The maintenance Cost Allocation in Product Life Cycle

ISSN 1392-2785 ENGINEERING ECONOMICS. 2005. No 4 (44)
ECONOMICS OF ENGINEERING DECISIONS
The maintenance Cost Allocation in Product Life Cycle
Rūta Lapašinskaitė, Vytautas Boguslauskas
Kauno technologijos universitetas
K. Donelaičio g. 73, LT-44029, Kaunas

This article describes the concept by the customer view
Keywords: Life cycle costing, product life cycle, regression
of the consuming life cycle. Because the purchase price the
analysis, iteration method, string method.
customer pays is equal to the cost of the producer plus
value added, the life cycle costs of the customer perspec-
Introduction
tive will most often be complete. The article focuses on the
customer’s perspective to the lifecycle costs and not so
The earliest reference to S-shaped curve similar to
much on the product life cycle.
product life cycle was detected in 1922-23 by Prescott,
There are developed four main different ways of per-
who proposed an equation that fits the growth of the auto-
forming LCC depending on the amount of resources avail-
motive industry from 1900 to 1920 very well. The product
able, the time available, the degree of accuracy and other
life cycle concept is almost certainly one of the best-known
aspects. This study utilizes a combination of product life
if not most important concepts in marketing. Product life
cycle analysis, advanced modern costing methods and
cycle is almost an inexhaustible concept because it touches
regression data analysis processing for the product main-
on nearly every facet of marketing and drives many ele-
tenance costs calculations in its life cycle. The combination
ments of corporate strategy, finance and production.
is necessary for solving the research task; life cycle costs
These statements are excerpts from Gardner’s litera-
analysis considers only product maintenance costs in this
ture review of about 130 references. Gardner summarizes
article. In this article we use life time as a cost driver help-
his findings by concluding that there is much agreement
ing us to allocate the maintenance costs between different
among the writers concerning the life cycle concept as a
trucks in their different life time.
descriptive variable, but it does not fulfill the criteria of
being a theory. At the end of his review, Gardner suggests
This study presents the evaluation of the regression
that “future work should be tied, not only to increase our
functions, describes its elements, illustrates the compari-
understanding of the phenomenon, but also increase our
son and chooses the best. The elasticity analysis presenting
predictive ability.” (Gardner, 1987).
the percent of the maintenance costs change if time has
Uusi-Rauva et al. define life cycle as “the period of a
changed 1 %, is also used. The life cycle curve’s estima-
product in the market”. This interpretation emphasizes the
tion shows that the longer exploitation period is, the bigger
marketing point of view and revenue planning, but ex-
maintenance costs are. This can help to make a decision
cludes the impacts of product creation and disposal for life
about the further exploitation of the truck during its valu-
cycle profitability. Life cycle analysis should consider the
able life cycle and after it. It is the main purpose why life
period between birth and decease. Even the definition of
cycle costing system was created and developed, using non
CAM-I excludes the period between withdrawal from the
traditional life cycle costing curve estimation.
market and decease. “The period that starts with the initial
After the regression-correlation and elasticity analysis
product specification and ends with the withdrawal of the
between trucks’ maintenance costs and the time of its exploi-
product from the marketplace. A product life cycle is char-
tation, it is clear that the exponential correlation exists be-
acterized by certain defined stages, including research,
tween them because correlation and determination as well
development, introduction, maturity, decline and aban-
as elasticity rates are the biggest in this model. At the end of
donment.” (Lasse, 2001).
the article it is calculated at what point of time the direct
The interpretation of the term life cycle differs from
regression curve breaks exponent regression curve. The
decision maker to decision maker, as it is evident from the
break even means the point where companies should use
literature. A marketing executive will most likely think in
exponential regression formula for allocating maintenance
terms of the marketing perspective, which consists of at
costs to different trucks in order to get the most exact result
least four stages (Adamany & Gonsalves, 1997):
for cost management. The procedure is demonstrated ac-
cording to one of the iteration methods – string method. The
1. Introduction
main aspect of this method is that the chosen interval should
2. Growth
be isolating and it should meet all the requirements for iso-
3. Maturity
lating interval: 1. Function changes its sign in the interval;
4. Decline.
2. The first derivative function does not change its sign in
A manufacturer will think in terms of the production
the interval; 3. The second derivative function does not
perspective, which can be described using five main stages
change its sign in the interval. The calculation manifests
or processes:
that the break even exists and is equal 6.15568 periods for
1. Product conception
Mercedes Benz trucks in the real transport company.
2. Design

17

---

3. Product and process development
are (Emblemsvag, 1999):
4. Production
• The sum total of the direct, indirect, recurring, non-
5. Logistics.
recurring, and other related cost incurred, or esti-
When the product has reached the customer, user or
mated to be insured, in the design, development,
consumer, a different perspective occurs: the customer
production, operation, maintenance, and support of
perspective. This perspective often includes five stages or
a major system over its anticipated useful life span.
processes:
• The amortized annual cost of a product, including
1. Purchase;
capital costs, installation costs, operating costs,
2. Operating;
maintenance costs, and disposal costs discounted
3. Support;
over the lifetime of a product.
4. Maintenance;
• The total cost throughout its (an asset’s) life, includ-
5. Disposal.
ing planning, design, acquisition and support costs,
and any other costs, directly attributable to owing or
Burstein (1988) points out that life cycle costing be-
using the asset.
comes more and more crucial when the technology
changes rapidly and the product life cycles become shorter.
In this article the life cycle cost of a product is defined
In addition, he enhances the concept by the customer view
as “maintenance costs”.
of the consuming life cycle. The idea presented in Figure 1
The life cycle concept is also recommended by
applies especially to durable goods, such as cars.
Barksdale & Harris to optimize the allocation of resources
and guide strategic decisions of business units in multi
product companies. They consider this important while the
concept recognizes the life span of products and empha-
sizes the changes of opportunities associated with different
stages of growth (Barksdale & Harris 1982).
The purpose of this article is to find the break even
where the direct regression curve breaks the regression
curve describing relations between maintenance costs
and time, as cost driver, the most exactly.
The object is maintenance costs in the truck’s life cycle.
The method used in this article is one of the iteration
methods – string method.

Four ways of LCC
As most concepts, LCC has evolved over time, and today
Figure 1. The customer’s perspective to life cycle costs
LCC serves three main purposes (Barringer & Weber, 1996):
(Burstein 1988)
1. LCC can be an effective engineering tool for pro-
Because the purchase price the customer pays is equal
viding decision support in the design and procure-
to the cost of the producer plus value added, the life cycle
ment of major open systems, infrastructure, and so
costs of the customer perspective will most often be com-
on. This way it is the original intent for which it
plete (Day, 1981).
was developed. It was soon realized that it is better
Finally, we have the most comprehensive perspective,
to eliminate costs before they are incurred instead
namely that of the product itself. The product life cycle is
of trying to cut costs after they are incurred.
essentially all the activities that the product, or parts of the
2. LCC overcomes many of the shortcomings of tradi-
product, undergo regardless of which decision makers are
tional cost accounting and can therefore give useful
involved. It may involve the proceeding perspectives ex-
cost insights in cost accounting and management.
cept one: the marketing perspective (Bian, 1974). The
3. LCC has remerged as a design and engineering tool
reason is that the product life cycle is on the individual
for environmental purposes.
level of each product unit, whereas the marketing perspec-
tive is on the type level of the product (Levitt, 1965).
Depending on the amount of resources available, the
This article focuses on the customer’s perspective to
time available, the degree of accuracy, and other factors
the lifecycle costs. In any case two genuinely unique life
such as data availability, four main different ways of per-
cycles exist: one on the individual product level (the prod-
forming LCC exist: analogy, parametric, engineering cost
uct life cycle) and one on the product type level (the mar-
methods, and cost accounting (Fuller & Petersen, 1996).
ket life cycle).
The different ways suspect to different advantages and
The literature also makes an important distinction be-
disadvantages (Emblemsvag, 2004).
tween product’s life cycle costs and its whole life costs.
Life cycle costs refer to all the costs that the producer will
Analogy Models
incur and whole life cycle costs also include the costs that
An LCC estimate made by an analogy identifies a
consumers incur, i.e. installation, operation, maintenance,
similar product or component and adjusts its costs for dif-
revitalization and disposal. (Shields & Young 1991).
ferences between it and the target product. This way of
What is life cycle cost? Some of the better definitions
conducting LCC is common in shipbuilding, for example,

18

---

where mass is the factor they relate costs to.
dles overhead costs correctly because none captures the
This way of handling costs may sound crude. It says
complexity of modern organizations, and many of them
nothing about direct labor or overhead costs. It simply
include only simple mathematical manipulations of already
looks at what the costs have been historically and scales
identified costs. These costs estimates that are taken as
them according to the most important cost driver, which in
input are probably generated by traditional cost accounting
shipbuilding is mass. Such methods can serve well when
systems and are therefore likely to be distorted.
extensive historical material is available, the products are
Engineering cost models although offering much more
produced unit by unit, one dominant cost driver is used,
insight than analogy and parametric models are therefore
and the products do not differ much (such as in size, tech-
also limited in usage. But they are useful in engineering
nology, use patterns, and operational characteristics). To
and development situations to give an early cost estimate.
ensure the relevance of historical data, it is vital that the
As information becomes more and more available, the
products do not change much. Thus, such method has lim-
next type of models is preferable: cost accounting models.
ited usage.
Cost Accounting Models
Parametric Models
The literature contains numerous cost accounting
Parametric models are in many ways more advanced
models and system. Here these systems are grouped into
analogy models. A parametric LCC model is based on
three groups for simplicity:
predicting a product’s or a component’s cost either in total
•
or for various activities by using several models describing
Volume-based costing systems
•
the relationships between costs and some product- or proc-
Unconventional costing methods
•
ess-related parameters. The predicting variables typically
Modern cost management systems.
include:
Some of the most important cost accounting ap-
proaches are briefly discussed below.
• Manufacturing complexity
Volume base costing systems are often referred to both
• Design familiarity
as conventional costing systems and traditional costing
• Mass
systems; an example is standard costing. These costing
• Performance
systems have the well known limitations of using only
• Schedule compression.
direct labor as an allocation base. So volume based costing
Compared to the analogy models, three main differ-
systems are not attractive under any circumstances for Life
ences exist. First, an analogy model depends on one single,
cycle costing purposes because they perform too poorly.
dominant cost driver, whereas a parametric model can use
Unconventional Costing Methods are quite different
several parameters. Second, an analogy model is based in
from most cost management approaches or not popular.
linear relationships between costs and cost drivers, while
The first is called Attribute-Based-Costing, which is a
parametric models rely only on one or more nonlinear
development of ABC and hence is simply denoted ABCII.
regression models. Third, whereas analogy model uses an
The purpose is to provide a detailed cost-benefit analysis
analogy (such as mass) as a driver, parametric models are
of customer needs aimed at providing effectiveness. ABCII
essentially regressions, or response surface. Model can be
appears to be hybrid between ABC, Target costing and
linear, quadratic, multidimensional and so on.
Quality Function Deployment (QFD) (Walker, 1992). QFD
Like the analogy models, parametric models do not
brings in a lot of subjectivity and caution is advised, which
handle overhead costs in a credible fashion, nor do they go
probably explains why such an interesting idea has re-
beyond simply presenting an assessment number without
ceived so little attention in the literature.
any further insight, except what is a direct consequence of
The second unconventional costing method is Feature
their parameters. It is clear that parametric models are easy
Costing (FC). In FC the product features are the focal
to use in optimization algorithms.
point. FC can be an improvement over ABC in that it leads
Since parametric models can offer more insight and
to a more direct reduction of costs and an improvement of
higher accuracy than analogy models, they are often found
performance. Nonetheless, how FC is an improvement
in the engineering literature. A parametric model can also
over ABC in general cases is unclear.
perform well as models within accost accounting system,
Modern cost management systems will not be dis-
preferably one that can handle overhead costs well, such as
cussed in this article. One of the few management inven-
Activity Based Costing.
tions that actually have its roots in industry and that is
interesting itself is Activity Based Costing (ABC). Al-
Engineering Cost Models
though ABC has great potential for use in all companies, it
According to the New South Wales Government Asset
is important to implement it step by step to ensure efficient
Management Committee in Australia, The engineering organizational learning (Kaplan, 1998). Using ABC for
Cost method is used where there is detailed and accurate
LCC purposes does not raise the risk of integrated ABM
capital and operational cost data for the asset. It involves
systems because LCC is ad hoc in nature, at least for the
the direct estimation of a particular cost element by exam-
time being (Shank & Dudy, 1997). Activity-Based LCC is
ining the asset component-by component. It uses standard
a sound next step up from traditional LCC and the hind-
established cost factors to develop the cost for each ele-
sight of cost management in general (Maccarone, 1998).
ment and its relationships to other elements.
Life cycle analysis together with modern cost account-
Numerous methods in literature probably mix three be-
ing systems can help to correct lots of problems of the
fore mentioned methods. None of these approaches han-
traditional cost accounting systems, and that’s why it can

19

---

be useful for cost accounting and management.
The life cycle curve’s estimation shows that the longer
In this article we use life time as a cost driver what can
exploitation period is, the bigger maintenance costs are.
help us to allocate the maintenance costs between different
This can help us to make a decision about the further ex-
trucks in their different life time.
ploitation of the truck during its valuable life cycle and
after it. It is the main purpose why life cycle costing sys-
The comparison of regression models
tem was created and developed, using non traditional life
cycle costing curve estimation.
After we have defined the activities with the most re-
sources and attributed the cost drivers for them we still do
The break even analysis
not know how to allocate the costs for different trucks in
the different trucks’ groups because the exploitation time
Because the exponential dependence discover mainte-
of the trucks’ is not the same. During the exploitation of
nance costs state in product’s life cycle the most exactly,
the truck the costs are growing all the time. That’s why we
and companies use linear dependence usually, this article
can not divide the maintenance costs to trucks in the same
describes the analytical calculation of break even where
group in equal parts. We are going to solve this problem
linear regression curve breaks the exponential regression
with the help of life cycle concept.
curve :
The calculated life cycle cost curve should show how
a + bx −
dx
e
c
= ∆
(1)
the maintenance costs are growing when the exploitation

period is increasing. This dependence should help to make
In Figure 3 you can see the graphical view of mainte-
a decision about the usage of the trucks during the exploi-
nance costs of trucks Mercedes Benz break even in real
tation time and after it.
transport company.
The calculation of the maintenance cost curve in the
truck’s life cycle, the determination of the functions was
5000
made with computer program “Statistica”.
4500
The regression and correlation analysis is used for re-
4000
3500
search of random dependence upon expressions having no
3000
strict functional character. The regression and correlation
s
t
s 2500
Co
theory, as one of the main mathematical-statistical science
2000
areas, gives opportunities:
1500
1000
• To express the connection and the form of the eco-
500
nomic expression quantitatively
0
•
0
1
2
3
4
5
6
7
8
9
10
11
12
13
To determine the influence over the factors operat-
ing the same index at the same time.
Time

The elasticity analysis shows the percent at which the
Figure 3. Maintenance costs break even
maintenance costs change if time has changed 1 %,.
for Mercedes Benz trucks
The result is given in the Table.
The break even means the point where companies
Table
should use exponential regression formula for allocating
The regression models analysis
maintenance costs to different trucks in order to get the
most exactly result for cost management.

Direct regression Gradual regression Index regression
Exponential regres-
model
model
model
sion model
We will find the break point where the line
For-
costs=335.771+
costs=304.1361x costs=595.1204x
costs=595.1206x
y = a + bx breaks curve
dx
y = ce , with the help of one
mula +212.9882x time
xtime0.9803
x1.17978time
xe0.165358 x time
D
ε=bx/y D ε=b D
ε=lnbxX D ε=EXP(bxX)
iteration solution method for nonlinear equation – string
ranges 0.2236 0.89946 0,.81297 0.9803 0.8368 2.5167 0,8368 5.6761
method. We will find roots with accurate ε=0, 000001.

After the regression-correlation and elasticity analysis
We have the equation
dx
a + bx − e
c
=∆, where a, b, c,
between trucks’ maintenance costs and the time of its ex-
d, ∆ are the real figures.
ploitation, it is clear that the exponential correlation exists
We change the equation in a comfortable forma:
between them because correlation and determination and
dx
a + bx − ∆ = e
c
, divided by c≠0 (if c is never equal zero).
elasticity rates are the biggest of this model. So we can come
Here a − ∆ = u ;
to the conclusion that the life cycle curve differs from the
traditional curve, and we can draw it as in Figure2.
bx u
dx
+ = e

c
c

u
Maintenance
We mark b

=
;

= ;
1
a
1
b
costs
c
c

Then
dx
a x
1 + b1 = e


Let’s say, the parameters a, b, c, d and ∆ are equal:

Time of exploitation

a :=
771
.
335

Figure 2. The truck’s maintenance costs curve
b := 212.9882
in product’s life cycle
c :=
1206
.
595


20

---

d := 0 165358
.

That’s why we analyze the first (5) and the second (6)
∆ := .
0 000001
derivatives.

d
=

(5)
Then
f (
1 x) :
f (x)
u := a − ∆ = 335 771
.

dx

0
a1:= b
212 9882
.
=
= .
0 3579
2
3
4
5
6
7
8
c
595 1206
.
-500

u
335.771
1
b :=
=
= 0.56421
-1000
c
595.1206
s
t
s
Co

-1500
We divide the given equation into two functions:

-2000
f (x) := 1
a x + 1
b
(2)
-2500
f (x) → 0.3579x + 0.56421
Time
dx
g(x) =
: e
(3)

Figure 6. The first derivative graph
g(x) → exp(0.165358x)
F (x) =
: a + bx −
dx
ce − ∆
(4)
From the Figure 6 we can see that our function does

not change its sign.
2
Then we draw the graph of the given functions:
d
f (
2 x) =
f (x)
(6)
2
3,5
dx
3
0
2,5
2
3
4
5
6
7
8
2
-500
s
t
s
f (x)
Co
g(x)
1,5
-1000
1
s
t
s
-1500
Co
0,5
-2000
0
0
1
2
3
4
5
6
7
8
-2500
Time

-3000
Figure 4. Maintenance costs graph in the product’s life cycle
Time
We choose the interval [3; 7], where one function

breaks the over function.
Figure 7. The second derivative graph

From Figure 7 we can also see that our function does
f(3)
-2.657799668 not change its sign.
f(4)
34.58898933

f(5)
40.23476323
We can see that our chosen interval [3; 7] is not isola-
tive because it does not meet all the requirements for isola-
f(6)
8.597172302 tive interval (Kvedaras & Sapagovas, 1974):
f(7)
-67.027907

24

1. Function changes its sign in the interval
2. The first derivative function does not change its
500
sign in the interval
0
3. The second derivative function does not change its
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
-500
sign in the interval.
-1000
The interval [6; 7] meets all the conditions for isolative
-1500
s
t
s
interval and we will further analyze this interval.
Co -2000
We will find the constant end of the interval [6; 7]: it is
-2500
where the second derivative sign is equal to the function
-3000
sign in the end of interval.
-3500
The second derivative of the function is negative in the
-4000
whole interval, the function is negative in the point x=6, so
Time

the constant point is x=6.
Figure 5. Function (4) graph in the chosen interval
x _ const := a _ pr
We can see from Figure 5 that the given function
x0 := b _ gl
changes its sign in it.
a _ pr := 6
We check if our chosen interval [3; 7] is isolation.
b _ gl := 7

21

---

We calculate proximities according to the formula:
HC.Barksdale, C.E.Harris //Ong Range Planning, 1982, Vol.15, De-
f (x, n)
cember, p. 74-83.
x(n + )
1 = x(n) −
(x _ const − x(n)) (7)
f (x _ const) − f (x, n)
4. Bian, D. Using the product life cycle as a marketing tool// Product
management, 1974, Vol.3, October, p. 38-42.
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f (x) →
771
.
335
+
9882
.
212
x −
0.165358
1206
.
595
e
− ∆ (8)
// Fifth International Conference on Process Plan Reliability, Hous-
We need to know the module minimum of the first de-
ton, TX: Gulf Publishing Company and Hydrocarbon Processing,
rivative function for error of calculations:
1996.
6. Burstein, M. Life-cycle costing. NAA conference proceedings, cost
m := f (
1 x )
0 (9) accounting for the 90’s: Responding to technological change. P. 257-
271.
m = 1379 461951
.


7. Day, G. The product life cycle: Analysis and application issues//
We use the formula of the string method till we get the
Journal of Marketing, 1981, Vol. 45, p. 60-67.
wanted error of calculation ε=0.000001
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CONCEPT – Clean Electronics Products and Technology/ T.Dowie,
│xn←x0

(10)

M.Simon, B.Fogg//1995 9-11 October, Conference Publication No
f (xn)
415, IEE, p. 202-207.
xx: = │while
> ε
9.
m
Emblemsvag, J. Activity-Based Cost and Environmental Manage-
ment: A Different Approach to the ISO 14000 Compliance/ J. Em-
│ xn←
f (x, n)
x(n) −
(x _ const − x(n))
blemsvag, B.Bras. Boston, MA: Kluwer Academic Publishers, 2000.
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317 p.
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We have got the answer: x= 6.15568±0.000001
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We check the answer with the help of MathCAD func-
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tions:
John Wiley &Sons, inc. 2004.
f (x)
,
solve x → .
6 1556857531937244159
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The following conclusions may be drawn:
ment Committee, 2001.
1. After the regression-correlation and elasticity analy-
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sis between trucks’ maintenance costs and the time
nique//Management accounting, 1976, October, p. 343-347.
of its exploitation, it is clear that the exponential
17. Haworth, D. The principles of life-cycle costing//Industrial forum,
correlation exists between them.
1975, Vol. 6, p 13-20.
2.
18.
The life cycle curve’s estimation shows that the
Kaplan, R. Measure cost right: Make the right decisions//Harvard
Business Review, 1998. Reprint 88503.
longer exploitation period is, the bigger mainte-
19.
nance costs are. This can help us to make a decision
Kvedaras B. Skaičiavimo metodai / B.Kvedaras, M.Sapagovas.
Vilnius: Mintis, 1974.
about the further exploitation of the truck during its
20. Lasse, T. Implementation of design to profit in a complex and dy-
valuable life cycle and after it.
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3. The break even between exponential and usually
Oulu Finland, 2001.
used linear dependence means the usage time when
21. Levitt, T. Exploit the Product Life Cycle //Harvard Business Review,
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4.
23. Ray, H. Garrison. Managerial Accounting (9thed.)/ H.Garrison Ray,
The break point can be found with the help of one
W. Eric Norean. Irwin Mc Graw Hill, 2000.
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March, p.42-45.

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Rūta Lapašinskaitė, Vytautas Boguslauskas
laikas nevienodas. Eksploatuojamo vilkiko reikalingų išteklių
skaičius nuolatos auga. Taigi negalime vilkikų grupėse sugeneruotų
Remonto išlaidų paskirstymas produkto gyvavimo cikle
sąnaudų išdalyti vienodomis dalimis atskiriems vilkikams. Iškilusią
Santrauka
problemą apibūdina gyvavimo ciklo sąvoka. Produkto gyvavimo
ciklas apima esmines visų veiklų, kurias produktas patiria ek-
Literatūroje susiduriama su skirtingais termino „gyvavimo cik-
sploatacijos laikotarpiu, išlaidas.
las“ apibrėžimais. Prekybininkai gyvavimo ciklo stadijas vertina
Apskaičiuota gyvavimo ciklo kaštų kreivė parodo, kaip didė-
prekybiniu požiūriu, gamybininkams svarbesni produkcijos gamybos
jant eksploatacijos laikotarpiui auga eksploatacijos sąnaudos vilkiko
aspektai, produktui pasiekus vartotoją, toliau žvelgiama į gyvavimo
gyvavimo cikle. Ši priklausomybė gali padėti priimti sprendimą dėl
ciklą vartotojų požiūriu. Tiksliausias ir išsamiausias požiūris į gy-
tolimesnio vilkikų naudojimo per jų eksploatacijos laikotarpį ir jam
vavimo ciklą vadinamas produkto gyvavimo ciklu. Jis apima esmin-
pasibaigus. Tai pagrindinis tikslas, dėl kurio gyvavimo ciklo vertinimo
ius visų veiklų, kurias produktas ar jo dalys pereina gamyboje ar
sistema buvo sukurta ir toliau vertinama, pasitelkus netradicinį gy-
eksploatacijos laikotarpiu, kaštus. Gyvavimo ciklo vertinimas yra
vavimo ciklo kaštų kreivės vertinimą.
metodas, padedantis numatyti būsimus kaštus bei skaičiuoti gy-
Remonto sąnaudų kreivės vilkikų gyvavimo cikle skaičiavimai,
vavimo ciklo kaštus specifiniams produktams.
funkcijų nustatymas ir grafikų braižymas buvo atliekama su kompi-
Kaip ir dauguma koncepcijų, gyvavimo ciklo vertinimas ilgain-
uterine programa „Statistika“.
iui vystėsi ir dabar apima tris pagrindinius tikslus:
Remiantis atliktos vilkikų remonto sąnaudų priklausomybės nuo
1. Gyvavimo ciklo vertinimas gali būti efektyvus projektavimo
vilkikų eksploatacijos laiko koreliacinės-regresinės analizės rezulta-
įrankis sprendimams priimti, produkcijai kurti, tiekimui or-
tais, sąnaudų daliai, tenkančiai kiekvienam vilkikui, nustatyti buvo
ganizuoti, infrastruktūrai plėtoti ir pan. Tai pagrindinis tik-
panaudota eksponentinė priklausomybė, nes šio modelio koreliacijos
slas, dėl kurio gyvavimo ciklo vertinimo sistema buvo su-
ir determinacijos koeficientai bei elastingumo koeficientas yra didži-
kurta.
ausi. Tai rodo, kad pasirinktas regresinis modelis tinka eksperi-
2. Gyvavimo ciklo vertinimas ištaiso daugybę tradicinių kaštų
mentiniams duomenims, ir yra reikšmingas koreliacinis ryšys tarp
apskaitos sistemų trūkumų ir dėl to gali suteikti naudos kaštų
vilkikų eksploatacijos laiko ir remonto išlaidų.
apskaitai ir valdymui.
Norėdami nustatyti sąnaudų dalį, tenkančią kiekvienam vilkikui,
3. Gyvavimo kaštų vertinimas iškilo kaip tikslų siekimo pro-
naudosime eksponentinio regresijos modelio eksploatacijos laiko ir
dukto projektavime ir plėtojime įrankis.
išlaidų priklausomybės lygtį:
Straipsnio tikslas yra surasti tašką, kuriame tiesinės regresijos
0 165358
,
laikas
Išlaidos =
1206
,
595
⋅ e

kreivė kerta eksponentinės regresijos kreivę, tiksliausiai įvertinančią
remonto kaštų ir laiko kaip išlaidų paskirstymo vieneto, santykį.
Taigi galima padaryti išvadą, kad gyvavimo ciklo kaštų kreivė
skiriasi nuo tradicinių.
Tyrimo objektas yra vilkiko remonto kaštai jo gyvavimo cikle.
Kaštų kreivės gyvavimo cikle vertinimas parodo, kad didėjant
Straipsnyje naudotas tyrimo metodas yra vienas iš iteracinių
eksploatacijos laikotarpiui gyvavimo ciklo kaštai auga, ir tai gali
metodų – stygų metodas.
padėti priimti sprendimą dėl tolimesnio vilkikų naudojimo per jų
Priklausomai nuo turimų išteklių, turimo laiko ir kitų veiksnių,
eksploatacijos laikotarpį ir jam pasibaigus. Gyvavimo ciklo vertini-
tokių kaip duomenų prieinamumas, apimtis, išskiriami keturi skirtingi
mas kartu su moderniosiomis kaštų apskaitos sistemomis gali padėti
būdai atlikti gyvavimo ciklo vertinimą:
ištaisyti daugybę tradicinių sistemų trūkumų ir dėl to gali suteikti

analoginis,
naudos kaštų apskaitai ir valdymui.

parametrinis,
Kadangi eksponentinės regresijos kreivė remonto kaštus pro-

kaštų inžinerijos metodas,
dukto gyvavimo cikle įvertina tiksliausiai, o kompanijos dažniausiai

kaštų apskaita.
naudoja tiesinės regresijos kreivę, šiame straipsnyje aprašomas
Visi šie modeliai turi savų privalumų ir trūkumų.
analitinis lūžio taško, kuriame eksponentinė kreivė kerta tiesinės
Gyvavimo ciklo kaštų įvertinimas pagal analogijos modelį
regresijos kreivę, apskaičiavimas:
pritaiko panašaus produkto ar komponentų kaštus atsižvelgiant į šių
a + bx −
dx
e
c
= ∆


produktų skirtumus. Tačiau, norint užtikrinti pasirinktų praeities
duomenų tinkamumą, produktai bėgant laikui neturėtų labai keistis.
Lūžio taškas reiškia tašką, kuriame kompanijos turėtų rinktis
Taigi tokių modelių taikymas yra labai ribotas.
eksponentinės regresijos formulę kaštams paskirstyti tarp skirtingų
Parametrinis modelis gali naudoti keletą parametrų, be to, remi-
vilkikų, kad galėtų gauti kuo tikslesnį rezultatą kaštų valdymui.
asi vienu ar daugiau kreivinės regresijos modelių ir naudoja analogiją
Lūžio taškas buvo apskaičiuojamas vienu iš iteracinių sprendimo
kaip kaštų veiksnį, Kadangi parametriniai modeliai gali pasiūlyti
metodu – stygų metodu. Šio metodo esmė ta, kad lygčių sistema turi
didesnį tikslumą už analoginius modelius, jų dažnai pasitaiko tech-
sprendinį pasirinktame intervale, jeigu tenkina visas tris izoliacinio
ninėje literatūroje.
intervalo sąlygas:
Kaštų inžinerijos metodas pasirenkamas ten, kur yra išsamūs ir
1. Funkcija keičia ženklą šiame intervale;
tikslūs kapitalo ir valdymo kaštų duomenys turtui analizuoti. Čia
2. Pirmoji funkcijos išvestinė nekeičia ženklo šiame intervale;
tiesiogiai apskaičiuojami kaštai, tikrinant kiekvieną turto detalę, taip
3. Antroji funkcijos išvestinė taip pat nekeičia ženklo šiame in-
pat pasitelkiami kaštų faktorių standartai, padedantys nustatyti kiek-
tervale.
vieno elemento kaštus ir jų ryšį su kitais elementais.
Apskaičiavimai buvo atliekami ε=0, 000001 tikslumu. Ap-
Gamybos apimties vertinimo sistemos dėl savo silpnybių nėra
skaičiavus intervalą, kuris tenkina visas tris izoliacinio intervalo
tinkamos gyvavimo ciklui vertinti, o netradiciniai vertinimo metodai
sąlygas, apskaičiavus artinius ir nustačius išvestinės modulio mini-
yra nepopuliarūs.
mumą, buvo gautas lūžio taškas. Šis taškas buvo patikrintas,
Iš moderniųjų žinomiausia ir plačiausiai taikoma ABC kaštų ap-
pasitelkus MathCAD funkcijas.
skaitos sistema. Nors ji viena ir negali įgyvendinti visų sistemos
Iš šio rezultato galima teigti, kad lūžio taškas egzistuoja ir yra
pokyčių, tačiau, ją integravus į gyvavimo ciklo sistemą, būtų galima
lygus 6,15568 periodams Mercedes Benz markės vilkikams realioje
tiksliausiai įvertinti gyvavimo ciklo kaštus.
transporto kompanijoje.
Nustatę daugiausia išteklių reikalaujančias veiklas bei priskyrę
joms išlaidų paskirstymo vienetus, vis dar nežinome, kaip išlaidos
Raktažodžiai: gyvavimo ciklo kaštai, produkto gyvavimo ciklas, regresinė
pasidalija vilkikų grupėse atskiriems vilkikams, nes jų eksploatacijos
analizė, iteracijos metodai, stygų metodas.

The article has been reviewed.

Received in April, 2005; accepted in October, 2005.





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