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81 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
1. Introduction
In this chapter, in the first part, we illustrate a process (Section 2) for built and in-use assets
maintenance management and to characterize maintenance engineering techniques within that
process. This has become a research topic and a fundamental question to reach the effective-
ness and efficiency of maintenance management and to fulfill enterprise objectives [15]. We
Asset Management. The state of the Art in Europe from a Life Cycle Perspective
Van der Lei, Telli; Herder, Paulien; Wijnia, Ype (Eds.)
2012, 2012, XIV, 172 p.
ISBN 978-94-007-2723-6
Chapter 6
Life Cicle Cost Analysis (LCCA) consideration
within the built and in-use assets maintenance
management.
A. Crespo Márquez, C. Parra Márquez**, J.F. Gómez Fernández,
M. López Campos & V. González Díaz
Dept. Industrial Management. University of Seville
School of Engineering, University of Seville, Spain
**Email: [email protected]
Abstract
The chapter presents a generic model for assets maintenance management. This model inte-
grates other models found in the literature for built and in-use assets, and consists of se-
quential management building blocks. More precisely we want to show the reader the im-
portance of selecting an appropriate method when considering the estimation of the non-
reliability cost of an asset. By doing so, we show the impact of maintenance in life cycle
costing and provide arguments to claim about the needs for proper assets maintenance con-
trol.
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82
review a model/process proposed in this chapter tries somehow to integrate other models
found in the literature (see for instance [6,7]) and presents a total of eight sequential manage-
ment building blocks. Each block, as will be discussed, is a key decision area for asset
maintenance and life cycle management.
In the second part of the chapter (Section 3), among referred decision areas and according
to the editorial team of this project, we have selected to explore methods and models that may
be used to do a suitable asset life cycle cost analysis. More precisely we want to show the
reader the importance of selecting an appropriate method when considering the estimation of
the non reliability cost of an asset. By doing so, we somehow show the impact of maintenance
in life cycle costing and provide arguments to claim about the needs for proper assets mainte-
nance control.
2. Characterizing the Maintenance Management Process The maintenance management process can be divided into two parts: the definition of the
strategy, and the strategy implementation. The first part, conditions the success of mainte-
nance in an organization, determines the effectiveness of maintenance. Maintenance effec-
tiveness allows the minimization of the maintenance indirect costs [3] associated with produc-
tion losses and customer dissatisfaction [4], reduces the overall company cost, obtained
because production capacity is available when needed [5].
The second part of the process, the implementation of the strategy will allow us to mini-
mize the maintenance direct cost (labour and other maintenance required resources). Efficien-
cy is acting or producing with minimum waste, expense, or unnecessary effort.
Phase 1:
Definition of the
maintenance
objectives and
KPI’s
Phase 2:
Assets priority
and maintenance
strategy definition
Phase 3:
Immediate
intervention
on high impact
weak points
Phase 4:
Design of
the preventive
maintenance
plans and
resources
Phase 5:
Preventive plan,
schedule
and resources
optimization
Phase 7:
Asset life cycle
analysis
and replacement
optimization
Phase 6:
Maintenance
execution
assessment
and control
Phase 8:
Continuous
Improvement
and new
techniques
utilization
Assessment Efficiency
Effectiveness
Improvement
Figure 1. Maintenance management model (Adapted from [2])
Our model for maintenance management consists of eight sequential management building
blocks, as presented in Figure 1. At the same time, our idea is that there are maintenance engi-
neering tools that may be used to improve each building block decision making process (see
Figure 2).
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83 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
Phase 1:
Definition of the
maintenance
objectives and
KPI’s
Phase 2:
Assets priority
and maintenance
strategy definition
Phase 3:
Immediate
intervention
on high impact
weak points
Phase 4:
Design of
the preventive
maintenance
plans and
resources
Phase 5:
Preventive plan,
schedule
and resources
optimization
Phase 7:
Asset life cycle
analysis
and replacement
optimization
Phase 6:
Maintenance
execution
assessment
and control
Phase 8:
Continuous
Improvement
and new
techniques
utilization
Assessment Efficiency
Effectiveness
Improvement
Phase 1:
Balance
Score Card
(BSC)
Phase 2:
Criticality
Analysis
(CA)
Phase 3:
Failure Root
Cause Analysis
(FRCA)
Phase 4:
Reliability-
Centred
Maintenance
(RCM)
Phase 5:
Risk―Cost
Optimization
(RCO)
Phase 7:
Life Cycle
Cost Analysis
(LCCA)
Phase 6:
Reliability
Analysis (RA)
& Critical Path
Method
(CPM)
Phase 8:
Total Productive
Maintenance
(TPM),
e-maintenance
Figure 2. Sample of techniques within the maintenance management framework (Adapted from [2])
Phase 1 tries to avoid that the maintenance objectives and strategy could be inconsistent
with the declared overall business strategy [8]. This can indeed be done by introducing the
Balanced Scorecard (BSC) [9]. The BSC is specific for the organization for which it is devel-
oped and allows the creation of key performance indicators (KPIs) for measuring maintenance
management performance which are aligned to the organization’s strategic objectives (See
Figure 3).
Maintenance
planning
and scheduling
Quality Learning
Maintenance
Cost Effectiveness
Maintenance cost (%)
per unit produced (7%)
Data integrity
(95%)
Accomplishment
of criticality analysis
(Every 6 months)
PM
Compliance
(98%)
Maintenance
planning
and scheduling
Quality Learning
Maintenance
Cost Effectiveness
Maintenance cost (%)
per unit produced (7%)
Data integrity
(95%)
Accomplishment
of criticality analysis
(Every 6 months)
PM
Compliance
(98%)
Figure 3. A KPI and its functional indicators (Adapted from [2])
Unlike conventional measures which are control oriented, the Balanced Scorecard puts
overall strategy and vision at the centre and emphasizes on achieving performance targets
[10].
Once the Maintenance Objectives and Strategy are defined, there are a large number of
quantitative and qualitative techniques which attempt to provide a systematic basis for
deciding what assets should have priority within a maintenance management process (Phase
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84
2). Most of the quantitative techniques use a variation of a concept known as the
“probability/risk number” (PRN) [11]. In professional risk assessments, risk combines the
probability of an event occurring with the impact that event would cause R=PxC, where P is
probability and C is consequence (Figure 4). Risk assessment techniques can be used to
prioritize assets and to align maintenance actions to business targets at any time.
3
CriticalCritical
SemiSemi--criticalcritical
NonNon--criticalcritical
10 20 30 40 5010 20 30 40 50
ConsequenceConsequence
44
33
22
11
FFrreeqquueennccyy
1 2 1 3
4 2
3
CriticalCritical
SemiSemi--criticalcritical
NonNon--criticalcritical
10 20 30 40 5010 20 30 40 50
ConsequenceConsequence
44
33
22
11
FFrreeqquueennccyy
1 2 1 3
4 2
Figure 4. Generic criticality matrix and assets location
As mentioned above, once there is a certain ranking of assets priority, we have to set up
the strategy to follow with each category of assets. Of course, this strategy will be adjusted
over time, and will consist of a course of action to address specific issues for the emerging
critical items under the new business conditions (see Figure 5).
A
B
C
Ass
et c
ate
gory
Main
tenance
stra
tegy
Sustain – improve
current situation
Ensure certain
equipment availability
levels
Reach optimal reliability,
maintainability and
availability levelsA
B
C
Main
tenance
stra
tegy
Figure 5. Example of maintenance strategy definition for different category assets [2]
An example of detailed maintenance actions for category A assets — where we try to
reach optimal reliability, maintainability and availability levels — could be: 1) Apply FMECA
for critical failure mode analysis; 2) Apply RCM for optimal maintenance task selection; 3)
Standardise maintenance tasks; 4) Analyse design weaknesses and 5) Continue review
FMECA and RCM.
Phase 3 deals with finding and eliminating, if possible, the causes of certain repetitive fail-
ures that take place in high priority items. There are different methods developed to carry out
this weak point analysis, one of the most well known being root-cause failure analysis
(RCFA). This method consists of a series of actions taken to find out why a particular failure
or problem exists and to correct those causes.
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85 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
Phase 4 is devoted to the design of the preventive maintenance plan for a certain system
and this requires identifying its functions, the way these functions may fail and then establish
a set of applicable and effective preventive maintenance tasks, based on considerations of sys-
tem safety and economy. A formal method to do this is the Reliability Centred Maintenance
(RCM), as in Figure 6.
Figure 6. RCM implementation process
Optimization of maintenance planning and scheduling (Phase 5) can be carried out to en-
hance the effectiveness and efficiency of the maintenance policies resulting from an initial
preventive maintenance plan and program design. Models to optimize maintenance plan and
schedules will vary depending on the time horizon of the analysis [13].
Phase 6 deals with the execution of the maintenance activities ― once designed planned
and scheduled using techniques described for previous building blocks —. This execution has
to be evaluated and deviations controlled to continuously pursue business targets and ap-
proach stretch values for key maintenance performance indicators as selected by the organiza-
tion.
A life cycle cost analysis (Phase 7) calculates the cost of an asset for its entire life span (see
Figure 7). The analysis of a typical asset could include costs for planning, research and devel-
opment, production, operation, maintenance and disposal. A life cycle cost analysis is im-
portant when making decisions about capital equipment (replacement or new acquisition)
[12], it reinforces the importance of locked in costs, such as R&D, and it offers important
benefits. We concentrate on techniques for LCCA in Section 3 of this Chapter.
RCM
team
conformation
Application of
the RCM
logic
Operational
context
definition
and asset
selection
FunctionFunctional
failuresFailure modes
Effect of
failure modes
FMEA
Failure Mode and
Effects Analysis
Tool to answer the first 5
RCM Questions
RCM
Implementation phase
Initial
Phase
Criticality
Analysis
(level?)
Tool to answer
the last 2
RCM Questions
Maintenance
plan
documentation
Final
Phase
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86
Corrective Maintenance + Security, Environment, Production =
Non Non ReliabilityReliability CostsCosts = = RiskRisk
Operation + Planned Maintenance Costs.
CAPEX
Capital Costs
OPEX
Operational Costs
Development
costs
Investment
costs
Operation
costs
Time (years)
Acquisition
Construction
Design
Investigation
Remove
Corrective Maintenance + Security, Environment, Production =
Non Non ReliabilityReliability CostsCosts = = RiskRisk
Operation + Planned Maintenance Costs.
CAPEX
Capital Costs
OPEX
Operational Costs
Development
costs
Investment
costs
Operation
costs
Time (years)
Acquisition
Construction
Design
Investigation
Remove
Figure 7. Life cycle cost analysis
Finally, continuous improvement of maintenance management (Phase 8) will be possible
due to the utilization of emerging techniques and technologies in areas that are considered to
be of higher impact as a result of the previous steps of our management process. Regarding
the application of new technologies to maintenance, the “e-maintenance” concept (Figure 8) is
put forward as a component of the e-manufacturing concept [14], which profits from the
emerging information and communication technologies to implement a cooperative and dis-
tributed multi-user environment. E-Maintenance can be defined [10] as a maintenance support
which includes the resources, services and management necessary to enable proactive decision
process execution.
Top Management
Middle Management
Maintenance Dept
Assets /
Information Source
Reports
Reports
Inspections/Complaints
Conventional Maintenance
Top Management
Middle Management
Maintenance Dept
Assets /
Information Source
E-maintenance
Login to
iScada
Precise &
Concise
Information
Top Management
Middle Management
Maintenance Dept
Assets /
Information Source
Reports
Reports
Inspections/Complaints
Conventional Maintenance
Top Management
Middle Management
Maintenance Dept
Assets /
Information Source
Login to
iScada
Precise &
Concise
Information
Figure 8. Implementing e-maintenance (http://www.devicesworld.net)
3. Evaluating the economic impact of the failure in the LCCA Life cycle costing is a well-established methodology that takes into account all costs arising
during the life cycle of the asset. These costs can be classified as the ‘capital expenditure’
(CAPEX) incurred when the asset is purchased and the ‘operating expenditure’ (OPEX) in-
curred throughout the asset’s life. LCCA is a method that can be used, for instance, to evalu-
ate alternative asset options [1], or/and assets maintenance management strategies [2].
For all these potential purposes, a key aspect to introduce in a LCCA is the failure costs. In
order to model that cost we will now introduce the Non-homogeneous Poisson Process model
(NHPP, repairable systems). With the NHPP model we can estimate the frequency of failures
and the impact that could cause the diverse failures in the total cost of ownership of a produc-
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87 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
tion asset. This section also contains a case of study to illustrate the above mentioned con-
cepts.
3.1. Characterizing the total costs of failures (non reliability) Life cycle cost analysis (LCCA) can be defined [14] as a systematic process of technical-
economical evaluation that considers, in a simultaneous way, economic and reliability aspects
of an asset, quantifying their real impact along its life cycle cost. Reliability is related to op-
erational continuity. We normally say that a production system is "reliable" when it is able to
accomplish its function in a secure and efficient way along its life cycle. Low reliability caus-
es normally high costs, mainly associated to the asset function recovery (direct costs) besides
the corresponding escalated impact in the production process (penalization costs). The totals
costs of non reliability can be then classified as follows ([20], [21] and [22]):
Costs for penalization: Downtime, opportunity losses/deferred production, production
losses (unavailability), operational losses, impact in the quality, impact in security and en-
vironment.
Costs for corrective maintenance: Manpower, direct costs related with the manpower
(own or hired) in the event of a non planned action; and materials and replacement
parts, direct costs related with the consumable parts and the replacements used in the
event of an unplanned action.
3.2. Using NHPP for Reliability Analysis NHPP is a stochastic discrete process where, in its initial formulation, we assume that the
equipment is “as bad as old” (ABAO) operating condition after a repair (this is also referred as
minimal repair in the maintenance modelling literature [24, 25]). In this process the probabil-
ity of occurrence of n failures in any interval [t1, t2] has a Poisson distribution with the mean
[24]:
1
2)(
t
tdtt (1)
Where )(t is the rate of occurrence of failures (ROCOF).
Therefore, according to the Poisson process:
!
)(exp)(
])()(Pr[
2
1
2
1
12n
dttdtt
ntNtN
t
t
nt
t
(2)
Where n = 0, 1, 2,… are the total expected number of failures in the time interval [t1,t2].
Let us represent with )(t the expected number of failures in a time interval [0, t], then
t
dttt0
)()( (3)
One of the most common forms of ROCOF used in reliability analysis of repairable systems
is the Power Law Model ([24] and [25]), that estimates the failure rate as follows: 1
)(
tt (4)
This form comes from the assumption that the inter-arrival times between successive fail-
ures follow a conditional Weibull probability density function, with parameters α and β. The
Weibull distribution is typically used in maintenance area due to its flexibility and applicabil-
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88
ity to various failure processes (however, solutions to Gamma and Log-normal distributions
are also possible). As we know by reliability theory, λ(t) is a conditional probability for which
we can consider the following definition (see Figure 10):
Figure 10. Conditional probability of occurrence of failure [26]
)1
(
)(1
)1
(
)(1)(1
)1
(
)1
()()
1(
tR
tR
tR
tRtR
tR
tFtFtTtTP
(5)
where F(t) and R(t) are the probability of failure and the reliability at the respective times.
Assuming a Weibull distribution, Eq. (5) yields:
i
ti
t
itF 1exp1)( (6)
Therefore, the conditional Weibull density function is:
it
it
it
itf 1exp.
1
)( (7)
Now we will use this function in order to obtain the maximum likelihood (ML) estimators
of the parameters of the Power Law model. For the case of the NHPP, different expressions
for the likelihood function may be obtained. We will use expression based on estimations at a
time t after the occurrence of the last failure and before the occurrence of the next failure, see
details on these expressions in [27].
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89 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
3.2.1. Time terminated NHPP maximum likelihood estimators In the case of time terminated repairable components, the maximum likelihood function L
can be expressed as:
)
2
()()1
(
1
)( tn
tn
i
Ri
tftfn
ii
tfL
(8)
Therefore:
1exp
11
ttL
n
i
iin
i
nttt
2
1
2
1
1
1
exp
(9)
Then the ML estimators for the parameters are calculated. The results are ([24] and [25]):
1
ˆ
n
n
t
(10)
it
ntn
i
n
1
ln
(11)
Where ti is the time at which the ith failure occurs, tn is the total time where the last fail-
ure occurred, and n is the total number of failures. The total expected number of failures in the
time interval [tn, tn+s] by the Weibull cumulative intensity function is [27]:
nt
st
nt
snt
nt
1),( (12)
Where t s is the time after the last failure occurred in the one which needs to be considered
the number of failures and tn is:
n
ii
tn
t
1
(13)
3.3. A NHPP MODEL FOR FAILURE COST ASSESSMENT IN LCCA Our previous NHPP model structure can be used for the quantification of the costs of fail-
ures in the LCCA (cost of non reliability [28]). With this model we propose to assess the im-
pact of main failures on a production system LCC structure by following the next procedure:
1. Identify for each alternative to evaluate the main types of failures. This way for certain
equipment there will be f = 1… F types of failures.
2. Determine for the n (total of failures), the times to failures ft . This information will be
gathered by the designer based on records of failures, databases and/or experience of
maintenance and operations personnel.
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90
3. Calculate the Costs for failures fC ($/failure). These costs include: costs of penalization
for production loss and operational impact Cp ($/hour), costs of maintenance corrective
Cc ($/hour) and the mean time to repair MTTR (hours). The expression used to estimate
the fC is shown next:
MTTRCcCpC f )( (14)
4. Define the expected frequency of failures per year ),( snn tt . This frequency is assumed
as a constant value per year for the expected cycle of useful life. The ),( sntnt is calcu-
lated starting from the expression (12). This process is carried out starting from the times
to failures registered ft by failure type (step 2). The parameters and , are set starting
from the following expressions (10) and (11). In the expression (12), st it will be a year (1
year) or equivalent units (8760 hours, 365 days, 12 months, etc.). This time st represents
the value for estimate de frequency of failures per year.
5. Calculate the total costs per failures per year fTCP , generated by the different events of
stops in the production, operations, environment and security, with the following expres-
sion:
f
CF
fsn
tn
tf
TCP
, (15)
The obtained equivalent annual total cost, represents the probable value of money that
will be needed every year to pay the problems of reliability caused by the event of failure,
during the years of expected useful life.
6. Calculate the total costs per failures in present value f
PTCP . Given a yearly value
fTCP , the quantity of money in the present (today) that needs to be saved, to be able to
pay this annuity for the expected number of years of useful life (T), for a discount rate (i).
The expression used to estimate the fPTCP is shown next:
Tii
Ti
fTCP
fPTCP
1
11 (16)
Once this cost is estimated, it is added to the rest of the evaluated costs (investment,
planned maintenance, operations, etc.). Finally, the total cost is calculated in present value for
the selected discount rate and the expected years of useful life. Different results can be ob-
tained, for instance for different assets options or/and maintenance strategy options.
3.4. CASE STUDY The following case study proposes the evaluation of the economic impact of the failures us-
ing the method NHPP. The analysis was developed for the oil company PETRONOX (con-
tractor of Petróleos of Venezuela), located in the field of gas and petroleum Naricual II, in
Monagas, Venezuela. In general terms, it is requires to install a compression system to man-
age a flow average of 20 millions of cubic feet of gas per day. The organization PETRONOX,
evaluates the information of two suppliers of compressors. Next, are shown the data of costs
of: initial investment, operation and maintenance for the two options to evaluate (value esti-
mated by the suppliers, see Table 1):
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91 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
Option A:
Reciprocant Compressor, 2900-3200 hp, caudal: 20 millions of feet cubic per day
Option B:
Reciprocant Compressor, 2810-3130 hp, caudal: 20 millions of feet cubic per day
Data Option A Option B
I: Investment 1.100.000 $ 900.000 $
OPC: opera-
tionals costs
100.000 $/year 120.000 $/year
PRC: preven-
tive costs
60.000 $/year 40.000 $/year
OVC: overhauls
costs
100.000 $ every 5
years
80.000 $ every 5
years
i: interest 10% 10%
T: expected
useful life
15 years 15 years
Table 1. Economical data
With this information the organization PETRONOX carried out a first economic LCCA and
a comparison made among the two alternatives, in this first evaluation, no failure cost analysis
was considered and results are presented in Table 2:
Results Option A Option B
1) I: Invesment 1.100.000 $ 900.000 $
2) OPC(P): operation-
als costs in present
value
760.607,951 $ 912.729,541 $
3) PRC(P): preventive
costs in present value
456.364,77 $ 304.243,18 $
4) OVC(P): overhauls
costs in present value,
t = 5 years
62.092, 1323 $ 49.673,7058 $
5) OVC(P): overhauls
costs in present value,
t = 10 years
38.554,3289 $ 30.843,4632 $
6) OVC(P): overhauls
costs in present value,
t = 15 years
23.939,2049 $ 19.151,3639 $
TLCC(P): Total Life
Cycle Costs in pre-
sent value, i: 10%, T:
15 years (Sum 1…6)
2.441.558,387 $ 2.216.641,254 $
Table 2. Economical results without to evaluate the costs per failures
In Table 2, the oil company doesn't consider the possible costs of failures events. The op-
tion B results to be the best economic alternative (more economic alternative for a lifespan pe-
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92
riod of 15 years). There is a difference of approximately: 224.917,133 $ between the two al-
ternatives (this quantity would be the potential saving to select the option B, without consider-
ing the possible costs for failures).
Later on, a proposal consisting on the evaluation of the same figures taking into considera-
tion now the failure costs was made to the organization. It was suggested using a NHPP model
for this evaluation, the total expected number of failures the interval of time [tn, tn+s] is es-
timated by the NHPP stochastic model (Weibull cumulative intensity function) [27]. Next, are
shown the data of costs and times of failures to be used inside the NHPP model (the data of
times to failures f
t were gathered by PETRONOX of two similar compression systems that
operate under very similar conditions in those that will work the compressor to be selected):
Data Option A Option B
Cp ($/hour) 6.000 6.000
Cc ($/hour) 700 400
MTTR (hours) 9 8
ft (months) 5, 7, 3, 7, 2, 4, 3, 5,
8, 9, 2, 4, 6, 3, 4, 2,
4, 3, 8, 9
2, 3, 3, 5, 6, 6, 5,
6, 5, 6, 4, 3, 2, 2,
2, 2, 3, 2, 2, 3, 2,
2, 3, 3
nt (total of
months)
98
82
n (total of fail-
ures)
20 24
Table 3. Failure costs and maintainability/reliability data
With the information of the Table 3, the equation (16) was used to calculate the frequency
of failures per year ),( snn tt . The parameters and of the Distribution of Weibull con-
tained in the equation (16) were calculated from the equations (14) and (15). The total costs
for failures per year f
TCP were calculated from the equations (18) and (19); these costs are
converted to present value f
PTCP with the equation (20). Next, are shown the results of the
frequency of failures and the total costs for failures for year obtained starting from the NHPP
model, for the two evaluated options:
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93 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
Results Option A Option B
6,97832 6,13985
1,13382 1,22614
),(sn
tn
t
= fail-
ures/year
2,7987 = 2,8 4,3751=4,38
fTCP = $/year 168.840 224.256
fPTCP = $
(i=10%, T=15 years)
1.284.210,46
1.705.708,97
Table 4. Results from NHPP model
Later on, a second LCC economic evaluation was carried out including the results of costs
of failures obtained from the NHPP model. The results are presented in Table 5:
Results Option A Option B
1) I: Invesment 1.100.000 $ 900.000 $
2) OPC(P): operation-
als costs in present val-
ue
760.607,951 $ 912.729,541 $
3) PRC(P): preventives
costs in present value
456.364,77 $ 304.243,18 $
4) OVC(P): overhauls
costs in present value,
t = 5 years
62.092, 1323 $ 49.673,7058 $
5) OVC(P): overhauls
costs in present value,
t = 10 years
38.554,3289 $ 30.843,4632 $
6) OVC(P): overhauls
costs in present value,
t = 15 years
23.939,2049 $ 19.151,3639 $
7)PTCPf: total costs
per failures in present
value
1.284.210,46 $ 1.705.708,97 $
TLCC(P): Total Life
Cycle Costs in present
value, i: 10%, T: 15
years (Sum 1…7)
3.725.768,851 $ 3.922.350,22 $
PTCPf / TLCC(P) = %
(total costs per failures
/ total life cycle costs)
34,46% 43.48%
Table 5. Economical results with the costs per failures
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94
In the results of this second evaluation (see Table 5), the total costs for failures are included
in present value PTCPf. Notice that now Option A turns out to be the best economic alterna-
tive, with a difference of approximately: 196.581,368 $ (this quantity would be the potential
saving if selecting the option A instead of B). An important aspect to be considered in this
analysis, is that PTCPf category of cost turns out to be the highest economic factor, with
more weight, inside the process of the two alternatives comparison. Specifically, this category
of costs represents the 43,48% (Option B) and the 34,46% (Option A) of the total LCC of
these two assets (with an interest rate of 10% and a prospective cycle of life of 15 years).
Finally, as per previous results discussion, PETRONOX decided to consider failures cost
analysis in their LCCA. Additionally, the organization PETRONOX decided to develop an in-
ternal procedure allowing the evaluation of reliability opportunity cost, this procedure would
be used in a continuous and obligatory basis every time different options are analyzed inside
the processes of: design, selection, substitution and/or purchase of assets.
3.4.1. Limitations of the NHPP proposed model The analysis of the failure is an important facet in the development of maintenance strategy
in the life cycle cost analysis of the asset. Only by properly understanding the mechanism of
failure, through the modeling of failure data, can a proper maintenance plan and an analysis of
costs be developed [47]. This is normally done by means of probabilistic analysis of the fail-
ure data. From this, conclusions can be reached regarding the effectiveness and efficiency of
preventive replacement (and overhaul) as well as that of predictive maintenance. The optimal
frequency of maintenance can also be established by using well developed optimization mod-
els. These optimize outputs, such as profit, cost and availability. The problem with this ap-
proach is that it assumes that all repairable systems are repaired to the ‘good-as-new’ condi-
tion at each repair occasion. Maintenance practice has learnt, however, that in many cases
equipment slowly degrades even while being properly maintained (including part replacement
and periodic overhaul). The result of this is that failure data sets often display degradation.
This renders conventional probabilistic analysis useless.
The NHPP model has proved to provide good results even for realistic situations with bet-
ter-than-old but worse-than-new repairs [29]. Based on this, and given its conservative nature
and manageable mathematical expressions, the NHPP was selected for this particular work.
The NHPP models can be considered as simple curve-fitting approach that can be easily un-
derstood and implemented by software engineers and developers [47]. It is also this type of
models that have been used by practitioners in most cases. On the other hand, without an in-
depth understanding, the models and analysis are more likely to be misused and further analy-
sis, which could been possible are not carried out. There is a need for more in depth study of
NHPP model and their effectiveness in predicting future failure behaviour. Most of current re-
search focuses on developing more complex models, see other models found in the literature
([48] and [49]). However more research is needed with regard to model selection. When com-
paring models, the focus should be on the prediction rather than fitting as a model can fit the
past data correctly, but has a poor predictive ability. Knafl and Morgan [50] provides some in-
itial discussion on this area.
The model described above has advantages and limitations. In general, the more realistic is
the model, the more complex are the mathematical expression involved. The main strengths
and weakness of this model are summarized next:
Strengths:
It is a useful and quite simple model to represent equipment under aging (deterioration).
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95 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
Involves relatively simple mathematical expressions.
It is a conservative approach and in most cases provides results very similar to those of
more complex models like Generalized Renewal Process [29].
Weakness:
Is not adequate to simulate repair actions that restore the unit to conditions better than new
or worse than old.
4. Conclusions
The orientation of this chapter is towards maintenance management models, and within
them, to the presentation of techniques to consider LCCA within the process (Phase) of assets
maintenance assessment, control and improvement.
We have shown how the reliability factor and its impact on costs can be critical for LCCA
and may influence in final results produced with this analysis for assets options and/or for
maintenance management strategy alternatives.
Prevision of unexpected failure events and their cost is crucial for correct decision making
and profitability of production process. Improvements of process reliability (quality of the de-
sign, used technology, technical complexity, frequency of failures, costs of preven-
tive/corrective maintenance, maintainability levels and accessibility) may have a great impact
on the total cost of the life cycle of the asset, and on the possible expectations to extend the
useful life of the assets to reasonable costs.
5. Future trends We believe that, within LCCA techniques, there is a potential area of research related to the
optimization of the reliability impact evaluation techniques on LCC. Some interesting trends
that we have identified are as follows:
Stochastic methods see ([30], [31] and [32]). Table 6 shows the stochastic processes used
in reliability investigations of repairable systems, with their possibilities and limits [27].
Advanced maintenance optimization using genetic algorithms see ([33] and [34]).
Monte Carlo simulation techniques see ([35], [36] and [37]).
Advanced Reliability distribution analysis see ([38], [39], [40], [41] and [42]).
Markov simulation methods see ([43], [44], [45] and [46]).
Reliability methods in phase of design see ([51] and [52]).
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96
Stochastic pro-
cess
Can be used Back-
ground/
Difficulty
Renewal process
Alternating
renewal process
Markov process
(MP)
Semi-Markov
process (SMP)
Semi-Regenerative
process
Nonregenerative
process
Spare parts provisioning
in the case of arbitrary
failure rates and negligi-
ble replacement or repair
time (Poisson process)
One-item repairable (re-
newable) structure with
arbitrary failure and re-
pair rates
Systems of arbitrary
structure whose elements
have constant failure and
repair rates during the
stay time (sojourn time)
in every state (not neces-
sarily at a state change,
e.g. because of load shar-
ing)
Some systems whose el-
ements have constant or
Erlangian failure rates
(Erlang distributed fail-
ure-free times) and arbi-
trary repair rates
Systems with only one
repair crew, arbitrary
structure, and whose el-
ements have constant
failure rates and arbitrary
repair rates
Systems of arbitrary
structure whose elements
have arbitrary failure and
repair rates
Renewal the-
ory/
Medium
Renewal the-
ory/
Medium
Differential
equations
or integral
equations/
Low
Integral
equations/
Medium
Integral
equations/
High
Partial diff.
eq.; case by
base sol./
High to very
high
Table 6. Stochastic processes used in reliability analysis of repairable systems
Finally, it is not feasible to develop a unique LCCA model, which suits all the require-
ments. However, it is possible to develop more elaborate models to address specific needs
such as a reliability cost-effective asset development.
6. Acknowledgements This research is funded by the Spanish Department of Science and Innovation project
DPI2008-01012 (Modelling e-maintenance policies for the improvement of production sys-
tems dependability and eco-efficiency).
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97 Draft Versión # 3. Carlos A. Parra M. Email: [email protected] www.confiabilidadoperacional.com
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Corresponding authors
A. Crespo Márquez can be contacted at: [email protected] C. Parra Márquez can be contacted at: [email protected]