Monte Carlo-based assessment of system availability. A case study for cogeneration plants

Reliability Engineering and System Safety 88 (2005) 273–289 www.elsevier.com/locate/ress

Monte Carlo-based assessment of system availability. A case study for cogeneration plants Adolfo Crespo Marqueza,*, Antonio Sa´nchez Heguedasb, Benoit Iungc a

Department of Industrial Management, School of Engineering, University of Seville, Camino de los Descubrimientos s/n. 41092 Sevilla, Spain b Qualmaint, S.L. Maintenance Engineering, Av. San Francisco Javier, 2. 41018 Sevilla, Spain c Faculte´ des Sciences, Nancy Research Centre for Automatic Control, University Henri Poincare´, BP 239, 54506 Vandoeuvre le`s 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

* Corresponding author. Tel.: C34 954 487215; fax: C34 954 486112. E-mail addresses: [email protected] (A. Crespo Marquez), [email protected] (A. Sa´nchez Heguedas), [email protected] (B. Iung). 0951-8320/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ress.2004.07.018

conform to arbitrary failure and repair distributions for maintained systems; these studies should be coupled with economic analyses to manage for the system the compromise 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 independence, i.e. that if one component fails and it is repaired,

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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.

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 maintenance 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 considering 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 1 The reader is referred to [17] for a discussion regarding both simulation practices.

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Table 1 Steps in the availability/reliability assessment Step name

Description

Result

1. System’s configuration definition

List of functional blocks: function, input, output, etc.

4. Simulation

Determination of the basic functional blocks for the plant configuration and for every function to analyze Determination of the dependencies among functional blocks for the fulfillment of every function Compilation of the necessary reliability and maintenance data (and information) for each one of the considered blocks Continuous time stochastic simulation model building Simulation scenarios and experiments design

5. Results and analysis

Simulation results calculation

2. Data collection

3. Model building

Simulation results discussion

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 corresponding 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

Functional chart of the system that contains the relations among blocks and their reliability features Reliability and maintenance data for each block: MTTR, MTBF, MTTM, preventive schedule, times, etc. VENSIM simulation models Scenario listings, required simulation replications, confidence intervals for the results, etc. Result of the parameters of availability and reliability of the functions of our interest in the different configurations Interpretation of results and their discussion

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 maintenance 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 dependencies 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 corrective maintenance action in t LCt time when the last corrective maintenance, for a system in t, started LPt time when the last preventive maintenance, for a system in t, started

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PAt decrease in system’s age due to preventive maintenance action in t RNt random number within the interval (0,1), generated in t Tt system’s age in t TI increase of system’s age in period t TOt decrease of system’s age in period t l(Tt) failure rate of the system in t At system availability (1 available, 0 unavailable) at t AAt all sub-systems available (1 yes, 0 no) at t SMt sheduled maintenance (1 yes, 0 no) in period t MBt maintenance backlogged (1 yes, 0 no) at t RMt maintenance released (1 yes, 0 no) in period t Model parameters CT average time of a corrective maintenance action n minimum age of the system to do preventive maintenance actions PT average time of a preventive maintenance action T1 maximum time the system operates without a failure

3.1. Modeling system’s age The process requires first to model the age of the system (Tt): Tt Z Tt C TIt K TOt

(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

( PAt Z

Tt ;

if Tt R n

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 8 > < 1 K ðPulseðLCt ; CT; tÞ At Z CPulseðLPt ; PT; tÞÞ; if LCt O 0 or LPt O 0 > : 1; Otherwise (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: ( 1; a! t! a C b Pulseða; b; tÞ Z (7) 0; Otherwise 3.4. Modeling maintenance backlog

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.

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 dependencies 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:

3.2. Modeling age based preventive maintenance

AAt Z

TIt Z At

(2)

and age will decrease when the system is maintained ( if PAt !O0 and CAt !O0 PAt ; TOt Z PAt C CAt ; Otherwise ( CAt Z

Tt ;

if lðTt ÞR RNt

0;

Otherwise

(3)

(4)

iZ2 Y

At;i ; with i Z 1;2

(8)

iZ1

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

( SMt;i Z

1; ti =n Z Intðti =nÞ and ti O0 0; Otherwise

(9)

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MBt;i Z MBtK1;i CSMt;i KRMt;i ( RMt;i Z

1; ðSMt;i Z1 or MBt;i Z 1Þ and AAt Z 1 0; Otherwise

(10)

(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 simulation, 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 configurations of the system will fall within the interval that we 2

Trade Mark of Ventana Systems, Inc.

277

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 deterministic 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

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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/h 15 days/yr. † Phase 2. Steam 600 psi: 70 Tn/h 350 days/yr, 35 Tn/h 15 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 MW without back-up for 15 days/yr. † Phase 2. 40 MW with back-up for 335 days/yr, 20 MW with 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.)

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).

Fig. 1. Description of an electrical power and steam cogeneration unit.

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Table 2 Functional blocks considered in the simulation study Functional block

Components

Inputs

Outputs

Function

Power generation system named: [RgasTGasGen]

Gas network Turbine Generator Transformer Circuit switch

Natural gas (or fuel, eventually)Cair

Electrical power (30/45 MW) in 12 kVCwarm exhaust gasses

Steam generation system named: [RAguaCaldera]

Boiler 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)

Demineralized waterC turbine exhaust gases (Cnatural gasCair eventually)

Steam 600 psiC steam 150 psiC water drain C exhaust gases

Local electrical transportation network (LETN) named: [RedElec]

LETN

25 MW in 12 kV

25 MW in 12 kV

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 turbinecoupled generator. Exhaust gasses will be then used to generate steam 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-combustion 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 Supply constrained to a maximum of 25 MW of power

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 configurations 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 all three boilers work simultaneously. † The 35 Tn/h flow requirements are met those days that two, 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

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Fig. 2. Steam production diagram with 3 Bs.

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 all two Bs work simultaneously. † The 35 Tn/h flow requirements are met those days only one out of two Bs works.

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 this case. The production of 45 MW of electrical power (not only 20 MW) without any 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

Fig. 3. Electrical power production diagrams with 2 TGs.

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Table 3 Reliability data (in failures per running day) Functional block

Components

Data bank

TG [RgasTGasGen]

Gas network Turbine Generator Circuit Breaker Transformer Boiler 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 2nd economizer) 10 joints and connections (water network system) LETN

Selected value

FARADIP

B [RaguaCaldera]

LETNl [RedElec]

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 judgments (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.

IEEE

Own value 0.0000 0.00548

0.001320 0.004800 0.000036

0.00046300 0.00000821 0.00002700

0.000480 0.000480 0.000120 0.000480

0.000024 0.0110 0.0001 0.0110 0.0110

0.03405088

0.00000000 0.00547945 0.00046300 0.00000821 0.00002700 0.01100000 0.00000000 0.00500000 0.00500000 0.00048000 0.00048000 0.00012000 0.03405088

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 maintenance plan for the plant. But the following consideration, operational dependencies related to maintenance, have to be taken into account to build the final maintenance schedule: † The preventive maintenance of the plant will be conditioned by the preventive maintenance of the turbine sets, so that in the subsequent simulation model we will

Table 4 Functional blocks MTTR (mean time to repair, in days) Functional block

Components

Data source IEEE

TG [RGasTGasGen]

B [RAguaCaldera]

LETN [RedElec]

Gas network Turbine Generator Circuit breaker Transformer Boiler Steam network Pump 1 Pump 2 Valve 1 Valve 2 Water network LETN

Selected value Own value 2.54166667

1.36250000 0.50000000 3.54166667 9 > > > > > > > =

1.000 1.000 1.000

2.54166667 1.36250000 0.50000000 3.54166667 1.000 1.000

1.000

1.000

> > > > > > > ;

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Table 5 Basic functional blocks data Functional block

Failure rate

TG [RGasTGasGen] B [RAguaCaldera] LETN [RedElec]

0.00597766 0.02208000 0.03405088

P

li

MTTR

P P ðli =mi Þ= li

2.45204697 !1 !1

In failures per day (l) and repair days (MTTR).

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 is that 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 4

Trade Mark of Ventana Systems, Inc.

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) Each 4.000 operating hours Each 8.000 operating hours Each 50.000 operating hours

6 48 120 240

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 maintenance action scheduled). 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 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 simulation 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, availability 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).

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283

Fig. 4. Example of the maintenance program for Configuration 2.

4.3. Sensitivity analysis In this case study several univariate (changing one parameter at a time) and multivariate (changing many

parameters at a time) sensitivity analysis were carried out. As an example, we present here results for the multivariate sensitivity analysis to variations in the corrective time for both TG blocks of configuration 2 which was

Fig. 5. Example of TGs corrective maintenance (repairs).

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Fig. 6. TGs backlog of maintenance activities for Configuration 2. These were activities carried out after the scheduled date.

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

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

Fig. 7. TGs availability over time.

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Fig. 8. Days of electrical power production for different power requirements. Second phase of the project.

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 corresponding scenarios. We will therefore present now a set of simulations containing, for each one of the two plant

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.

Fig. 9. Days of high pressure steam production for different flow requirements. Second phase of the project.

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A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 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) Phase 1 20MW with back-up (note: MINZ700 days)

20 MW without back-up (note: MAXZ30 days) Fig. 10. Sensitivity analysis results for MTTR of the TGs [2,10] days.

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 configuration 1, with three turbines. Requirements are presented in the first column and in terms of service quality required over

75.6 Tn/h of 600 psi steam (note: MINZ700 days)

50.4 Tn/h of 600 psi steam (note: MAXZ30 days of 35 Tn/h)

Phase 2 50 MW with back-up (note: MINZ5025 days 40 MW with back-up)

20 MW with BC20 MW without B (note MAXZ450 days)

75.6 Tn/h 600 psi steam (note: MINZ5250 days 70 Tn/h)

50.4 Tn/h 600 psi steam (note: MAXZ225 days 35 Tn/h)

75.6 Tn/h 150 psi steam (note: MINZ5475 days 70 Tn/h)

Fig. 11. Curve topology for the failure rate of the block [RGasTGasGen1] in the simulation study.

Repl.

Values

Statistics

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

723 725 729 725 729 8 6 2 6 2 678 664 666 665 672 19 36 31 49 32

Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min

726.20 2.68 2.35 728.55 723.85 4.80 2.68 2.35 7.15 2.45 669.00 5.92 5.19 674.19 663.81 33.40 10.78 9.45 42.85 23.95

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

4792 4783 4781 4810 4736 647 665 656 604 707 4746 4789 4783 4818 4846 638 620 617 548 559 4746 4789 4783 4818 4846

Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min

4780.40 27.34 23.96 4804.36 4756.44 655.80 36.97 32.40 688.20 623.40 4796.40 37.75 33.09 4829.49 4763.31 596.40 40.17 35.21 631.61 561.19 4796.40 37.75 33.09 4829.49 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.

A. Crespo Marquez et al. / Reliability Engineering and System Safety 88 (2005) 273–289 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) Phase 1 45 MW with back-up (note: MINZ700 days 20 MW with B)

20 MW without back-up (Note: MAXZ30 days)

75.6 Tn/h of 600 psi steam (note: MINZ700 days)

35 Tn/h of 600 psi steam (Note: MAXZ30 days of 35 Tn/h)

Phase 2 45 MW with back-up (note: MINZ5025 days 40 MW with back-up)

45 MW without back-up (note MAXZ450 days 20 MW with B. C20 MW without) 70 Tn/h 600 psi steam (note: MINZ5250 days 70 Tn/h)

35 Tn/h 600 psi steam (note: MAXZ225 days 35 Tn/h)

70 Tn/h 150 psi steam (note: MINZ5475 days 70 Tn/h)

Repl.

Values

Statistics

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

703 695 701 696 695 28 32 24 34 34 680 691 693 681 683 44 30 26 40 36

Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min

698.00 3.74 3.28 701.28 694.72 30.40 4.34 3.80 34.20 26.60 685.60 5.98 5.24 690.84 680.36 35.20 7.29 6.39 41.59 28.81

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

5115 5100 5135 5110 5134 352 366 338 352 338 4980 5006 4996 5026 4999 425 409 412 383 419 4980 5006 4996 5026 4999

Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min

5118.80 15.32 13.43 5132.23 5105.37 349.20 11.71 10.27 359.47 338.93 5001.40 16.73 14.66 5016.06 4986.74 409.60 16.12 14.13 423.73 395.47 5001.40 16.73 14.66 5016.06 4986.74

4.5. Results for requirements fulfillments in Configuration 2 (2 TGs) 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

287

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 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.9886 0.989 0.9905 0.9869 0.9835 0.9697 0.9592 0.9655 0.9553 0.9647 0.9885 0.9922 0.9857 0.9929 0.9937 0.9808 0.9815 0.982 0.9865 0.9811

Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min Mean Std. dev. Conf(G95%) Max Min

[RedElec], LETN, BLOCK

[RedAgua], Water network, SUB-BLOCK

[Caldera1], Boiler 1, SUB-BLOCK

0.9877 0.0027 0.0023 0.9900 0.9854 0.9629 0.0056 0.0050 0.9678 0.9579 0.9906 0.0034 0.0030 0.9936 0.9876 0.9824 0.0023 0.0021 0.9844 0.9803

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 configurations. 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 postcombustion 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 10 Example of results for days of post-combustion needed in Configuration 1 Post-combustion days

Repl.

Values

Statistics

Total days in postcombustion for three boilers (Conf. 1)

1 2 3

240 198 161

4 5

207 164

Mean Std. dev. Conf(G 95%) Max Min

194.0000 32.7490 28.7053 222.7053 165.2947

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Table 11 Example of results for days of post-combustion needed in Configuration 2 Post-combustion days

Repl.

Values

Statistics

Total days in postcombustion for two boilers (Conf. 2)

1 2 3 4 5

109 146 122 162 125

Mean Std. dev. Conf(G95%) Max Min

132.8000 21.0404 18.4424 151.2424 114.3576

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 † Regarding the fulfillment of the power and steam supply requirements. See Table 12. † Regarding availability and reliability of the blocks. A key aspect 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.

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 consumption 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 postcombustion, 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 postcombustion 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.

5. Conclusions This paper discusses the opportunity to use Monte Carlo simulation techniques for reliability/availability assessment

Table 12 Simulation results discussion Config.

Phase

Production of electrical power

Production of steam

1 (3TG)

F1

All requirements are fulfilled working with three turbines from the start of Phase 1. A higher supply quality could even be offered. No contract with the LETN is considered

1 (3TG)

F2

The minimum of 5025 days of 40 MW with back-up is not reached in this phase. A reasonable estimation could be around 4756 days of 50 MW with back-up, assuming the existence of a contract with the LETN The system runs over the maximum number of days supplying 20 MW with B.C20 MW without B

2 (2TG)

F1

2 (2TG)

F2

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 MW with back-up during 694 days in this phase would be reasonable The system exceeds the requirement for maximum number of days supplying 20 MW without back-up, but now even increasing this power to 45 MW 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 now not applicable. However an availability of 45 MW without back-up during 339 days can now be reached and offered

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

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 estimations 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 electrical 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 configuration. 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 comprehensive 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

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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 Herna´ndez, Francisco Pe´rez and Emilı´o Rodrı´guez for their knowledge sharing and more than generous help. We also thank Jesu´s Ivars from INTERQUISA for his thoughtful comments and interest in potential outcomes 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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