libro de confiabilidad

1. 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: parrac37@yahoo.com
Abstract
The chapter presents a generic model for assets maintenance management. This model integrates other models found in the literature for built and in-use assets, and consists of sequential management building blocks. More precisely we want to show the reader the importance of selecting an appropriate method when considering the estimation of the nonreliability 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 control.
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 effectiveness and efficiency of maintenance management and to fulfill enterprise objectives [15]. We
81
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

2. 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 management 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 maintenance 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 maintenance in an organization, determines the effectiveness of maintenance. Maintenance effectiveness allows the minimization of the maintenance indirect costs [3] associated with production 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 minimize the maintenance direct cost (labour and other maintenance required resources). Efficiency is acting or producing with minimum waste, expense, or unnecessary effort.
Effectiveness
Phase 1:
Definition of the
maintenance
objectives and
KPI’s
Phase 8:
Continuous
Improvement
and new
techniques
utilization
Phase 7:
Asset life cycle
analysis
and replacement
optimization
Assessment
Phase 2:
Assets priority
and maintenance
strategy definition
Phase 3:
Immediate
intervention
on high impact
weak points
Improvement
Phase 4:
Design of
the preventive
maintenance
plans and
resources
Phase 6:
Maintenance
execution
assessment
and control
Phase 5:
Preventive plan,
schedule
and resources
optimization
Efficiency
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 engineering tools that may be used to improve each building block decision making process (see
Figure 2).
82

3. Effectiveness
Phase 1:
Definition of the
Phase 1:
maintenance
Balance
objectives and
Score Card
KPI’s
(BSC)
Phase 8:
Phase 8:
Continuous
Total Productive
Improvement
Maintenance
and new
(TPM),
techniques
e-maintenance
utilization
Phase 7:
Phase 7:
Asset life cycle
Life Cycle
analysis
Cost Analysis
and replacement
(LCCA)
optimization
Phase 2:
Phase 2:
Criticality
Assets priority
Analysis
and maintenance
strategy(CA)
definition
Phase 3:
Phase 3:
Immediate
Failure Root
intervention
Cause Analysis
on high impact
(FRCA)
weak points
Improvement
Phase 4:
Design of
Phase 4:
theReliabilitypreventive
maintenance
Centred
plans and
Maintenance
resources
(RCM)
Phase 6:
Phase 6:
Reliability
Maintenance
Analysis (RA)
execution
& Critical Path
assessment
Method
and control
(CPM)
Phase 5:
Phase 5:
Preventive plan,
Risk―Cost
schedule
Optimization
and resources
(RCO)
optimization
Efficiency
Assessment
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 developed 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
Cost Effectiveness
Maintenance cost (%)
per unit produced (7%)
Maintenance
planning
and scheduling
Quality
Learning
PM
Compliance
(98%)
Accomplishment
of criticality analysis
(Every 6 months)
Data integrity
(95%)
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
83
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

4. 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.
4
F
r
e 3
q
u
e 2
n
c
y
1
1
2
1
4
2
3
Critical
Semi-critical
SemiNon-critical
Non-
3
10
20
30
40
50
Consequence
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).
Ensure certain
equipment availability
levels
Sustain – improve
current situation
Maintenance strategy
B
C
Asset category
A
Reach optimal reliability,
maintainability and
availability levels
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 failures 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.
84

5. 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 system safety and economy. A formal method to do this is the Reliability Centred Maintenance
(RCM), as in Figure 6.
Initial
Phase
RCM
team
conformation
Criticality
Analysis
(level?)
RCM
Implementation phase
Operational
context
definition
and asset
selection
Function
Functional
failures
FMEA
Failure Mode and
Effects Analysis
Failure modes
Effect of
failure modes
Tool to answer the first 5
RCM Questions
Tool to answer
the last 2
RCM Questions
Final
Phase
Application of
the RCM
logic
Maintenance
plan
documentation
Figure 6. RCM implementation process
Optimization of maintenance planning and scheduling (Phase 5) can be carried out to enhance 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 approach stretch values for key maintenance performance indicators as selected by the organization.
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 development, production, operation, maintenance and disposal. A life cycle cost analysis is important 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.
85
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

6. CAPEX
Capital Costs
Development
costs
OPEX
Operational Costs
Investment
costs
Operation
costs
Acquisition
Corrective Maintenance + Security, Environment, Production =
Non Reliability Costs = Risk
Design
Operation + Planned Maintenance Costs.
Investigation
Construction
Remove
Time (years)
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 distributed 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.
Conventional Maintenance
E-maintenance
Top Management
Top Management
Reports
Middle Management
Reports
Middle Management
Login to
iScada
Maintenance Dept
Maintenance Dept
Precise &
Concise
Information
Inspections/Complaints
Assets /
Information Source
Assets /
Information Source
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) incurred throughout the asset’s life. LCCA is a method that can be used, for instance, to evaluate 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 produc86

7. tion asset. This section also contains a case of study to illustrate the above mentioned concepts.
3.1. Characterizing the total costs of failures (non reliability)
Life cycle cost analysis (LCCA) can be defined [14] as a systematic process of technicaleconomical 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 operational 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 causes 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 environment.
 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 probability of occurrence of n failures in any interval [t1, t2] has a Poisson distribution with the mean
[24]:


t1
t2
 (t )dt
(1)
Where  (t ) is the rate of occurrence of failures (ROCOF).
Therefore, according to the Poisson process:
n
 t2  (t )dt  exp  t2  (t )dt 
 t

 t1




Pr[ N (t 2 )  N (t1 )  n]   1
(2)
n!
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
(t )    (t )dt
(3)
0
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:
t 
 (t )   
  
 1
(4)
This form comes from the assumption that the inter-arrival times between successive failures 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 applicabil87
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

8. 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]
P(T  t T  t ) 
1
F (t )  F (t ) 1  R(t )  1  R(t )
R(t )
1 
 1
R(t )
R(t )
R(t )
1
1
1
(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:
 t
 t
 i  1 

  i
F (ti )  1  exp 
  














(6)
Therefore, the conditional Weibull density function is:
 1
  t  
 t
  ti 
 i  1 
 

  i  
f (ti ) 
. exp 


 
 



 

 
 
(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].
88

9. 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:
n
n
(8)
L   f (t )  f (t )  f (t ) R(t t )
i
1
i
n
i 1
i2
Therefore:

 1
 t  
  
   t1 
L  
exp   1   
   
 
   
   



  n1 n t  1
 n  t    t    
 1
 

(9)
      exp    i 1    i   
 i 2   
    
   i 2   
 
 

Then the ML estimators for the parameters are calculated. The results are ([24] and [25]):
t
ˆ
(10)
 n
1
n

n
(11)
n  tn 
 ln  
 
i  1  ti 
Where ti is the time at which the ith failure occurs, tn is the total time where the last failure 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]:
1 
(12)
(t , t
)
t t   t  
n ns
n 
  n s



ˆ


  
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
(13)
t   t
n
i
i 1
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 failures in the LCCA (cost of non reliability [28]). With this model we propose to assess the impact 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 t f . This information will be
gathered by the designer based on records of failures, databases and/or experience of
maintenance and operations personnel.
89
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

10. 3. Calculate the Costs for failures C f ($/failure). These costs include: costs of penalization
for production loss and operational impact Cp ($/hour), costs of maintenance corrective
Cc ($/hour) and the mean time to repair MTTR (hours). The expression used to estimate
the C f is shown next:
C f  (Cp  Cc)  MTTR
(14)
4. Define the expected frequency of failures per year (t n , t n s ) . This frequency is assumed
as a constant value per year for the expected cycle of useful life. The (tn , tns ) is calculated starting from the expression (12). This process is carried out starting from the times
to failures registered t f by failure type (step 2). The parameters  and , are set starting
from the following expressions (10) and (11). In the expression (12), t s it will be a year (1
year) or equivalent units (8760 hours, 365 days, 12 months, etc.). This time t s represents
the value for estimate de frequency of failures per year.
5. Calculate the total costs per failures per year TCPf , generated by the different events of
stops in the production, operations, environment and security, with the following expression:
F
TCP    t , t
C
(15)
f
n ns
f
f
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 PTCP . Given a yearly value
f
TCP , the quantity of money in the present (today) that needs to be saved, to be able to
f
pay this annuity for the expected number of years of useful life (T), for a discount rate (i).
The expression used to estimate the PTCPf is shown next:

PTCP  TCP 
f
f

1  i T  1
i  1  i T
(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 obtained, 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 using the method NHPP. The analysis was developed for the oil company PETRONOX (contractor 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 manage 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 estimated by the suppliers, see Table 1):
90

11.  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
I: Investment
OPC: operationals costs
PRC: preventive costs
OVC: overhauls
costs
i: interest
T: expected
useful life
Option A
1.100.000 $
100.000 $/year
Option B
900.000 $
120.000 $/year
60.000 $/year
40.000 $/year
100.000 $ every 5
years
10%
15 years
80.000 $ every 5
years
10%
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
1.100.000 $
900.000 $
2) OPC(P): operationals 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 present value, i: 10%, T:
15 years (Sum 1…6)
2.441.558,387 $
2.216.641,254 $
1) I: Invesment
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 option B results to be the best economic alternative (more economic alternative for a lifespan pe91
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

12. riod of 15 years). There is a difference of approximately: 224.917,133 $ between the two alternatives (this quantity would be the potential saving to select the option B, without considering the possible costs for failures).
Later on, a proposal consisting on the evaluation of the same figures taking into consideration 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 estimated 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 t f 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
t f (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
t n (total of
98
82
20
24
months)
n (total of failures)
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 (tn , tn  s ) . The parameters  and  of the Distribution of Weibull contained in the equation (16) were calculated from the equations (14) and (15). The total costs
for failures per year TCP were calculated from the equations (18) and (19); these costs are
f
converted to present value PTCP
with the equation (20). Next, are shown the results of the
f
frequency of failures and the total costs for failures for year obtained starting from the NHPP
model, for the two evaluated options:
92

13. Results
Option A
Option B

6,97832
6,13985

1,13382
1,22614
(t , t
) = failn ns
ures/year
2,7987 = 2,8
4,3751=4,38
TCPf = $/year
168.840
224.256
PTCP = $
f
(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
1.100.000 $
900.000 $
2) OPC(P): operationals costs in present value
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 $
34,46%
43.48%
1) I: Invesment
PTCPf / TLCC(P) = %
(total costs per failures
/ total life cycle costs)
Table 5. Economical results with the costs per failures
93
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

14. 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 alternative, 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 internal 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 failure 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 models. These optimize outputs, such as profit, cost and availability. The problem with this approach is that it assumes that all repairable systems are repaired to the ‘good-as-new’ condition 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 better-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 understood 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 indepth understanding, the models and analysis are more likely to be misused and further analysis, 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 research 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 comparing 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 initial 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).
94

15. 

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 design, used technology, technical complexity, frequency of failures, costs of preventive/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]).
95
Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com

16. Stochastic process
Can be used
Background/
Difficulty
Renewal theory/
Medium
Renewal process
Spare parts provisioning
in the case of arbitrary
failure rates and negligible replacement or repair
time (Poisson process)
Alternating
renewal process
One-item repairable (renewable) structure with
arbitrary failure and repair rates
Renewal theory/
Medium
Markov process
(MP)
Systems of arbitrary
structure whose elements
have constant failure and
repair rates during the
stay time (sojourn time)
in every state (not necessarily at a state change,
e.g. because of load sharing)
Differential
equations
or integral
equations/
Low
Semi-Markov
process (SMP)
Some systems whose elements have constant or
Erlangian failure rates
(Erlang distributed failure-free times) and arbitrary repair rates
Integral
equations/
Medium
Semi-Regenerative
process
Systems with only one
repair crew, arbitrary
structure, and whose elements have constant
failure rates and arbitrary
repair rates
Integral
equations/
High
Systems of arbitrary
structure whose elements
have arbitrary failure and
repair rates
Partial diff.
eq.; case by
base sol./
High to very
high
Nonregenerative
process
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 requirements. 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 systems dependability and eco-efficiency).
96

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Corresponding authors
A. Crespo Márquez can be contacted at: adolfo@esi.us.es
C. Parra Márquez can be contacted at: parrac37@yahoo.com
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Draft Versión # 3.
Carlos A. Parra M.
Email: parrac37@yahoo.com
www.confiabilidadoperacional.com