Monte Carlo-based assessment of system availability.
A case study for cogeneration plants
Adolfo Crespo Marqueza,*, Antonio Sanchez Heguedasb, Benoit Iungc
aDepartment of Industrial Management, School of Engineering, University of Seville, Camino de los Descubrimientos s/n. 41092 Sevilla, SpainbQualmaint, S.L. Maintenance Engineering, Av. San Francisco Javier, 2. 41018 Sevilla, Spain
cFaculte des Sciences, Nancy Research Centre for Automatic Control, University Henri Poincare, BP 239, 54506 Vandoeuvre les Nancy Cedex, France
Received 21 May 2004; accepted 30 July 2004
Available online 22 October 2004
Abstract
The complexity of the modern engineering systems besides the need for realistic considerations when modeling their availability and
reliability render analytic methods very difficult to be used. Simulation methods, such as the Monte Carlo technique, which allow modeling
the behavior of complex systems under realistic time-dependent operational conditions, are suitable tools to approach this problem.
The scope of this paper is, in the first place, to show the opportunity for using Monte Carlo simulation as an approach to carry out complex
systems’ availability/reliability assessment. In the second place, the paper proposes a general approach to complex systems
availability/reliability assessment, which integrates the use of continuous time Monte Carlo simulation. Finally, this approach is exemplified
and somehow validated by presenting the resolution of a case study consisting of an availability assessment for two alternative configurations
of a cogeneration plant.
In the case study, a certain random and discrete event will be generated in a computer model in order to create a realistic lifetime scenario
of the plant, and results of the simulation of the plant’s life cycle will be produced. After that, there is an estimation of the main performance
measures by treating results as a series of real experiments and by using statistical inference to reach reasonable confidence intervals.
The benefits of the different plant configurations are compared and discussed using the model, according to their fulfillment of the initial
availability requirements for the plant.
q 2004 Elsevier Ltd. All rights reserved.
Keywords: Availability assessment; System simulation; Operational evaluation; Simulation results
1. Introduction
Availability and/or reliability studies of industrial
systems such as the large scale-ones, have now to take
into account a lot of constraints [1]: the system structure
may be very complex (different abstraction levels; vast
array of units, components, etc.); the components have a
range of potential failure modes and follow various failure
distributions which have sometimes to integrate the initial
state of the system at the failure time, the operating mode,
the environmental context, etc. the components may
0951-8320/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ress.2004.07.018
* Corresponding author. Tel.: C34 954 487215; fax: C34 954 486112.
E-mail addresses: [email protected] (A. Crespo Marquez),
[email protected] (A. Sanchez Heguedas), [email protected]
(B. Iung).
conform to arbitrary failure and repair distributions for
maintained systems; these studies should be coupled with
economic analyses to manage for the system the compro-
mise between safe operation and economic service; The
failure modeling may be complicated because based on
various (functional, technical) dependencies between the
components [2] and requires a lot of data about component
failure which are sometimes no sufficient and/or not
available, etc.
Taking into account these considerations, the opportunity
to carry out system availability assessments through
analytical models, will be many times very restrictive. Let
us discuss some of the reasons for this: Some analytical
models like replacement after failure and/or periodic
testing/replacement assume system components indepen-
dence, i.e. that if one component fails and it is repaired,
Reliability Engineering and System Safety 88 (2005) 273–289
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A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289274
all the other components in the system will function as
normal without regard to the repair going on, which is very
unrealistic for many systems as the ones referred above
[3, p. 181]. An alternative approach could be based on
Markov models. These models can take into account a wide
range of dependencies, however, they are rather restrictive
in terms of components’ life, preventive maintenance and
repair time distributions. Furthermore it is not possible to
take into account any trends or seasonal effects. This is the
case of items with variable profiles for which the MTBF
varies with some process output or when there is any
seasonal effect in the system [4]. Another alternative could
be the use of semi-Markov models. Semi-Markov models
[16] generalize the Markov models by: (a) allowing, or
requiring, the decision maker to choose actions whenever
the system state changes; (b) modeling the system
evolution in continuous time; (c) allowing the time spent
in a particular state to follow an arbitrary probability
distribution. The scalability in terms of number of possible
states of the system, and number of maintenance actions, is
an important advantage of this models, however they are
also complex and therefore very difficult to handle when
the number of the system possible states increases (see a
trade-off study in [5]).
After highlighting the complexity and relevance of the
problem in this short introduction, we have organized the
rest of the paper as follows: We first explain the interest of
using Monte Carlo modeling for availability/reliability
assessment in Section 2, where we discuss the pros
and cons of this approach. Section 3 is devoted to present
a generic approach for the assessment of a system
availability/reliability, based on continuous time Monte
Carlo modeling of the system’s operation and maintenance.
The case study is presented in Section 4, this section
includes the presentation and discussion of the results of the
study. Finally, Section 5 concludes the paper with a
summary of our findings and some useful directions for
future research.
1 The reader is referred to [17] for a discussion regarding both simulation
practices.
2. Monte Carlo simulation in availability/reliability
assessments
A more general approach to our problem than previously
mentioned analytical models can be based in Monte Carlo
(stochastic) simulation [6]. The idea of this method is the
generation of certain random and discrete events in a
computer model in order to create a realistic lifetime
scenario of the system. Therefore the simulation of the
system’s life process will be carried out in the computer,
and estimates will be made for the desired measures
of performance [3]. The simulation will be then treated as
a series of real experiments, and statistical inference will
then be used to estimate confidence intervals for the
performance metrics. The events can be simulated either
with variable time increments (discrete event simulation)
or with fix time increments, at equidistant points of time
(continuous time simulation).1
The Monte Carlo simulation method allows us to
consider various relevant aspects of systems operation
which cannot be easily captured by analytical models such
as K-out-of-N, redundancies, stand-by nodes, aging,
preventive maintenance, deteriorating repairs, repair teams
or component repair priorities. By doing so, we can avoid
restrictive modeling assumptions that had to be introduced
to fit the models to the numerical methods available for their
solution, at the cost of drifting away from the actual system
operation and at the risk of obtaining sometimes dangerous
misleading results [7]. Lately the utilization of this method
is growing for the assessment of overall plants availability
[8] and the monetary value of plant operation [9].
In this paper, we will use the continuous time simulation
technique. This simulation will evaluate the system state
every constant time interval (Dt), the new system state will
be recorded and statistics collected. We will consider
chronological issues by simulating the up and down cycles
of all the components, and then the system operating
cycle will be obtained by combining all the components
cycles and their dependencies (as explained by Billington
and Tang [10], for their Monte Carlo sequential approach).
Then the time is incremented another Dt, and so on. As a
simulation tool we will use VENSIM (Ventana Systemsw),
which has special features to easy Monte Carlo type of
simulation experiments, and to provide confidence
interval estimations.
The weak point of the Monte Carlo method is the
computing time [9] specially when we deal with the problem
of finding suitable maintenance control policies, and the
search space for the control variables of the problem to test
increases. In our case, however, testing values of a set of
control variables is not the problem; we will not be trying to
find an optimal maintenance policy. The scope of our case
study will be assessing the availability of two alternatives of
plant configuration and for a certain predetermined main-
tenance strategy. In our case, randomness is constrained to
the failure generation process and maintenance policy is set
by the plant manufacturer. Pseudo random numbers will be
generated every time interval, and therefore when consider-
ing the entire simulation horizon, the requirements in terms
of number of simulation is expected not be very exigent, as
we will have time to test later in the paper.
3. A general approach to system availability/reliability
assessment
The procedure that we propose in this paper, in order to
develop the availability/reliability study using continuous
Table 1
Steps in the availability/reliability assessment
Step name Description Result
1. System’s configuration definition Determination of the basic functional blocks for the
plant configuration and for every function to
analyze
List of functional blocks: function, input, output, etc.
Determination of the dependencies among func-
tional blocks for the fulfillment of every function
Functional chart of the system that contains the
relations among blocks and their reliability features
2. Data collection Compilation of the necessary reliability and
maintenance data (and information) for each one
of the considered blocks
Reliability and maintenance data for each block:
MTTR, MTBF, MTTM, preventive schedule, times,
etc.
3. Model building Continuous time stochastic simulation model
building
VENSIM simulation models
4. Simulation Simulation scenarios and experiments design Scenario listings, required simulation replications,
confidence intervals for the results, etc.
5. Results and analysis Simulation results calculation Result of the parameters of availability and reliability of
the functions of our interest in the different configur-
ations
Simulation results discussion Interpretation of results and their discussion
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 275
time stochastic simulation, is described in Table 1, where
we distinguished a total of five steps.
Step 1: System’s configuration definition. The first step of
the study is the definition of the configuration of the system,
that means the selection/determination of the system’s
functional blocks, and how they relate to each other. A
functional block provides the output of a system as the
outcome of a joint event defined by the inputs to the system
and its various states. Functional blocks corresponding to
different subsystems are combined together to form a
functional block diagram representing the functional
characteristics of the combined system [11]. Conversely, a
complex system represented by a single functional block is
decomposed to constituent components with a correspond-
ing functional block diagram.
As a result of this step, we will obtain a functional chart of
the system that contains the relations among its blocks and
their reliability features. It is important to know how this
functional chart will have to be obtained for each function
provided by the system. For instance, if our system produces
electric power and steam, we will need two separate charts
indicating the dependencies of the different functional blocks
to provide each one of these two functions.
Step 2: Data collection. Before starting to build the
simulation model in step 3, we need to know the design, the
complete taxonomy of components of the plant, and we will
try to find out full reliability and maintainability information
of each item [8]. Once the functional blocks and their
interactions are identified, it is required to define for
each block two categories of data: failure rates, and repair/
restoration and preventive maintenance times and
dependencies.
In terms of components failure rate and repair date
data information, there are several sources to find this
information [3]: (1) public data books and databanks,
(2) performance data from the actual plant, (3) ‘expert’
judgments, and (4) laboratory testing. An introduction to
reliability data collection and management is given in [12].
Once the data for each functional block component is
gathered, MTBF and MTTR can be calculated for each
functional block of the system attending to their configuration
and probability rules.
In terms of block’s preventive maintenance, we will have
to gather complete information about the system’s main-
tenance plan. At the same time, we will have to find out the
elements conditioning the final preventive maintenance
program. The preventive maintenance program of the
system might be conditioned by any of the components
(many times, one of the block most relevant component
conditions opportunistic maintenance of the rest of the
components), but can also be conditioned by the dependen-
cies among system elements, or even between blocks.
For instance, in some occasions, although scheduled
hours for maintenance may arrive, it is possible that
elements/blocks will remain operating until the repair or
the preventive maintenance of another element/block is
finished (maintenance is therefore backlogged). All these
types of dependencies will have to be clarified before
advancing to the next step.
Step 3: Building the simulation model. A generic
system’s maintenance model, which will be applied to the
maintenance of each functional block in our model, will
now be built following some of the basic principles as
explained in [13]. The notation will be as follows
(notice that this variable list will be later subscripted by
functional block of the model in our case study).
System status information related variables
CAt
decrease in system’s age due to correctivemaintenance action in t
LCt
time when the last corrective maintenance, for asystem in t, started
LPt
time when the last preventive maintenance, for asystem in t, started
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289276
PAt
decrease in system’s age due to preventivemaintenance action in t
RNt
random number within the interval (0,1), generatedin t
Tt
system’s age in tTI
increase of system’s age in period tTOt
decrease of system’s age in period tl(Tt)
failure rate of the system in tAt
system availability (1 available, 0 unavailable) at tAAt
all sub-systems available (1 yes, 0 no) at tSMt
sheduled maintenance (1 yes, 0 no) in period tMBt
maintenance backlogged (1 yes, 0 no) at tRMt
maintenance released (1 yes, 0 no) in period tModel parameters
CT
average time of a corrective maintenance actionn
minimum age of the system to do preventivemaintenance actions
PT
average time of a preventive maintenance actionT1
maximum time the system operates without a failure3.1. Modeling system’s age
The process requires first to model the age of the
system (Tt):
Tt Z Tt CTIt KTOt (1)
We will consider that age will increase when the system
is available. That means that we assume that available
means ‘running’, no idling nor standing-by, therefore
TIt Z At (2)
and age will decrease when the system is maintained
TOt ZPAt; if PAt !O0 and CAt !O0
PAt CCAt; Otherwise
((3)
CAt ZTt; if lðTtÞRRNt
0; Otherwise
((4)
where RNt is a random number generated for every t within
the range (0,1), l(Tt) is the failure rate of the system, and
CAt and PAt are decreases in the system’s age as a
consequence of the corrective and preventive maintenance
actions, respectively.
3.2. Modeling age based preventive maintenance
In the age based maintenance policy, the only one
considered in our case study, if the system does not fail until
a given time n, then it is preventively maintained.
Otherwise, it is correctively maintained at the failure time
PAt ZTt; if Tt Rn
0; Otherwise
((5)
Here, we also assume that a failed system will be maintained
correctively at failure.
3.3. Modeling system’s availability
The conditions of the system that will make it
unavailable will be the corrective or preventive maintenance
that is being carried out
At Z
1 K ðPulseðLCt;CT; tÞ
CPulseðLPt; PT; tÞÞ; if LCt O0 or LPt O0
1; Otherwise
8><>:
(6)
Notice that when tZ0, LCtZLPtZ0 (LCt and LPt, are
the times when the last corrective [or preventive,
respectively] maintenance, for a system in t, started).
The function Pulse, previously introduced to calculate
STMt is defined as follows:
Pulseða; b; tÞ Z1; a! t!a Cb
0; Otherwise
((7)
3.4. Modeling maintenance backlog
In some occasions, although scheduled hours for the
preventive maintenance of an equipment may arrive,
it could be suitable that this equipment would remain
functioning until the repair or the preventive maintenance of
another equipment is finished. In this way, we will be able to
consider in the model functional and operational dependen-
cies of the functional blocks. This will be the case, for
instance, of the scheduled maintenance of each of the
turbines of the plant of our case study, and in order to avoid
losing back-up of the power supply provided by
the cogeneration. Therefore, it is necessary to model the
possible backlog of maintenance activities, i.e. activities
which are due and waiting to be carried out by the
maintenance department. Let then imagine for instance
that we have a system with two units (iZ1, 2), and both of
them need to be in operating conditions in order to
preventively maintain one of them, i.e. AAtZ1, where
AAt is defined in Eq. (8) as follows:
AAt ZYiZ2
iZ1
At;i; with i Z1;2 (8)
SMt;i Z1; ti=n Z Intðti=nÞ and tiO0
0; Otherwise
((9)
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 277
MBt;i ZMBtK1;i CSMt;i KRMt;i (10)
RMt;i Z1; ðSMt;i Z1 or MBt;i Z1Þ and AAt Z1
0; Otherwise
((11)
Maintenance activities will be scheduled according to (9),
then could be backlogged according to (10), and finally
released as explained in (11). Notice that if both units are OK
(i.e. AAtZ1) a scheduled maintenance is immediately
released, just in time, without being backlogged. Then,
when a preventive activity is released, we will record this
time (in LPt) to allow downtime modeling as explained
previously in (6). Notice that, in this example, to make this
formulation simple, we suppose that a backlogged activity
will be released before a new preventive maintenance will be
scheduled, but of course, this could not be the case, and we
would need extra formulation to consider that case. The
model formulation as presented above, is in our case built
using the software named VENSIM.2 VENSIM is a entire
simulation environment package for continuous time simu-
lation, this software allows to represent the functional blocks
and easy their parameterization. At the same time, VENSIM
offers special features to deal with stochastic simulation
within the continuous time models. For instance, sensitivity
analysis is easily performed, as well as parameters
optimization, etc. When writing the simulation model code
we will have to specify simulation parameters like: initial and
final time of the simulation, and the time step.
Finally, and within this third step, we cannot forget the
importance of validating our model prior to start producing
any results for their discussion. We have to make sure that the
structure of the whole model is properly considered, that the
simulation of each block’s performance is consistent and
expected according to existing dependencies within
the entire system.
Step 4: Simulation. Once model validation is done,
Andijani and Duffuaa [14] have remarked how many
simulation studies on maintenance systems ignored proper
design of experiments and some way of output analysis.
Now we start to deal with this issues in our process.
For each one of the system configurations considered in
our simulation study, we will have to define the number of
replications that, using different seeds in the generation of
pseudorandom numbers for failure distributions of the
different functional blocks, will be carried out. This can be
many times an iterative process. Once a few simulation
results are obtained (n), the mean values and standard
deviation of the samples are calculated. With these values,
and once the size of the sample is known (n), the confidences
intervals of the results can be calculated. That is to say, we
estimate with a certain percentage of results confidence, that
the final values of the variables for the different configur-
ations of the system will fall within the interval that we
2 Trade Mark of Ventana Systems, Inc.
provide. In case we may require a higher accuracy, we will
need to increase the sample size.
Step 5: Results and analysis. This step will include the
presentation of result for the availability and reliability
parameters corresponding to the functions of our interest in
the different configurations. These results will later require
their discussion when compared with availability and
reliability requirements that may be established for the
functions provided by the system. This step implies
explaining the results obtained with the simulation, and the
factors that may lead to those results, but also providing
possible actions to improve system’s availability or
reliability to meet system’s functional requirements.
Another important aspect of the study that has to be
introduced at this time is the sensitivity analysis. Once input
parameters may not be very accurate sometimes, the influence
that parameters have on the final results, specially those more
important and uncertain for the study, must be explored.
4. COGEPLANT case study. Availability assessment
of a cogeneration plant
Electrical power generation systems represent examples
of processes where Monte Carlo techniques have traditionally
provide a practical approach to reliability analysis (Henley
and Kumamoto, 1991, p 480). Reasons for this are related to
feasible configurations of the systems (on-line and stand-by),
scheduled or un-scheduled shut-downs, repair and preventive
times distribution functions, etc. Clearly, an attempt to obtain
reliability parameters for this kind of problems by determi-
nistic methods is virtually impossible [15].
The cogeneration plant that we will describe in this paper
(that we will now refer as COGEPLANT) is currently being
designed in Seville, and will have equipment to produce
electrical power and to co-produce steam according to
certain very high availability requirements established by a
large refinery located near by, consuming 100% of
COGEPLANT’s output. At the moment of producing this
paper, the plant is in the design phase and the most suitable
configuration is being evaluated. The plant will supply
100% of the electrical power required by the refinery
by means of two independent systems, in automatic
stand-by, and with a transparent operation with regards to
the Refinery. It is accepted that one of these system is the
Local Electrical Transportation Network (LETN), providing
that the proposed configuration fulfils the reliability
demanded in the project. From the LETN the possible
supply will be constrained to a maximum of 25 MW of
power. The justification to build a cogeneration is mainly
the reach of a substantial improvement in the operational
stability of the refinery, through a dedicated electrical power
and steam generation system. Therefore, the steam and
electricity supply must guarantee maximum reliability and
availability ratios. In the technical conditions included in
the documentation that was provided in order to elaborate
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289278
the bidding of the project, we could find the following
availability requirements.
4.1. COGEPLANT availability requirements
The project that we will analyze is said to be articulated
in two phases: Phase 1 will last 2 years and will consider a
lower demand than the final one. Phase 2 will be for a total
of 15 years after Phase 1, at full level of plant designed
supply. For each of those phases, the availability
requirements for electrical power and steam production
will be the following.
Steam production availability:
†
Phase 1. Steam 600 psi: 70 Tn/h 350 days/yr, 35 Tn/h15 days/yr.
†
Phase 2. Steam 600 psi: 70 Tn/h 350 days/yr, 35 Tn/h15 days/yr. Steam 150 psi: 70 Tn/h 365 days/yr.
Electrical power production availability:
†
Phase 1. 20 MW with back-up for 350 days/yr, 20 MWwithout back-up for 15 days/yr.
†
Phase 2. 40 MW with back-up for 335 days/yr, 20 MWwith back-upC20 MW without backup for 30 days/yr.
Let us now use our approach described above to validate
through simulation whether the previous user’s availability
requirements will be satisfied or not, and according to the
plant technical structure/configuration and the dependability
parameters of each of their components (Turbine,
Generator, Boiler, etc.)
Fig. 1. Description of an electrical pow
Step 1: COGEPLANT configurations definition. The
system used for the generation of the electrical power is
conformed by a dual turbine (where dual refers to the
possibility to of using gas or fuel as combustible, with
natural gas used under normal operating conditions), and
a turbine-coupled generator. Two configurations are
considered to be analyzed: The first one is three turbine–
generators that will provide energy of 30 MW each;
The second one is a two- turbine configuration with
45 MW output per unit. Output in both cases will be to a
nominal voltage of 12 kV. It is also foreseen the existence of
a transformer and a circuit-breaker per turbine–generator
subsystem. The generation of steam will be done using a
boiler that will benefit from the turbine exhaust gasses
temperature in order to generate the necessary steam flow
(see Fig. 1). The boiler, using a by-pass system, allows a set of
post-combustion burners to be used, providing back-up in
case of a turbine–generator set failure (obviously, it is
considered no post-combustion under normal operating
conditions). Clearly, this provides 100% back-up to
the solution adopted against potential failures in the turbine
system. Finally, the use of several economizers permits the
production of steam in low (150 psi) and high pressure
(600 psi). A demineralized water plant will produce equal
amount of water than the steam generation of the system.
This is required once the water produced by steam
condensation in the refinery facilities will not be directly
recycled to the cogeneration unit. Besides this, there will
exist a water tank to allow total supply of water during a
sufficiently wide period (this provides 100% water
supply back-up).
er and steam cogeneration unit.
Table 2
Functional blocks considered in the simulation study
Functional block Components Inputs Outputs Function
Power generation
system named:
[RgasTGasGen]
Gas network Natural gas (or fuel,
eventually)Cair
Electrical power
(30/45 MW) in
12 kVCwarm
exhaust gasses
The generation of the electrical power is done
by a dual turbine (where dual refers to the
possibility to of using gas or fuel as
combustible, with natural gas used under
normal operating conditions), and a turbine-
coupled generator. Exhaust gasses will be then
used to generate steam
Turbine
Generator
Transformer
Circuit switch
Steam generation
system named:
[RAguaCaldera]
Boiler Demineralized waterC
turbine exhaust gases
(Cnatural gasCair
eventually)
Steam 600 psiC
steam 150 psiC
water drain Cexhaust gases
The generation of steam will be done using a
boiler that will benefit from the turbine
exhaust gasses temperature to generate the
necessary steam flow. The boiler, using a
by-pass system, allows a set of post-combus-
tion burners to be used. The use of several
economizers permits the production of steam
in low (150 psi) and high pressure (600 psi).
The water produced by steam condensation in
the refinery facilities will not be directly
recycled to the cogeneration unit. Besides this,
there will exist a water tank to allows total
supply of water during a sufficiently wide
period
Steam extraction and
network system
Pump 1
(from degasifier to boiler)
Pump 2
(between economizers)
Valve 1
(after pump 1 before boiler)
Valve 2 (after pump 2, to
bypass second economizer)
10 joints and connections
(water network system)
Local electrical trans-
portation network
(LETN) named:
[RedElec]
LETN 25 MW in 12 kV 25 MW in 12 kV Supply constrained to a maximum of 25 MW
of power
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 279
To the effects of these paper calculations, we will
consider perfect water supply to the steam generation
system, therefore we will only include in our study those
elements that compose the water network, the boilers
and the steam network in the plant. Taking into account
previous considerations, the operating mode of the plant and
its environmental constraints, we have decided to model
the three different functional blocks that we describe in
Table 2, where also the components of the blocks are
described. Some of these blocks will be then replicated,
according to the specific physical system configuration
which is being analyzed.
As we mentioned above, there are two plant configur-
ations that will be the object of our analysis in this paper.
These two configurations will lead to the implementation of
interactions between the functional blocks in order to meet
project requirements. We will now express, for both
configurations, the possible interactions of their functional
blocks, and in the different phases, for the availability
requirements to be fulfilled:
Configuration 1:3 Three TGs of 30 MW in stand-by, with
one B each, for the production of 25.2 Tn/h of steam in high
and low pressure.
Steam availability (see, as an example of chart, Fig. 2).
Phase 1. The steam production at 600 psi with volumes
of 70 and 35 Tn/h will be obtained when the following
conditions are met:
3 Note: TG, turbine–generator set; B, boiler.
†
The 70 Tn/h flow requirements are met those days that allthree boilers work simultaneously.
†
The 35 Tn/h flow requirements are met those days thattwo, out of three boilers work simultaneously (actually
50.4 Tn/h will be produced those days).
Phase 2. The conditions for the steam production at
600 psi with volumes of 70 and 35 Tn/h. are the same that
in the previous phase. Moreover, it will be necessary that
all three boilers work together to reach 70 tn/h. with
150 psi.
Availability of electrical power.
Phase 1: 20 MW of electrical power, with 20 MW
back-up in standby, will be available those days that two
out of the three TGs are available. In case that a contract with
LETN exist, for the supply of 25 MW during this phase, it
would be enough then with two out of four blocks
(RGasTGasGen1, RGasTGasGen2, RGasTGasGen3,
LETN) availability to obtain the required electrical power.
The production of 20 MW of electrical power without any
back-up will correspond with those days where only one TG
is available (or only one of above mentioned four blocks is
available in case that a contract with the LETN is in place).
Phase 2: The 40 MW of electrical power with 40 MW
back-up in standby will be available the days that all
four functional blocks offering electrical power to the
refinery are available (RGasTGasGen1, RGasTGasGen2,
RGasTGasGen3, LETN). Notice how it will be necessary
the contract with the LETN to fulfill this requirement
with this configuration of the plant. For the production of
Fig. 2. Steam production diagram with 3 Bs.
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289280
20 MW with standbyC20 MW without standby three of
the previous four blocks need to be available.
Configuration 2. Two TGs of 45 MW in stand-by, with
one B each, for the production of 35 Tn/h of steam in high
and low pressure.
Steam availability.
Phase 1. The steam production at 600 psi with volumes
of 70 and 35 Tn/h will be obtained when the following
conditions are met:
†
The 70 Tn/h flow requirements are met those days that alltwo Bs work simultaneously.
†
The 35 Tn/h flow requirements are met those days onlyone out of two Bs works.
Fig. 3. Electrical power product
Phase 2. The conditions for the steam production at
600 psi with volumes of 70 and 35 Tn/h. are the same that in
the previous phase. Besides this, it will be necessary the two
Bs to work to reach 70 tn/h with 150 psi.
Availability of electrical power (see, as an example of
chart, Fig. 3).
Phase 1. 45 MW of electrical power (not only 20 MW)
with 45 MW back-up in stand-by will be available the days
that the 2 TGs are available. No contract with LETN is
considered in thiscase.Theproductionof45 MW ofelectrical
power (not only 20 MW) withoutany back-up in stand-by will
correspond with those days where only one TG is available.
Phase 2: The 45 MW of electrical power (not only 40)
with 45 MW backup in stand-by will be available the days
ion diagrams with 2 TGs.
Table 3
Reliability data (in failures per running day)
Functional block Components Data bank Selected value
FARADIP IEEE Own value
TG [RgasTGasGen] Gas network 0.0000 0.00000000
Turbine 0.001320 0.00548 0.00547945
Generator 0.004800 0.00046300 0.00046300
Circuit Breaker 0.000036 0.00000821 0.00000821
Transformer 0.00002700 0.000024 0.00002700
B [RaguaCaldera] Boiler 0.0110 0.01100000
Steam extraction and network system 0.0001 0.00000000
Pump 1(from degasifier to boiler) 0.0110 0.00500000
Pump 2 (between economizers) 0.0110 0.00500000
Valve 1(after pump 1 before boiler) 0.000480 0.00048000
Valve 2(after pump 2, to bypass 2nd economizer) 0.000480 0.00048000
10 joints and connections (water network system) 0.000120 0.00012000
LETNl [RedElec] LETN 0.000480 0.03405088 0.03405088
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 281
that the 2 TGs are available. The production of 20 MW with
20 MW back-up in stand-byC20 MW without back-up does
not apply for this case. No contract with LETN is considered
in this case.
Step 2: COGEPLANT’s data collection. Step 1 has
provided a clear definition of the plant configuration
alternatives. At the same time, we had opportunity to
clarify functional dependencies among defined blocks in
order to produce a certain COGEPLANT service. Now we
have to gather data in order to have then the possibility to
model the plant properly.
In this occasion, we have searched and found data items
in two data banks (FARADIP and IEEE) and at the same
time we have retrieved some information from the company
designing the plant, according to their experience in similar
projects and sometimes according to their experts judg-
ments (we call this ‘own value’ in Table 3). In Table 3
failure rate data of the different components in the
considered functional blocks is presented. The criteria
followed in this paper, according to company designing the
plant, has been to select the final value has been by order of
preference: IEEE, Own value and FARADIP.
Table 4
Functional blocks MTTR (mean time to repair, in days)
Functional block Components Data source
IEEE
TG [RGasTGasGen] Gas network
Turbine
Generator 1.36250000
Circuit breaker 0.50000000
Transformer 3.54166667
B [RAguaCaldera] Boiler
Steam network
Pump 1
Pump 2
Valve 1
Valve 2
9>>>>>>>=>>>>>>>;
Water network
LETN [RedElec] LETN
In Table 4, mean time to repair of the different components
in the considered functional blocks are defined. In this
occasion, we have found data items in the IEEE data bank and
at the same time we have retrieved some information from the
company designing the plant, according to their experience in
similar projects and sometimes according to their experts
judgments (we call this again ‘own value’ in Table 4). The
criteria followed in this paper, according to company
designing the plant, has been to select the final value has
been by order of preference: IEEE and Own value.
From Table 4, mean time to repair is calculated for every
functional block and presented in Table 5.
To complete the blocks with preventive maintenance
data, Table 6 identifies the information about the mainten-
ance plan for the plant.
But the following consideration, operational dependen-
cies related to maintenance, have to be taken into account to
build the final maintenance schedule:
†
The preventive maintenance of the plant will beconditioned by the preventive maintenance of the turbine
sets, so that in the subsequent simulation model we will
Selected value
Own value
2.54166667 2.54166667
1.36250000
0.50000000
1.000 3.54166667
1.000 1.000
1.000 1.000
1.000 1.000
Table 5
Basic functional blocks data
Functional block Failure rateP
li MTTRP
ðli=miÞ=P
li
TG [RGasTGasGen] 0.00597766 2.45204697
B [RAguaCaldera] 0.02208000 !1
LETN [RedElec] 0.03405088 !1
In failures per day (l) and repair days (MTTR).
Table 6
Maintenance steps and scheduled downtime for the whole turbo-generator
and boiler set
Maintenance step Scheduled down time hours
Monthly (off-line wash) 6
Each 4.000 operating hours 48
Each 8.000 operating hours 120
Each 50.000 operating hours 240
4
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289282
suppose that every set turbine–generator–boiler will stop
together for the accomplishment of the different steps of
maintenance. The maintenance of the boilers will be
therefore opportunistic and determined by that of the
turbo-generator sets.
†
An important aspect of the preventive maintenance isthat it will pursue that no more than one turbo-generator
set will be stopped for the accomplishment of a
preventive task (i.e. no simultaneous stop of TG sets
due to preventive maintenance). Therefore, in some
occasions, although scheduled hours for the maintenance
may arrive, it is possible that groups remain operating
until the repair or the preventive maintenance of another
group is finished (maintenance is backlogged).
Step 3: COGEPLANT simulation model. So far, we have
complete information about plant configurations, functional
and operational dependencies, and we have to gather
required reliability and maintainability data of the plant.
Our next step will be to introduce all this into a continuous
time Monte Carlo simulation model. The model is built with
VENSIM4 tool (for instance, Figs. 2 and 3 are produced by
VENSIM while modeling this problem) and simulates a
temporary horizon of 6205 days with a time step for the
simulation of one day. Every day, the failures that will take
place in the available functional blocks will be randomly
obtained, in the event that a failure takes place in a block, this
will turn to be unavailable. Then the time will be advanced
for those preventive or corrective maintenance operations
that are in process of accomplishment (and blocks will return
to the availability state in case these operations are finished).
The breakdowns of the turbo-generator sets will not affect the
steam production since there is a back-up system with natural
gas post-combustion. Similarly, breakdowns in the boiler
will not affect the production of electrical power (a bypass
system for the exhaust turbine gases exists at the entry of the
boiler). The preventive maintenance operations are modeled
taking into account the possible backlog of preventive
actions.
4.2. Simulation model output validation
In this section, we present graphical examples for
relevant variables in the simulation model and we test
Trade Mark of Ventana Systems, Inc.
their behavior patterns. This will help us to validate
model structure and to achieve the necessary confidence
in results that will be later presented. For instance, in
Fig. 4, we do present maintenance program scheduling
for Configuration 2, and we show assigned maintenance
for different frequencies and TGs. It can be appreciated
how our simulation model represents the maintenance
operations when they are scheduled using binary
variables (1 maintenance action scheduled, 0 no main-
tenance action scheduled). These variables will be later
used by the model to calculate availability of the
different services according to previously defined inter-
actions among building blocks and according to
reliability and maintainability data that we estimated
for the building blocks.
In Fig. 5, the corrective maintenance of both turbine
sets in Configuration 2 are presented. These are repairs
resulting from failures generated randomly. Our simu-
lation model represents the corrective maintenance actions
using again binary variables (1 corrective maintenance
action released, 0 no corrective maintenance action
released). Again, these variables will be later used by
the model to calculate availability of the different services
according to previously defined interactions among
building blocks, and according to reliability and
maintainability data that we have estimated for the
building blocks.
Fig. 6 captures backlog of maintenance programmed
activities, i.e. moments in time where a given scheduled
maintenance activity could not be carried out (and was
backlogged), because it would cause losing back-up or losing
functionality of the system.
Fig. 7 shows availability of the TGs functional blocks
over the simulation timeframe. Despite initial failures
and therefore different starting TGs performance, avail-
ability over time will tend to be very similar in both blocks.
In Fig. 8, we can see three graphs for the accumulated
days of electrical power supply provided at different
requirement levels (40 MW with back-up, 20 MW with
back-upC20 MW without back-up, and other less exigent
supply).
In Fig. 9, we can see three graphs for the accumulated
days of high pressure steam (600 psi) supply provided at
different flow requirement levels (70, 35 Tn/h, and other
less exigent supply).
Fig. 4. Example of the maintenance program for Configuration 2.
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 283
4.3. Sensitivity analysis
In this case study several univariate (changing one
parameter at a time) and multivariate (changing many
Fig. 5. Example of TGs correcti
parameters at a time) sensitivity analysis were carried out.
As an example, we present here results for the multi-
variate sensitivity analysis to variations in the corrective
time for both TG blocks of configuration 2 which was
ve maintenance (repairs).
Fig. 6. TGs backlog of maintenance activities for Configuration 2. These were activities carried out after the scheduled date.
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289284
found to be interesting to analyze the suitable level of
spare equipment to keep stored on site. We assume
variations for the parameters CT[RGasTGasGen1] and
CT[RGasTGasGen2], uniformly distributed in the interval
[2,10] days of MTTR of each block. Fig. 10 Shows the
results. Worse case shown in the graph, MTTR of 10 days
Fig. 7. TGs availabi
for both TGs, shows 4850 days of correct 45 MW
with Backup supply in F2. These results should be then
considered later, they add additional information when
doing analysis in step 5.
Step 4: COGEPLANT simulations. After presenting all
these figures in previous step 3, we can conclude that
lity over time.
Fig. 8. Days of electrical power production for different power requirements. Second phase of the project.
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 285
the outputs of the COGEPLANT model are the ones expected
for the inputs considered, and that we can now proceed to
compare the different configurations, defining the corre-
sponding scenarios. We will therefore present now a set of
simulations containing, for each one of the two plant
Fig. 9. Days of high pressure steam production for differe
configurations considered in the study, five replications
using different seeds in the generation of pseudorandom
numbers for failure distributions of the different functional
blocks. Once these simulation results are obtained, the mean
values and standard deviation of the samples are calculated.
nt flow requirements. Second phase of the project.
Fig. 10. Sensitivity analysis results for MTTR of the TGs [2,10] days.
Table 7
Results for the fulfillment of the power and steam supply requirements in
Configuration 1. Two phases. Assuming contract with LETN in the second
phase.
Supply (requirements) Repl. Values Statistics
Phase 1
20MW with back-up
(note: MINZ700 days)
1 723 Mean 726.20
2 725 Std. dev. 2.68
3 729 Conf(G95%) 2.35
4 725 Max 728.55
5 729 Min 723.85
20 MW without back-up
(note: MAXZ30 days)
1 8 Mean 4.80
2 6 Std. dev. 2.68
3 2 Conf(G95%) 2.35
4 6 Max 7.15
5 2 Min 2.45
75.6 Tn/h of 600 psi steam
(note: MINZ700 days)
1 678 Mean 669.00
2 664 Std. dev. 5.92
3 666 Conf(G95%) 5.19
4 665 Max 674.19
5 672 Min 663.81
50.4 Tn/h of 600 psi steam
(note: MAXZ30 days of
35 Tn/h)
1 19 Mean 33.40
2 36 Std. dev. 10.78
3 31 Conf(G95%) 9.45
4 49 Max 42.85
5 32 Min 23.95
Phase 2
50 MW with back-up
(note: MINZ5025 days
40 MW with back-up)
1 4792 Mean 4780.40
2 4783 Std. dev. 27.34
3 4781 Conf(G95%) 23.96
4 4810 Max 4804.36
5 4736 Min 4756.44
20 MW with BC20 MW
without B
(note MAXZ450 days)
1 647 Mean 655.80
2 665 Std. dev. 36.97
3 656 Conf(G95%) 32.40
4 604 Max 688.20
5 707 Min 623.40
75.6 Tn/h 600 psi steam
(note: MINZ5250 days
70 Tn/h)
1 4746 Mean 4796.40
2 4789 Std. dev. 37.75
3 4783 Conf(G95%) 33.09
4 4818 Max 4829.49
5 4846 Min 4763.31
50.4 Tn/h 600 psi steam
(note: MAXZ225 days
35 Tn/h)
1 638 Mean 596.40
2 620 Std. dev. 40.17
3 617 Conf(G95%) 35.21
4 548 Max 631.61
5 559 Min 561.19
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289286
With these values, and once the size of the sample is known
(nZ5), the confidences intervals (for the 95% confidence) of
the results are obtained. That is to say, we estimate with a
95% o confidence, that the final values of the variables for the
different configurations of the plant will fall within the
interval that we provide (we do think that the selected number
of replications place the blocks reliability and availability
measures within reasonable intervals and with a reasonable
probability, therefore we have accepted this sample size).
Finally, we will mention that failure rates are not considered
constant in the model, although we use Table 5 values, we
have considered that exists infant mortality and wear out
effect, according to experience for similar plants and
equipment (a typical failure rate curve topology is presented
in Fig. 11).
COGEPLANT results and analysis. We will now present
and discuss the simulation results obtained for both plant
configurations.
4.4. Results for requirements fulfillments
in Configuration 1 (3 TGs)
In Table 7, we present results of the model for all the
different supply requirements fulfillments, and for configur-
ation 1, with three turbines. Requirements are presented in
the first column and in terms of service quality required over
Fig. 11. Curve topology for the failure rate of the block [RGasTGasGen1] in
the simulation study.
75.6 Tn/h 150 psi steam
(note: MINZ5475 days
70 Tn/h)
1 4746 Mean 4796.40
2 4789 Std. dev. 37.75
3 4783 Conf(G95%) 33.09
4 4818 Max 4829.49
5 4846 Min 4763.31
a certain period of time during each phase. This time is
measured in minimum or maximum number of days per year
of supply of the specific service. Second column contains the
number of replication and third column are the values
obtained for each variable. The fourth column presents the
statistics for each variable: mean value, standard deviation
and the 95% confidence interval. Table 8 presents the same
results for configuration 2.
Table 8
Results for the fulfillment of the power and steam supply requirements in
Configuration 2. Two phases. Assuming no contract with LETN in the
second phase.
Supply (requirements) Repl. Values Statistics
Phase 1
45 MW with back-up
(note: MINZ700 days
20 MW with B)
1 703 Mean 698.00
2 695 Std. dev. 3.74
3 701 Conf(G95%) 3.28
4 696 Max 701.28
5 695 Min 694.72
20 MW without back-up
(Note: MAXZ30 days)
1 28 Mean 30.40
2 32 Std. dev. 4.34
3 24 Conf(G95%) 3.80
4 34 Max 34.20
5 34 Min 26.60
75.6 Tn/h of 600 psi steam
(note: MINZ700 days)
1 680 Mean 685.60
2 691 Std. dev. 5.98
3 693 Conf(G95%) 5.24
4 681 Max 690.84
5 683 Min 680.36
35 Tn/h of 600 psi steam
(Note: MAXZ30 days of
35 Tn/h)
1 44 Mean 35.20
2 30 Std. dev. 7.29
3 26 Conf(G95%) 6.39
4 40 Max 41.59
5 36 Min 28.81
Phase 2
45 MW with back-up
(note: MINZ5025 days
40 MW with back-up)
1 5115 Mean 5118.80
2 5100 Std. dev. 15.32
3 5135 Conf(G95%) 13.43
4 5110 Max 5132.23
5 5134 Min 5105.37
45 MW without back-up
(note MAXZ450 days
20 MW with B. C20 MW
without)
1 352 Mean 349.20
2 366 Std. dev. 11.71
3 338 Conf(G95%) 10.27
4 352 Max 359.47
5 338 Min 338.93
70 Tn/h 600 psi steam
(note: MINZ5250 days
70 Tn/h)
1 4980 Mean 5001.40
2 5006 Std. dev. 16.73
3 4996 Conf(G95%) 14.66
4 5026 Max 5016.06
5 4999 Min 4986.74
35 Tn/h 600 psi steam
(note: MAXZ225 days
35 Tn/h)
1 425 Mean 409.60
2 409 Std. dev. 16.12
3 412 Conf(G95%) 14.13
4 383 Max 423.73
5 419 Min 395.47
70 Tn/h 150 psi steam
(note: MINZ5475 days
70 Tn/h)
1 4980 Mean 5001.40
2 5006 Std. dev. 16.73
3 4996 Conf(G95%) 14.66
4 5026 Max 5016.06
5 4999 Min 4986.74
Table 9
Example of results for final reliability of some blocks and sub-blocks in
Configuration 1
Block or sub-block Repl. Values Statistics
[RgasTGasGen3], TG3,
BLOCK
1 0.9886 Mean 0.9877
2 0.989 Std. dev. 0.0027
3 0.9905 Conf(G95%) 0.0023
4 0.9869 Max 0.9900
5 0.9835 Min 0.9854
[RedElec], LETN, BLOCK 1 0.9697 Mean 0.9629
2 0.9592 Std. dev. 0.0056
3 0.9655 Conf(G95%) 0.0050
4 0.9553 Max 0.9678
5 0.9647 Min 0.9579
[RedAgua], Water network,
SUB-BLOCK
1 0.9885 Mean 0.9906
2 0.9922 Std. dev. 0.0034
3 0.9857 Conf(G95%) 0.0030
4 0.9929 Max 0.9936
5 0.9937 Min 0.9876
[Caldera1], Boiler 1,
SUB-BLOCK
1 0.9808 Mean 0.9824
2 0.9815 Std. dev. 0.0023
3 0.982 Conf(G95%) 0.0021
4 0.9865 Max 0.9844
5 0.9811 Min 0.9803
Table 10
Example of results for days of post-combustion needed in Configuration 1
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 287
4.5. Results for requirements fulfillments
in Configuration 2 (2 TGs)
Post-combustiondays
Repl. Values Statistics
Total days in
postcombustion
for three boilers
(Conf. 1)
1 240 Mean 194.0000
2 198 Std. dev. 32.7490
3 161 Conf(G
95%)
28.7053
4 207 Max 222.7053
5 164 Min 165.2947
4.5.1. Sample results for availability/reliability
of functional blocks
In Table 9, we present as an example, the simulation
results for the reliability variables of several functional
blocks and sub-blocks. Regardless of the level of fulfillment
of the different supply requirements of the plant as a complete
system, these result show high levels of the reliability of the
blocks over the total simulation time. We have check that
values in Table 9 are in accordance with data provided by
several original equipment manufacturers (we have check for
instance turbine–generator sets and boilers data for other case
studies provided by the OEM). Once this data is validated, we
have another clear argument to support the reliability of our
study for the entire plant (in case of course that all
interactions among blocks were well defined).
4.6. Post-combustion natural gas consumption
This feature is of main interest for the economic
evaluation of the project with each one of the configur-
ations. In both cases, steam production availability will
require a certain number of days of post-combustion in the
boilers once TGs will suffer failures and will be out of order
while they are repaired. The total number of days of post-
combustion in the entire project will be then very important,
and although we do not provide economic estimations for
the project, we have calculated that data. In order to do that
Table 11
Example of results for days of post-combustion needed in Configuration 2
Post-combustion
days
Repl. Values Statistics
Total days in post-
combustion for two
boilers (Conf. 2)
1 109 Mean 132.8000
2 146 Std. dev. 21.0404
3 122 Conf(G95%) 18.4424
4 162 Max 151.2424
5 125 Min 114.3576
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289288
we add the days the Boiler is available and the TG of the
same set is not. Results are presented in Tables 10 and 11.
4.7. Simulation results analysis and discussion
†
Tab
Sim
Con
1 (3
1 (3
2 (2
2 (2
Regarding the fulfillment of the power and steam supply
requirements. See Table 12.
†
Regarding availability and reliability of the blocks. A keyaspect of the study is the confirmation that every
functional block meets a few minimal requirements in
terms of reliability and availability, when compared to
other facilities of similar recent plants or to the OEM
information. In this respect, it is important to verify, for
example, that the information offered by the simulation
establishes values of availability of the TGs within
the range [96–97%] with 95% of confidence, and that
the values for the reliability of the same equipment, with
identical confidence, are within the interval [98–99%].
We have also checked that simulations for both
configurations offer similar results for these two metrics.
le 12
ulation results discussion
fig. Phase Production of electrical power
TG) F1 All requirements are fulfilled working with three turbines from
the start of Phase 1. A higher supply quality could even be offer
No contract with the LETN is considered
TG) F2 The minimum of 5025 days of 40 MW with back-up is not
reached in this phase. A reasonable estimation could be aroun
4756 days of 50 MW with back-up, assuming the existence o
contract with the LETN
The system runs over the maximum number of days supplyin
20 MW with B.C20 MW without B
TG) F1 The requirement of 700 days of 20 MW with back-up is not
reached by a short margin, an estimation of a supply of 45 M
with back-up during 694 days in this phase would be reasona
The system exceeds the requirement for maximum number of
days supplying 20 MW without back-up, but now even increas
this power to 45 MW
TG) F2 The system fulfills the requirement of 5025 days providing
40 MW with back-up
The requirement of 20 MW with B. C20 MW without B. is n
not applicable. However an availability of 45 MW without
back-up during 339 days can now be reached and offered
With regard to the rest of the blocks, the simulation results
are considered to be equally reasonable.
†
With respect to number of days of natural gas consump-tion in post-combustion, to fulfill with the requirements in
Table 12. Table 12 of this report contains a series of
availabilities for the production of steam and of electrical
power that take into account the fact that a certain number
of days it will be necessary to produce steam through post-
combustion, once TGs could suffer failures and will be out
of order while they are being repaired. In Tables 10 and 11
of the results, we can find out interesting information. We
can know the days we will produce steam without TGs,
and therefore Boilers will be working using post-
combustion natural gas. This will have of course
important economical consequences and therefore it is a
fact very relevant and which needs to be assessed. We
have found for our specific case study that:
† In case of configuration 1 (3TG), we should consider
an incremental cost of gas consumption equivalent to
194 days of operation of a gas turbine of 30 MW.
† Configuration 2 (2TG): To consider an incremental
cost of consumption of gas equivalent to 133 days of
operation a of gas turbine of 45 MW.
ed.
d
f a
g
W
ble
ing
ow
5. Conclusions
This paper discusses the opportunity to use Monte Carlo
simulation techniques for reliability/availability assessment
Production of steam
The requirement of supplying 70 Tn/h of 600 psi steam a
minimum of 700 days/year is not fulfilled
A reasonable estimation, could be 664 days/year with a flow
of 75 Tn/h
The minimum of 5250 days of 70 Tn/h 600 psi steam is not
reached. A reasonable estimation could be 4763 days of 75.6 Tn/h
The system runs over the maximum number of days to supply
35 Tn/h of steam, even increasing to 50.4 Tn/h the amount
of this flow
The system does not reach the 5475 days of 70 Tn/h 150 psi steam
established as minimum value for this phase. A more reasonable
estimation would be 4763 days of 75.6 Tn/h
The requirement of 700 days of 70 Tn/h 600 psi steam is not met
in this phase. A reasonable estimation would be 680 days of
70 Tn/h
Supply of 35 Tn/h 600 psi of steam is over the maximum
for this phase
The requirement of a minimum of 5250 days of 70 Tn/h steam
600 psi supply is not obtained. A more reasonable estimation
would be 4987 days of 70 Tn/h
The system delivers more than 35 Tn/h flow of steam 600 psi.
in this phase
The minimum of 5475 days of 70 Tn/h 150 psi steam is not fulfill
either. A reasonable estimation is 4987 days of 70 Tn/h 150 psi
A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 289
studies of complex systems, and presents a generic approach
for these type of studies using continuous time Monte Carlo
simulation modeling, that is exemplified and validated in the
paper for an availability study of a cogeneration plant
(COGEPLANT). For this case study, we have assessed
availability of a couple of configurations considered by the
plant design engineers. We have shown how meeting
requirements expressed in the technical conditions appearing
in the initial documentation for bidding of this engineering
project is not totally possible with no one of the plant
configurations. That means that availability expectations of
proposed configurations should be lower, or reliability and
maintainability of the functional blocks should be higher to
meet requirements. At the same time, we provide reasonable
estimations for the availability of the production of power
and steam that could be included in a realistic engineering
project proposal to the same final customer. These esti-
mations are based in validated reliability and availability
calculations of each functional blocks that has been
considered in the simulation model, but we also showed the
importance and opportunity of sensitivity analysis when data
is important und uncertain.
The case study was carried out at the same time than the
engineering project proposal, and it was decisive for the final
selection of the technical configuration of the plant. The
configuration selected was Number 2 of this study, which
offers higher availability of supply, meeting current elec-
trical power supply requirements for phase 2, for the entire
project horizon. At the same time this study served to adjust
initial availability requirements of the technical conditions of
the bid for the cogeneration plants, once data in the model
was considered to be adjusted to real equipment including in
the bid.
Extensions of this work could be related to design aspects
of the plants in order to increase the assessed reliability and
availability. For instance, a current project is considering the
assessment of steam production availability increase by
adding parallel/auxiliary boilers to the original configur-
ation. At the same time, some logistics aspects, like spare
parts to keep in stock, could be also studied.
Finally, we would like to mention that when comparing
several configurations using this assessment, not only
availability and reliability are important (in our case were a
requirement), but also cost estimations are a key factor.
Therefore, a clear point to extend this work will be to transfer
the information provided by these models to a comprehen-
sive life cycle cost analysis model (LCCAM) in order to
produce a global value assessment for the plant.
Acknowledgements
This research has been carried out by members of a
group (Project number DPI 2004-01843) founded by
the Spanish Ministry of Science and Education and the
European Union (through FEDER funds). This particular
work was possible thanks to the support of the company
ABENER ENERGIA S.A. and especially we do thank
Juan Hernandez, Francisco Perez and Emilıo Rodrıguez
for their knowledge sharing and more than generous
help. We also thank Jesus Ivars from INTERQUISA for
his thoughtful comments and interest in potential out-
comes from this research. Finally we are very grateful to
the reviewers for their valuable anonymous contribution
to the final quality of this paper.
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