Simulation of products classification system for manufacturing cost forecasting/Gaminiu klasifikavimo sistemos procesui ir gamybos sanaudoms prognozuoti sukurimas.
Stasiskis, A. ; Cikotiene, D. ; Bargelis, A. 等
1. Introduction
Today's struggle competition in marketplace demands permanent
increase of productivity through new products and processes development.
The computerized actions of this task like CAD, CAPP, ERP, CAM and so on
must make a strong support creating and implementing novelties. Product
performance and cost are essential criteria in new product design. A key
part of a product development cycle is the conceptual design phase that
greatly influences the resulting performance, cost, quality, product
manufacturability and life cycle parameters of the product life cycle
[1]. In this phase it is necessary to forecast product or its part
manufacturing time, cost and delivery time to market. The products'
classification system could simplify solving of above mentioned tasks
and seeking the best solutions of product's manufacturing cost and
characteristics in the separate products' class level.
The research objective of this paper is creation of mechanical
engineering products' classification system that could help improve
and simplify its early stage development procedure, in particular,
looking for better product performance and less manufacturing cost. The
developed classification system was tested implementing it into
laboratory and industry for new products and processes development in
virtual reality.
2. Overview of objects classification methods
The mankind uses classification from ancient times. There are many
classification methods in use [2]. All classification methods apply
object parameters to characterize it. Parameters could be qualitative
and quantitative. It is not difficult to classify object that has one or
two parameters. It becomes rigid problem when the object has a lot of
quantitative and qualitative parameters.
There are number of well known standard classification methods [3]:
* neural network method;
* nearest neighbour method;
* decision tree method;
* other methods.
Each method has its own advantages and disadvantages. The biggest
advantage of neural network methods is that they can classify object
with big number of parameters and with high parameter's value
distribution. The disadvantage is that these methods are slow in both
training and application.
Neural network learning procedures and statistical classification
methods are applied and compared empirically in classification of
multisource remote sensing data [4]. Reliability measures are introduced
to rank the quality of the data sources. The data sources are then
weighted according to these rankings in the statistical multisource
classification.
The nearest neighbor method finds the closest object from training
set to the object that should be classified and the decision is made
that object belongs to the nearest neighbour class [5]. The Analytic
Hierarchy Process (AHP) methodology is quite simple and easy to
implement. But object parameters and features must be selected very
carefully. Even one unsuitable parameter (that does not separate
classes) could make the method fail. The presented research is for
suppliers' selection for different manufacturing industries. It was
concluded that AHP method works well in making decisions for many types
of companies that involve different types of suppliers.
Axis-parallel decision tree methods are based on the tree with
nodes in which each one parameter is compared with some value [6]. If a
parameter has greater value one branch of tree is taken, and if the
parameter has less value--other tree's branch is chosen. When the
last node is passed the decision is made that object belongs to this
certain class. This method is faster than the other above mentioned
methods. The disadvantage of this method is that it is not flexible in
parameter space.
Oblique decision tree methods have some advantages compared with
axis-parallel method [7]. At each node the combination of some
parameters is computed using a set of feature weights specific to that
node and the sum is compared with a considered value. One branch of the
tree is selected. When the last node is passed the decision is made that
the object belongs to this certain class. It is more difficult method to
realize comparing to axis-parallel decision tree methods. The main
advantages of decision tree methods are that they are fast and use only
a few parameters to classify the objects.
The reviewed research papers can not be directly applied for the
classification of mechanical engineering products in their performance
development and considering of economic manufacturing perspective. This
research objective has been solved in this paper.
3. Classification system development
Mechanical product classification system has been developed
adopting the above mentioned objects' classification methods. The
integrated approach of new product and process creation has been used in
this classification method development.
Aiming to accelerate both new product development and manufacturing
engineering at the early stage of itself product and its components
creation, the classification system could be used seeking minimization
of development time and cost. It enables to reduce manufacturing
engineering uncertainty classifying manufacturing products into separate
classes according to the quantitative and qualitative parameters.
Attributes such as mass, size, volume, power, speed and so on could be
applied for products classification. Two means could be used to
characterize an object by certain attribute. First: object k could be
characterized by quantitative attribute [b.sub.kl] (b means object mass
or size or so on). Second: it is possible to affirm that [b.sub.kl] = 1,
if object k satisfies 1 attribute, and [b.sub.kl] = 0, if object k does
not satisfy this condition.
Description of the objects by means of the first or second case
gives the matrix B(m x n) of the symbol [b.sub.kl] where objects
correspond to the lines and attributes--columns. Matrix B will be filled
with different format numbers in first case and similarly with 0 and 1
in the second case. Matrix B in the first case should be changed into
dimensionless matrix [??], where matrix [??] elements should be as
follows:
The mean value of any column 1
[v.sub.l] = [m.summation over (k=1)] [b.sub.kl]/m (1)
Mean square deviation [g.sub.l] from the mean value could be
calculated
[g.sub.l] = [square root of [m.summation over (k=1) [([b.sub.kl] -
[v.sub.l]).sup.2]/m] (2)
Then matrix [??] elements are
[[??].sub.kl] = [b.sub.kl]/[g.sub.l] (3)
Also the weight factor vector R([r.sub.1], ..., [r.sub.1], ...,
[r.sub.n]) is used. It relates the importance of component
characteristics with comparison with other attributes. The ratio of
[l.sub.1] and [l.sub.2] is expressed as [r.sub.l1]/[r.sub.l2].
Any class of products [S.sub.k] differs from another one by the
number of attributes or by their characteristics. Class [S.sub.k] is
defined by criterion of closeness of adjacent [S.sub.k]; and criterion
of exclusiveness and uniformity of adjacent [S.sub.k]; generalized
criterion which characterizes the level of exclusiveness and uniformity
of all classes.
Closeness criterion of i-th and j-th object is designated
[d.sub.ij]. The calculation depends on matrix B type. If matrix B
belongs to the second type, then
[d.sub.ij] = [n.summation over (k=1)] [d.sup.k.sub.ij] [r.sub.k]
(4)
where k is attribute number; [d.sub.ij] = 1 if i and j objects
possess k attributes, i.e. [b.sub.ik] = 1 and [b.sub.jk] = 1; [d.sub.ij]
= 0 in all other cases.
If matrix B belongs to the first type, then
[d.sub.ij] = 1/[n.summation over (k=1)][([[??].sub.ik] -
[[??].sup.jk]).sup.2] [r.sub.k] + 1. (5)
Bigger [d.sub.ij] values correspond to more close objects. Values
[d.sub.ij] form up matrix D, which is called matrix of closeness.
Attribute of uniformity
[d.sub.sk] = [summation] [d.sub.ij] (6)
where i, j [member of] [S.sub.k].
Uniformity ought is divided into internal (in the class) and
external. Internal uniformity could be expressed
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the
number of pairs of combinations of [S.sub.k] class.
Closeness value of the [S.sub.k] class objects is defined by
[W.sub.k]. But this is not sufficient for the class definition. It is
necessary to know how class [S.sub.k] is related with other objects of a
lot Q. Suppose [[??].sub.k] is a lot of objects do not belonging to the
class [S.sub.k]; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is
the sum of closeness between objects of class [S.sub.k] and objects do
not belonging to that class
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
where i [member of] [S.sub.k], j [member of] [[??].sub.k].
External exclusiveness of the [S.sub.k] class is characterized by
the expression
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
which shows the closeness value of the [S.sub.k] class objects to
the objects not belonging to that class. Difference F([S.sub.k]) =
[W.sub.k] - [[PSI].sub.k] [right arrow] max is the best characteristic
of both class and the quality of the classification.
Mechanical engineering products and their components using the
proposed classification system are classified into separate classes
applying the second type of matrix B. The matrix B of Lithuanian
mechanical engineering products is shown in Table 1. The six different
products and three types of mechanical engineering products'
components are included in the developed matrix B. This matrix presents
manufacturing companies where authors of the paper have made
considerations of products performance and characteristics, processes
capabilities and quality parameters, operations facilities, tooling and
their interfacing both in the early stage of product and process
development, and batch production stage. The carried out consideration
on the modeling of manufacturing processes and manufacturing resources
in virtual reality is based. Modeling objective was the creation and
evaluation of some product and process alternatives. The modeling
objective is searching the better alternative of new products and
processes, and looking for higher productivity and quality. The
forecasting models of processes and definition of manufacturing
resources have been proposed and tested in laboratorial and real
production conditions. The appropriate software has been developed for
manufacturing resources forecasting.
Next step in product classification is to classify components into
subclasses. For the metal mechanical parts (fourth class, Table 1) five
subclasses according to the part complexity have been chosen:
* very complex;
* complex;
* average;
* simple;
* very simple.
Part complexity is defined using design features classifier and
design feature quantity. Design feature (DF) classifier is developed
classifying them into rotational (1.1, 1.2, etc.), and nonrotational
form (2.1, 2.2, etc.) [8]. In this research the object is described
applying the first type matrix B, which is filled with different format
numbers. The matrix is shown in Table 2.
4. Research implementation
The created classifier of mechanical engineering products and
components is implemented in laboratory and Lithuanian industry. It has
two streams of application: 1) for new products design seeking better
performance and manufacturing cost being in separate class level, and 2)
for concurrent process design seeking less manufacturing cost and higher
quality.
New product designers working in one separate class are able to
acquire deep knowledge and best practice in narrow area of activity. It
is easier to create systematical product design methodology solving
trade-offs among product properties and characteristics, which is
closely related with product's value. This research considers the
second stream and is related with product manufacturing cost and quality
at the early stage of development.
Trade-off between product performance and manufacturing cost in
nowadays is becoming more and more important. Many alternatives are
necessary to check finding the best final product and process solution.
There are many jobs for process development at the early product
development stage. One from some the newest proposals [9] is divided on
the development of CAPP (Computer aided process planning) system for
mechanical parts applying their dynamic classification and group
technology. This development is for batch production, unfortunately,
does not fit for early product design stage. In this stage
product's designers prefer process and manufacturing cost
forecasting methods because they are more effective and faster, and are
giving sufficient accuracy of defined results. The process and
manufacturing cost forecasting model [10] has been applied for developed
classifier testing. Cost forecasting model was created applying
competitive advanced manufacturing guidelines decreasing direct labor
accounts [11] and assuming that total manufacturing cost consists of
material, burden and labor costs. Iterating statistical data of various
products latter cost and taking into account advanced manufacturing
technologies, the total cost S is defined as follows
S = [k.sub.1]M + [k.sub.2]B + [k.sub.3]L (10)
where M is material cost, B is burden cost, L is labor cost, k are
weight coefficients, the values of which depend on product class and are
defined experimentally.
Experiments and statistics showed that material cost ratio to the
total product cost S comprise from 0.45 to 0.55 for compressors class
products, while to the sheet metal products from 0.75 to 0.85. The
dependence between total product manufacturing cost S and material cost
M in relative money units for compressors class products is shown in
Fig. 1 (assumption is made that material cost is equal to 1.0
conditional money unit). It can be also calculated as follows
S = -4.1087M + 4.0845 (11)
[FIGURE 1 OMITTED]
The material consumption rate [M.sub.1] on the product mass m is
defined as follows [10]
[M.sub.1] = [a.sub.1]m + c (12)
where a1 and c constants (for sheet metal products 1.18 and -0.42,
while for forged steel parts 1.21 and -0.39).
5. Results and discussions
5.1 Forecasting cost of solid metal mechanical part
The mechanical part--compressor's crankshaft (Fig. 2) has been
chosen as an example for the developed classifier testing.
[FIGURE 2 OMITTED]
The part which mass 1.78 kg, is manufactured from a forged work
piece. The closeness matrix D of compressor's crankshaft is found
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Closeness criteria according to the matrix data are defined
(transformed into horizontal row) as follows
[d.sub.ij] = |6 9 6 12 10 11 11 10 10|.
As results show, the biggest closeness criterion is 13, so the part
belongs to "Mechanical part" class (Table 1). The next step in
mechanical product classification is to classify component into
subclasses. The DF number of crankshaft is defined
D = |50 20 30 0 0 14.3 57.1 0 28.6 0|
The closeness criteria
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
As results show, the biggest closeness criteria are 0.0003921 and
part belongs to "Average" class of parts complexity. Such
classification enables designer to use typical manufacturing process
planning and forecast manufacturing costs according to the part
complexity class. The comparison forecasted and experimental data are
illustrated in Table 3.
5.2 Forecasting product's process and manufacturing cost
As a case study 2 compressor class product has been chosen (Table
1). This product is applied as auto compressor in trucks and buses.
There are classified some products' types in accordance of their
properties and characteristics (Table 4). Over 26 different
modifications of compressors are produced in Lithuanian company X
through past twenty years. They are used mostly in trucks like: MAZ,
KAMAZ, VOLVO, IVECO, MANN, SCANIA and busses IKARUS. In this case study
five different truck compressors have been considered. The S has been
forecasted by equation (11) and experimental data by statistics.
The modelling procedure of forecasting cost of mechanical products
and their parts with interaction among all manufacturing system elements
is related. Manufacturing system elements as product and part design,
available suppliers of materials, partners and customers interact during
whole forecasting process. It shows the dynamic of change itself
manufacturing process and its cost fluctuation, and can be visible at
the early design stage. Developers can react and do influence to digital
numbers of cost having data of whole manufacturing system. The modelling
methodology of interaction among elements in complicated technical
system [12] has been applied in this research.
The slope and intercept of regression equation (11) have been
defined by iterating and comparing the industrial statistical data and
analytical calculations of compressor manufacturing process alternatives
and cost.
6. Conclusions and further research
The products classification system and manufacturing cost analysis
has helped to identify where the major material, workforce and burden
sources of cost for new product and process development at the early
stage are to be found. Both actions the product and process development
must be carried out applying concurrent engineering methodology and
increasing designers training, in particular, seeking collaborative
design principles. The main task of product and process designers is to
solve all appearing trade-offs in early stage because decisions in this
stage make leading influence on the manufacturing cost and quality.
Products' classification into different class levels can greatly
decrease the number of trade-offs and release engineers job because they
work in very specialised area and are able to acquire deeper domain
engineering knowledge.
The developed products' classification system presents an
intelligent attribution of different technical objects to the separate
class level according to their parameters and properties. It helps to
decrease the manufacturing cost for products being separated in one and
the same class level. The developed forecasting model of compressor
class products manufacturing cost accomplishes the research objective.
It has its advantages and disadvantages. The advantages are several: the
originated products' classification system has been simultaneously
used for product and process design taking into account the qualitative
and quantitative parameters of their design features (DF). The
mathematical formalization of forecasting model, particularly regression
expressions, aligns the manufacturing cost of the each process
alternative for products being separated on the same class level. The
principal shortcoming of the developed system is the applied interactive
regime of data input for new product that is to be classified.
Briefly it is concluded as followsio
1. The created intelligent products classification system can help
finding new ideas and decreasing the product and process development
time and cost.
2. The developed manufacturing cost forecasting model composes the
minimal error of manufacturing cost 2.89% and biggest error 21.62%.
3. The developed forecasting model has been tested and validated
for confirmation of the theoretical consumptions with the industrialists
experience without any additional preparation at the early design stage
and has potential capability to be increased of the forecasting model
accuracy.
4. The developed products classification system and manufacturing
cost forecasting model help to disclose the regularity of changes the
cost by changing the structure of product and process or use the
strategy 'make or buy' finding cheaper partners.
Future research will be focused on the modelling process iterations
amendment and generation of better products' and processes'
alternatives. These actions on closely collaboration among big range
specialists and experts in industrial and academia organizations must be
grounded. For increase of the collaboration efficiency, the web-based
system when new products' developers, suppliers, manufacturers and
partners are located in different organizations and countries is planned
to use. Appropriate portal could help to acquire experience, good
practice and methods of various nations' creativity and work
culture seeking improved competitiveness, productivity and benefit for
all business partners.
Acknowledgement
This research was partially supported by contract with industry No
8467-2008 "Development of knowledge base for productivity
increasing of CNC Laser cutting and punching machines".
Received December 14, 2010
Accepted May 19, 2011
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A. Stasiskis, Kaunas University of Technology, S. Daukanto 12,
35212 Panevezys, Lithuania, E-mail: andrius.stasiskis@ktu.lt
D. Cikotiene, Siauliai University, Vilniaus str. 141, 78222
Siauliai, Lithuania, E-mail: dalia@tf.su.lt
A. Bargelis, Kaunas University of Technology, Kestucio 27, 44312
Kaunas, Lithuania, E-mail: algirdas.bargelis@ktu.lt
Table 1
Mechanical engineering products' classifier (Matrix B)
Attributes
Domestic Mechatronic Displaying
Class of components appliances component image
TV & components 1 1 1
Compressors 0 0 1
Refrigerators 1 1 0
Solid metal mechanical parts 0 0 0
Non metal mechanical parts 0 0 0
Sheet metal parts 0 0 0
Dies & moulds 0 0 0
Machine tools & tooling 0 0 0
Transport means 0 0 0
Attributes
Cooling Transport Metal processing
Class of components device mean equipment
TV & components 0 0 0
Compressors 0 0 0
Refrigerators 1 0 0
Solid metal mechanical parts 0 0 0
Non metal mechanical parts 0 0 0
Sheet metal parts 0 0 0
Dies & moulds 0 0 0
Machine tools & tooling 0 0 1
Transport means 0 1 0
Attributes
Part from Part from Part from
Class of components metal plastic sheet metal
TV & components 1 1 1
Compressors 0 0 0
Refrigerators 1 1 1
Solid metal mechanical parts 1 0 0
Non metal mechanical parts 0 1 0
Sheet metal parts 1 0 1
Dies & moulds 1 0 0
Machine tools & tooling 0 0 0
Transport means 0 0 0
Attributes
Producess
Has electronic Die or compressed
Class of components parts presform air
TV & components 1 0 0
Compressors 1 0 1
Refrigerators 1 0 0
Solid metal mechanical parts 0 0 0
Non metal mechanical parts 0 0 0
Sheet metal parts 0 0 0
Dies & moulds 0 1 0
Machine tools & tooling 0 0 0
Transport means 0 0 0
Table 2
The number of DF in various subclasses of mechanical parts
Class of The number of DF, %
components
Rotational
1.1 1.2 1.3 1.4 1.5
Very complex 5 5 10 40 40
Complex 10 20 30 20 20
Average 50 25 15 5 5
Simple 70 25 5 0 0
Very simple 90 8 2 0 0
Non rotational
2.1 2.2 2.3 2.4 2.5
Very complex 5 5 5 40 45
Complex 15 25 30 20 10
Average 30 25 17 25 3
Simple 60 30 10 0 0
Very simple 80 10 10 0 0
Table 3
The comparison of forecasted and experimental data
Product name Forecasted cost, [euro] Experimental cost, [euro]
Crankshaft 6.56 6.05
Compressor 1 24.24 23.54
Compressor 2 23.56 25.56
Compressor 3 31.88 36.52
Compressor 4 36.55 46.63
Compressor 5 45.81 52.44
Table 4
The main parameters of different compressors
Compressor Number of Mass, Volume, Manufacturing
cylinders kg [cm.sup.3] time, h
No. 1 2 13.8 214 2.22
No. 2 2 13.6 214 2.62
No. 3 2 12.8 214 3.88
No. 4 1 9.9 306 5.27
No. 5 1 12.3 306 5.57
