Abstract The conventional approach is not the best choic e [609565]


Abstract — The conventional approach is not the best choic e
for optimizing the manufacturing process, because of its specific
structure, and of the specific definition of the optimization
problem in its case. During last years, the authors of this paper
have developed the concept of holistic optimization and a
method for its application in manufacturing process
optimization. The method works on the base of two procedures,
aiming the causal identification and the comparative assessment
of the manufacturing jobs. This paper presents a validation of
these procedures by applying them in the case of estimating the
manufacturing cost of roller bearings. The case study used a
database extracted from the industrial environment. Clusters of
condition -variables being the most approp riate for evaluating
the cost are determine d, at first. Then, neighborhoods of the
interrogated cases are extracted from the database and the
proximity function is identified. The estimated ranking (hence
the manufacturing cost) of the interrogated case is found on this
base, eventually.

Index Ter ms—Manufacturing cost estimation, comparative
assessment, causal identification, roller bearings .

I. INTRODUCTION
In the last years one of the most important problems in
industries was cost saving. In engineering terms a bearing is
defined “Any two surfaces rubbing against each other be it a
bush or sleeve around a shaft o r a flat surface moving over
another flat surface”.
The bearings can be produced in large quantities in the
required quality and accuracy. They are used nearly
everywhere, in industries suc h as automotive, aerospace,
machine tools, mining, medical, agriculture.
A standard bearing is composed by four basic components
an outer and inner ring, a number of Z rolling elements (ball
and roll) and a plastic or metal sheet cage (see fig.1) .
Bearin gs can be classified according to:
– the type of motion , as for plain bearings, where the gliding
motion takes place between the bearing and the supported
part, and as for rolling bearings, where the rolling bodies
describe a rolling motion;
– the direction of bearing force for radial and thrust bearings;

Manuscript received on February the 20 -th, 2020 .
G. F. Author is with the Manufacturing Engineering Department,
Dunarea de Jos University of Galati, Romania (e -mail: gabriel.frumusanu@
ugal.ro).
C. A . Author is with the Manufacturing Engineering Department,
Dunarea de Jos Univers ity of Galati, Romania (e -mail:
[anonimizat]) .
V. P. Author is with the Manufacturing Engineering Department,
Dunarea de Jos University of Galati, Romania (e -mail: viorel.păunoiu@
ugal.ro). – the function in fixed bearings which can take up shearing
forces and axial forces in both directions and in
non-locating bearings which allows displacement in a
longitudinal direction.

Fig. 1. Types of bearings

In the era of the mass customiz ation, rapid and accurate
estimation of the manufacturing cost improve the
competitiveness of a product.
The costs have become a major driver of business in many
industries. The strong economic motivation for cost
estimation and modeling comes from the requirement to
know future manufacturing costs required in the quotation
process.
There have been a number of researchers who studies on
accurate cost estimation for manufacturing product.
In traditional system, the cost and price of product is
calculated as follow:
1. Tracing: allocating direct material and direct payment to
products and services.
2. Allocating overhead costs to products or services based on
a definite attraction rate.
3. Calculating the cost and price of product s, [1].
In [2] is described the development of a cost estimating
methodology for predicting the cost of engine ering design
during the conceptual stages of product development. Cost
estimated and cost engineering are separate disciplines yet
inextricably linked. The cost estimating refers to a commercial
business process that provides the customer with an estimate of
product or service. The cost engineering is more involved and
concerned with design trade studies ratherthan that of providing
estimates for commercial proposals.
Shehab et al develop in [3] an intelligent knowledge -based
system that accomplishes an environment to assist
inexperienced users to estimate the manufacturing cost
modelling of a product at the conceptual design stage of the
production cycle. The main function of the system , besides
estimating the product cost, is to generate initial process
planning includes generation and selection of machining
processes, their sequence and their machining parameters.
The paper [4] presents a cost estimation methodology as
well as a cost estim ation model, which estimate the cost of
products by relative comparison of the attributes of new Estimation of Roller Bearings Manufacturing Cost by
Causal Identification and Comparative Assessment – Case
Study Performed on Industrial Data
Gabriel Frumușanu, Cezarina Afteni and Viorel P ăunoiu

product variants with the attributes of standard product
variants.
In [5] the author investigate experimentally the
applicability of neural networks for cost estimation in early
phases of product design. Experiments are based on pilot cost
data from a manufacturing company .
Ma et al propose d in [6] a generic semantic model for the
purpose of automatic cost estimation, and a new concept
named cost feature is suggested. In this paper, they investigate
a new ma nufacturing cost calculation model coherently
throught the lifecycle of a product series, especially
emphasizing at the conceptual design stage, which integrates
three funtional sub -models: feature -based costing, data
mining and semantic reasoning.
In pap er [7] is presented a mathematically advanced
method for improving fidelity of cost estimation for an
engineering system. The authors used a new methodology for
analyzing a set of cost data av ailable in the literature, and
compared the new cost model to results from a neural network
based analysis and to a cost regression model.
The paper [8] concerns a new approach of the finding
optimal decisions at all stages of the manufacturing process.
This approach involves estimating the results (for example the
cost of a product) based on the values of a descriptive
parameters by comparative assessment. The proposed method
works in three successive stages, namely two preparatory
stages, dedicated to the analysis of the past activity performed
by the manufacturing system and to the identification of
potential assessment tooling, and one operational stage for
actually optimizing the decisions process, by comparative
assessment.
In [9], the authors suggest a different approach in
performing the comparative assessment, based on alternatives
rankings. The rankings are as signed to potential alternatives,
by reffering them to tha cases of already performed
manufacturing activities, recorded as past instances database,
after ranking criteria such as cost, timespan, consumed energy
etc. The selection decision results by compa ring potentia l
alternativesrankings. They propose an expression for the
distance -function together with an algorithm for actually
finding the ranking of the analyzed alternative.
This paper presents a validation of two procedures, aiming
the causal identi fication and the comparative assessment of
the manufacturing jobs, by applying them in the case of
estimating the manufacturing cost of roller bearings.
The case study used a database extracted from the
industrial environment. Clusters of c ause-variables being
the most appropriate for evaluating the cost are determined,
at first. Then, neighborhoods of the interrogated cases are
extracted from the database and the proximity function is
identified. The estimated ranking (hence the manufacturing
cost) of the interrogated case is found on this base,
eventually.
The paper is organized as follows: the second section
present s a conventional cost modeling within a company
producing bearings and bearing assemblies . Next section
describes the two procedures, aiming the causal identification
problem and the comparative assessment problem. The fourth
section is dedicated to the validation of these procedures by
applying them in the case of estimating the manufacturing
cost of roller bearings. The last section presents the paper
conclusion. II. CONVENTIONAL COST MODELING
In order to adapt their stra tegies to the current economic
situation , the companies developed their own algorithms for
cost and price calculation.
Cost bre ak down becomes a tool which he lps sales people
to understand the main cost components and also designer to
observe the main influence of the technologies in the final cost
of the product.
One important component in price calculation it is
represented by the internal costs. These costs are determined
takin g into account the raw material consumption and related
purchasing price and other auxiliary materials price
including: tools, devices, measurement instructions a nd
technological liquids. Supple mentary to the mentioned
components in the cost calculation ot her factors are: salaries
costs, general expenses of the company (including taxes and
other financial expenses).
In the actual economic environment , companies define
their investment programs based on prediction of the sales,
taking into account the estim ated profits versus expenses. In
the investment programs are included objectives mainly for
technology up -grade or rene w which become more and more
soph isticated and consider also the impact of the process
developed through t he designed technology bo th on the
environment and workers on one side and on the other side the
impact of that technolo gy on the cost and price of the product.
The price of the product influence final ly the internal
decision to manufacture one or another product, to accept one
or another customer order and finally the main impact is on
the customer to decide. Before to take a st rategic deci sion
regarding manufacturing and also the placing of orders it
becomes very important to know and consider all the cost
components and their values.
Some companies use in their marketing strategies the cost
break down in order to explain to the potential customer how
the product it is made and how the value is added through the
main manufacturing process steps, starting with raw materia l
receiving tel l delivery of the product to end customer.
Also in some cases it is very important to consider the
distribution costs which could influence the decision of the
buyer/customer.
The total manufacturing cost (TMC) includes direct
materials, direct labor, and overhead costs.

TMC = Direct materials cost
(+) Direct labor cost
(+) Overheads costs

The cost of direct materials is the cost of the materials used
for the manufacturing of a product during a given period.
The cost of direct labor that contribute s to the
manufacturing of a product during a given period.
Overhead costs are the costs that are not directly related to
the manufacturing of a product.
For example, we will be considering a company that
produces bearings, for estimation of a total manufa cturing
cost of a certain type of bearing, namely axial type bearing
with the dimensions: inner diameter Di = 50 mm, outer
diameter De = 110 mm and height L = 64 mm.

The cost of direct materials includes direct materials, the
inventory at the beginning of the period and the inventory at
the end period.

Cost of direct materials
 Direct materials 28.32 u m
 Inventory at the beginning of period 14.27 um
 Inventory at the end of period (10.84 um )
Cost of direct materials 31.75 um

To calculate, the overh ead costs, include the cost of
indirect labor, the cost of indirect materials, the cost of
salaries, the maintenance, the technology, the quality, the
external services and repairs, the packing , taxes and
depreciation , CGI, the external services .

Overhea d costs
 Indirect labor 2.52 u m
 Indirect materials 2.30 um
 Salaries 11.35 um
 Maintenance 2.50 um
 Technology 0.72 um
 Quality 1.93 um
 External services and repairs 1.34 um
 Packing 1.83 um
 Taxes 3.21 um
 Depreciation 9.00 um
 CGI 29.69 um
 External s ervices 2.92 um
Overhead c osts 69.31 um

The TMC is calculating by adding the cost of direct
materials, the cost of direct labor and the overhead costs.

Total manufacturing cost
 Cost of direct materials 31.75 um
 Direct labor 14.27 um
 Overhead costs 69.31 u m
Total manufacturing cost 115.33 um

The traditional cost -estimation techniques known as single
price estimating models, elemental estimating, operational
estimating and resource related methods are also replaced by
advanced cost estimating syst ems known as casual empirical
models, regression models, simulation models and expert
systems that use hardware and software to convert data into
appropriate information for the ultimate users.
III. PROPOSED METHOD FOR COST ESTIMATION
The method works on the b ase of two procedures :
i) The causal identification ,
ii) The comparative assessment.
i) The causal identification
The method of identifying causal links in the
manufacturing process [10] is useful for finding the most
appropriate pattern structure for a particula r manufacturing
activity/process. The facility of the method aims at identifying
the groups of variables with potential for application in the modeling of the activity/process . The primary objective of
applying the method is to allow the selection of varia bles, the
most influential, easy to measure, and as few as possible, such
as the resulting least complex model, according to the
predicted estimate of precision. The method utilizes the past
case studies relating to the manufacturing system, registered
as a database, to reveal the causal links between the variables
that characterize the development of the manufacturing
processes on the considered system.
Applying the method for case -based identification of
causal links in the manufacturing process involves several
successive stages ( see Fig. 2).

Fig. 2. The algorithm of the proposed method

 Process identification
The first step of the alg orithm involves analyzing the
variant of target – manufacturing process to choose the
variables that characterize its achievement. It then defines the
set of variables (both cause – and effect -variables) with
potential in process modeling.

 Data concatening
The purpose of the stage is to generate the database of
previous cases, regarding the manufacturing process variant
considered. Several cases refer to same type of activity if they
can be characterized by the same cause -variables and
effect -variables.
Three actions are necessary in order to do data
concatening, namely clustering, updating and
homogenization.

 Instanc es comparing
The method of identifying causal links is based on the idea ,
that if there is a causal link between two or more variables, the
variance of a cause -variable will be reflected and therefore
measured by an appropriate metric in a variation of ano ther
cause- and/or effect -variables.

 Variables assessing
This step aims to assess the cause -variables in order to find
the ones having potential for evaluating the given
effect -variable.
Variables assessing is performed by applying two
algorithms, namely :
 The algorithm for dimensionality reduction,
 The algorithm for assessing the modeling potential of
variables.

 Causal models identifying
 This can be realized by successively and repetitively
applying a couple of algorithms, namely:
– The algorithm for gen erating smaller clusters,
– The algorithm for assessing the modeling potential of a
cluster.

 Causal links tree
The selection of the most suitable cluster of
cause -variables with which can be describing the effect is
made with the help of intuitive represen tation called the
causal links tree (see Fig. 3 ).

Fig. 3 . The generic causal links tree [10]
ii) The comparative assessment
The method of comparative assessment in the manufacturing
process proposes an innovative approach in the analysis of
potentially o ptimal solutions, based on their rankings.
The comparative assessment means to establish rankings
for two or more alternatives to proceed, after given criterion
(e.g. cost, time span, consumed energy etc.).
The comparative assessment of potential alterna tives it is
done by referring them to the cases of manufacturing
processes already carried out, whose parameters have been
registered in the past instances database, [11].
The algorithm after which the appropriate ranking is
assigned to a given alternative (further referred as current
case) by comparing it to the cases recorded in Instances
database is illustrated in figure 4.

Fig. 4. Ranking assignment algorithm [11]
The algorithm works on the base of two procedures,
especially conceived in this purpose:
– Neighborhood delimitation ,
– Nearness modeling .
The procedure for neighborhood delimitation to find a
neighborhood profile of a potential case through successive
comparisons with cases of processes already carried out (with
known results). The objective is to select from the instances
database, the set of instances that corresponds to a given
neighborhood profile.
The procedure for nearness modeling aims that, after a
delim iting the current neighborhood N i of the current case, the
nearness between included cases is modeled in order to find a
more expression of the nearness function. The modeling is
proposed to be performed by nonlinear multiple regression.
Both procedures a re succes sively run until two consecutive
forms of nearness parameters.
IV. COST ESTIMATION FOR THE ROLLER BEARING – CASE
STUDY PERFORMED ON INDUSTRIAL DATA
The roller bearings (fig. 5) manufacturing cost was
estimated by using the above proposed method in the case of a
database extracted from the industrial environment.

a) b) c)
Fig. 5. Profile of the bearing
i) The causal identification
For the application of the method by this procedure, the
steps of the algorithm presented in previous section
were fo llowed.

 Process identification
The next set of nine cause -variables was considered as
having potential in modeling the manufacturing
process, namely :
– the bearing exterior diameters , De;
– the bearing interior diameters , Di;
– the bearing width , L;
– the bea ring weight , m;
– dynamic capacity, Cd;
– static capacity, Cs;
– limit speed under greasing conditions , n1;
– limit speed under oil conditions n2,
– the complexity index Ic.
The cost of the bearing was selected as effect -variable.

 Data concatening
The collect ed database has 141 instances, some of t hem
being sampled in Tables I-a and I-b, before and after
homogenization, respectively.

TABLE I-a. REAL INSTANCES DATASET (ACTUAL VALUES , EXCERPT )
Instance
crt. no. De
[mm] Di
[mm] L
[mm] m
[kg] Cd
[kN] Cs
[kN] n1
[min-1] n2
[min-1] Ic
[-] C
[lei]
1 110 60 47 1.496 77.4 209 7.76 1900 2800 61.65
2 140 65 79 4.858 176 424 8.36 1300 1800 184.41
3 78 58 22 0.421 88 285 9.32 1400 4000 33.66
4 125 70 40 2.106 153 341 6.36 1400 1900 85.56
5 35 20 10 0.041 14.9 26.6 4.16 5300 7000 8.53
. . . . . . . . . . . . . . . . . .

TABLE I-b. REAL INSTANCES DATASET (SCALED VALUES , EXCERPT )
Instance
crt. no. De Di L m Cd Cs n1 n2 Ic C
1 0.518 0.357 0.413 0.131 0.18 0.137 0.624 0.218 0.205 0.151
2 0.698 0.392 0.760 0.432 0.445 0.288 0.724 0.120 0.076 0.489
3 0.325 0.342 0.141 0.035 0.209 0.19 0.885 0.136 0.358 0.074
4 0.608 0.428 0.336 0.186 0.383 0.23 0.389 0.136 0.089 0.217
5 0.066 0.071 0.010 0.001 0.013 0.008 0.020 0.771 0.743 0.004
. . . . . . . . . . . . . . . . . .

 Instances comparing
This time, the beams database generated with the Matlab
application has
2
141 9870NC beams. Seve ral beams are
sampled in Table II .

TABLE II. BEAMS DATABASE (EXCERPT )
Fascicul δDe δDi δL δm δCd δCs δn1 δn2 δIc δC
(1,2) 0.180 0.03 0.347 0.3 0.264 0.151 0.1 0.097 0.128 0.338
(1,3) 0.481 0.5 0.021 0.263 0.28 0.23 0.302 0.13 0.153 0.106
(1,4) 0.09 0.071 0.07 0.05 0.202 0.092 0.234 0.081 0.115 0.065
(1,5) 0.451 0.285 0.402 0.13 0.167 0.128 0.604 0.55 0.538 0.146
(1,6) 0.030 0.114 0.336 0.056 0.17 0.268 0.34 0.065 0.064 0.015
. . . . . . . . . . . . . . . . . .

 Variables assessing
Dimensionality reduction
At first, the references threshold has been to
ref 7h h 0.2097,
hence
k 2 5h h 0.3276. According
to the algorithm, windows having
H0 and
ref hh were
considered for the beams components corr esponding to eight
of the nine cause -variables, while for the ninety the image
dimensio n
i was measured (i = 1, 2, … 9, successively). The
values obtained for
i, by using a dedicated MatLab
application, are shown in Table III . As it can be noticed,
min 0.2179,
corresponding to variable Ic, hence one of
them may be discarded. At Step 2, the action from previous
step is repeated for the remaining eight cause -variables and
another one is discarded, namely De, and so on. After Step 3,
min 5 0.3209 h ,  
so the six cause -variables remainin g
until here can be considered relative independent and the
maximal cluster is [ Di, L, m, Cd, n1, n2].

TABLE III. IMAGES DIMENSIONS
i AND
min
Condition
variable Succes sive steps of dimensionality reduction
Step 1 Step 2 Step 3 Step 4
De 0.28915662 0.28915662 – –
Di 0.39285714 0.39285714 0.78571428 0.78571428
L 0.52173913 0.52173913 0.54347826 0.55434782
m 0.35587761 0.35587761 0.35587761 0.51171944
Cd 0.35924932 0.35924932 0.35924932 0.60321715
Cs 0.32090077 0.32090077 0.32090077 –
n1 0.92281879 0.92281879 0.92281879 0.92281879
n2 0.35830618 0.53745928 0.61889250 0.61889250
Ic 0.21794871 – – –
Assessment of variables modeling potential
The criteria for assessing the modeling potential have been
determina tes for each cause -variable of the maximal cluster,
according to the algorithm above presented, by calculating the
values of a, b, and RMSE , after considering the cost C as
effect -variable. The results obtained with the help of Curve
fitting tool from MatL ab are pr esented in Table IV .

TABLE IV. THE VALUES OF a, b AND RMSE
Di L m Cd n1 n2
a 0.1272 0.2241 0.05765 0.0041 0.02191 0.3234
b 0.0445 0.03765 0.04864 0.05269 0.04961 0.03479
RMSE 0.0011 0.00058 0.00176 0.00112 0.00185 0.00171

 Causal models i dentifying
The MC (assessed through the values of b) was adopted as
criterion for selecting the cause -variables to be discarded
when generating smaller clusters. Three clusters with 5
cause -variables each has been generated from the maximal
cluster in the first stage. Then, two clusters with 4
cause -variables resulted from each of these three, in the
second stage. Finally, two clusters of 3 cause -variables were
obtained from each cluster with 5 variables. After assessing
clusters potential in order to ident ify causal models, the
process of generating smaller clusters had to be stopped at the
level of 3 -variables clusters. Variables selection and resulted
clusters are presented in Tables V-a, b and c.

TABLE V-a GENERATION OF 5-VARIABLES CLUSTERS
Variables Di L m Cd n1 n2
b 0.0352 0.0283 0.0179 0.02651 0.04707 0.0509
Resulted
clusters [Di, L, m, C d, n1] [D i, L, m, C d, n2]

TABLE V-b GENERATION OF 4-VARIABLES CLUSTERS
Variables Di L m Cd n1
b 0.03625 0.02628 0.01739 0.02499 0.04405
Resulted
clust ers [Di, L, m, C d] [L, m, C d, n1]
Variables Di L m Cd n2
b 0.03552 0.02651 0.01663 0.02167 0.04639
Resulted
clusters [Di, L, m, C d] [L, m, C d, n2]

TABLE V-c GENERATION OF 3-VARIABLES CLUSTERS
Variables Di L m Cd
b 0.03384 0.02441 0.01748 0.01816
Resulted
clusters [Di, m, C d] [L, m, C d]
Variables L m Cd n1
b 0.03452 0.01986 0.02605 0.05446
Resulted
clusters [m, Cd, n 1] [L, m, C d]
Variables L m Cd n2
b 0.03896 0.01571 0.01366 0.06395
Resulted
clusters [m, Cd, n 2] [L, m, C d]

Finally, they resulted only 4 (instead of 6) distinct clusters
with 3 variables and 3 (instead of 6) clusters with 4 variables.
Hereby, the causal tree will be formed from 1 + 2 + 3 + 4 = 10
clusters.

 Assessment of clusters modeling potential
After finding the clusters of cause -variables that will
compose the causal tree, the values of ac, bc and RMSE were
found with Curve fitting tool from MatLab. These values are
presented in Table VI .

TABLE VI. THE VALUES OF ac, bc AND RMSE
Condition -variables from cluster ac bc RMSE
[Di, L, m, C d, n1, n2] 0.7988 0.004066 0.007391
[Di, L, m, C d, n1] 0.7748 0.002467 0.008119
[L, m, C d, n1, n2] 0.8605 -0.001428 0.009931
[Di, L, m, C d] 0.8438 -0.00216 0.010 61
[L, m, C d, n1] 0.7602 0.01108 0.004584
[L, m, C d, n2] 0.8323 0.01133 0.009419
[Di, m, C d] 0.8858 0.003786 0.006537
[L, m, C d] 0.8635 0.005654 0.00775
[m, C d, n1] 0.7895 0.01235 0.002351
[m, C d, n2] 0.9038 0.01406 0.005238

 Causal link tree
The ca usal tree drawn after MC c criterion is depicted in Fig. 6.

Fig. 6. Causal tree drawn after criterion MC c
ii) The comparative assessment
For application of the method by this procedure in the case
for the cluster with four cause -variables [L, m, C d, n2] of a
database extr acted from the industrial environment for
estimation of roller bearings manufacturing cost.
The database has five columns (first four for L, m, Cd and n2
cause -variables and the last for C effect -variable) and
n = 141 lines.

 Case ranking assignment
We supposed the current case ( L1 = 0.4, m1 = 0.2, Cd1 = 0.5,
n21 = 0.15), needing to be ranked relative to the instances
database from above. At first, the pivot ( L v1 = 0.38043, mv1 =
0.20987, Cdv1 = 0.46648, n2v1 = 0.12052, Cv1 = 0.27999) has
been chosen from instances database. Then, the algorithm for
case ranking assignment has been iteratively run, the results
being presented in Tables 6 and 7. The modeling by nonlinear
multiple regression has been performed in MatLab
(Optimization tools package).
The values for ε parameter have been selected at each
iteration such as the current case neighborhood includes the
same number of cases (here, 12 cases). The quality of
modeling the cases neighborhood by nonlinear multiple
regression is revealed by calculating the Root M ean Square
Error (RMSE ) parameter, well -known in Statistics. As one
can easily notice, the algorithm stabilizes rapidly, after only
two iterations – the three iteration s give same results as the
previous one. As consequence, relation (6) can be used (in t he form
resulted after last modeling by multiple nonlinear regression)
for calculating
1 1 v1C C C .   The obtained value is ΔC1 =
-0.00172, hereby C1 = 0.27827 and considered case ranking is
R1 = 108.

 Actual c omparative assessment
Let us consider two different current cases: first is the one
addressed in previous section, while second is
(L2 = 0.7, m2 = 0.35, Cd2 = 0.4, n22 = 0.2). The problem to be
solved is the selection, between the two cases, of the one with
the smallest value of the effect -variable.
The algorithm for case ranking assignment is applied once
again, for second potential case, to which the pivot
(Lv2 = 0.6 8478, mv2 = 0.34693, Cdv2 = 0.36997, nv2 = 0.16938,
Tv2 = 0.31331) is associated from the same instances database.
This time, the algorithm stabilizes after only one iteration –
the second iteration gives the same results as the previous one.
In the same m anner as above, we find ΔC2 = -0.00138,
C2 = 0.31470 and case ranking is R2 = 114.
In conditions of the addressed problem, we have R 2 > R 1, so
the solution to the problem is to selected the first case.

V. CONCLUSION
At the end of research presented in this paper, the following
conclusions can be drawn:
 Compared to the traditional cost estimation method,
which requires laborious calculations, estimating the
cost by the proposed method proves to be simple and
efficient.
 By causal identification, t he number of cause -variables
needed to evaluate the cost of roller bearing
manufacturing is reduced substantially : instead of the ten
variables a maximum clusters of six cause -variables has
been identified [Di, L, m, Cd, n1, n2], that shows very good
potential for pri ce modeling in the case of bear ing
production (b c = 0.004066).
 Also, the c lusters of three cause -variables has been
identified that model the cost well enough [ m, Cd, n2],
a significantly simpler solution for doing the same thing
with reasonable good res ults (bc = 0.01406 ).
 As can be seen from table VI, in two cases the value for b c
resulted negative. This can be explained by the static
character of the method, which, for a smaller number of
cases, can lead to such results. To overcome this
disadvantage, in the representation of the tree causal link,
the absolute value of b c was used in both cases.
 Comparative assessment cost provides plausible results,
after a very small number of iterations (2).

ACKNOWLEDGEMENT
This work was supported by the Romanian Ministry of
Research and Innovation, CCCDI – UEFISCDI, project
number PN -III-P1-1.2-PCCDI -2017 -0446 / Intelligent
manufacturing technologies for advanced production of
parts from automobiles and aeronautics industries (TFI
PMAIAA) – 82 PCCDI/2018, within P NCDI III.

REFERENCES
[1] F. Kowsari, „Changing in Costing Models from Traditional to
Performance Focused Activity Based Costing (PFABC) Activity
Based Costing 2 Time Driven Activity Based Costing 3 Performanc e
Focused Activity Based Costing”, Eur. Online J. Nat. Soc. Sci. , vol. 2,
nr. 3, pp. 2497 -2508, 2013.
[2] R. Roy, S. Kelvesjo, S. Forsberg, și C. Rush, „Quantitative and
qualitative cost estimating for engineering design”, J. Eng. Des. , vol.
12, nr. 2, pp. 147 -162, 2001.
[3] H. . Shehab, E.M and Abdalla, „Manufacturing cost modelling for
concurrent product development”, Robot. Comput. Integr. Manuf. ,
vol. 17, nr. 4, pp. 341 -353, aug. 2001.
[4] Y. H. P. K. and A. Korff -Krumm, „Cost Estimation in
Engineer -to-Order Manufacturing”, Open Eng. , vol. 6, nr. 1, pp.
22-34, 2016.
[5] J. Bode, „Neural networks for cost estimation: Simulations and pilot
application”, Int. J. Prod. Res. , vol. 38, nr. 6, pp. 1231 -1254, 2010.
[6] Y. S. Ma, N. Sajadfar, și L. Campos Triana, „A feature -based
semantic model for automatic product cost estimation”, IACSIT Int. J.
Eng. Technol. , vol. 6, nr. 2, pp. 109 -113, 2014.
[7] J. Colombi, John M.; Miller, Michael E.; Schneider, Michael;
McGroga n, Jason; Long, David S.; Plaga, „Model Based Systems
Engineering with Department of Defense Architectural Framework”,
Syst. Eng. , vol. 14, nr. 3, pp. 305 -326, 2012.
[8] C. Afteni, G. Fru mușanu, și A. Epureanu, „Method for Holistic
Optimization of the Manufacturing Process”, Int. J. Model. Optim. ,
vol. 9, nr. 5, pp. 265 -270, 2019.
[9] C. Afteni, G. Frumușanu, și A. Epureanu, „Instance -based
comparative assessment with application in manufa cturing”, IOP
Conf. Ser. Mater. Sci. Eng. Pap. , 2018.
[10] C. A. and A. E. Gabriel -Radu Frumusanu, „Causal identification of
the manufacturing system”, J. Manuf. Sci. Eng. , 2019.
[11] G. F. and A. E. C Afteni, „Instance -based comparative assessment
with ap plication in manufacturing”, IOP Conf. Ser. Mater. Sci. Eng. ,
vol. 400, nr. 042001, pp. 0 -8, 2018.

Gabriel Frumușanu , borne in Galați, Romania,
28/09/1964. Bachelor (1988), PhD (1999),
Habilitation (2016) in Industrial Engineering at
“Dunărea de Jos” Un iversity of Galați, Romania.
He is currently Professor at “Dunărea de Jos”
University of Galați, Romania, and head of the
Manufacturing Engineering Department. He
published over 150 scientific articles, some of them
in prestigious journals. He owns 5 paten ts. He
participated at numerous International conferences (Spain, Hungary, Tunisia, Israel, Moldova and Romania). Research interests in
machining systems control, cutting tools profiling and environmental impact of
the manufacturing process. Prof. Frumușan u is member of UASTRO, AUIF
and of editorial boards – Proceedings in Manufacturing Systems journal
(Romanian Academy), the Annals of „Dunărea de Jos” University, Fascicle V.

Cezarina Afteni was born in Galat i, Romania, on
December 02, 1990. She receive d his bachelor in
Economical Engineering in 2014 and in 2016
master in Quality Management in Industrial
Engineering from Du nărea de Jos University of
Galat i, Romania.
She is currently a PhD student at Du nărea de Jos
University of Galat i, Romania, in the
Manufacturing Engineering Department. Her
research interests are mainly related to
optimization problems by integrating process planning and scheduling.
Ms. Afteni is involved in different research works from industrial
environment. The main objectives deve loped within this colaboration are:
lead time improvement in bearing manufacturing process and optimization
of process chain in case of grinding and hard turning processes.

Viorel P aunoiu , born in Galati , Romania,
24/11/1959. He is professor of Mechan ical
Engineering at Dunarea de Jos University of
Galati (1987 -present), Faculty of Engineering.
Manufacturing Engineering Department is
main academic competences are technologies
and equipment ’s for metal forming; numerical
simulation of sheet metal formin g; control and
inspection in sheet metal forming; energetic
phenomenon’s studies in metal forming (deep drawing, flow forming,
extrusion). Prof. Paunoiu participated as director or member in over
35 research projects supported by Romanian Ministry of Educa tion
and Science; author/co -author of over 10 scientific or didactic books;
over 120 scientific papers written or co -authored, published to
International/National Conferences proceedings (France, Hungary,
Poland, USA, Moldavia, Italy) and Journals; author/ co-author of 3
patents. He was editor of the journal The Annals of Dunarea de Jos
University of Galati, Fascicle V, Technologies in Machine Building
(2008 -2019). He is founder and co -chairman of the International
Conference NEWTECH – Advanced Manufacturing Engineering and
Technologies (2009 -present).