇low (𝑢𝑢𝑖𝑖 ) 1 0,78 0,56 0,33 0,11
𝜇𝜇 average (𝑢𝑢𝑖𝑖 ) 0,56 0,81 1 0,81 0,56
𝜇𝜇 high (𝑢𝑢𝑖𝑖 ) 0,11 0,33 0,56 0,78 1
Thus, the numerical values of the membership functions for the linguistic variable K were
obtained, which will be used to calculate the quantitative value of the assessment of the quality
of the TPVMV at the VSHRA.
Conclusions
As a result of the study, a factor ranking method was implemented to build a model of assembly
quality factors, which takes into account the number and types of relationships between factors
and the different expert weight of each of these types. The obtained result confirms the
reliability of the obtained models. A universal set of values, as well as corresponding linguistic
terms for each linguistic variable of the assembly stage, was formed. A model of logical
derivation was built, the structure of which reflects the classification of factors and the process
of forming a forecasted indicator of the quality of production of small-volume editions at the
VSHRA.
The values of the membership functions of linguistic variables were calculated through the
construction and calculation of pairwise comparison matrices for a set of linguistic terms
relative to the dividing points of the value intervals of the universal set. Graphs were
constructed showing the relationships between the parameters of the LZ from the universal set
and the values of the membership functions of the corresponding linguistic terms.
A fuzzy knowledge base was designed and mathematical models for forecasting the quality
of assembly were developed based on the known values of influencing factors, for the
construction of which expert evaluations of fuzzy logical statements of the "IF-TH" type were
used. Fuzzy logic equations are built that determine the relationship between the membership
functions of input and output data.
The obtained results serve as a basis for creating a module for assessing the quality of the
production process in the industrial Internet of Things system of a printing company.
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