Availability Estimation of Air Compression and Nitrogen Generation Systems in LNG-FPSO Depending on Design Stages

: This study estimated availability of an air compression system and a nitrogen generation system in liqueﬁed natural gas—ﬂoating production storage and o ﬄ oading unit (LNG-FPSO) with di ﬀ erent design stages to investigate the gap between the availability at the early design stage and that at the late design stage. Although availability estimation in the early design stage is more important than the late design stage, it is di ﬃ cult to estimate the availability accurately in the early design stage. The design stage was divided into three depending on the design progress. Monte Carlo simulation technique was employed for the availability estimation. The results of the availability estimation showed that there was 0.434% di ﬀ erence between the early and late design stages. This meant that the availability in the early design stage was underestimated due to limited information. A sensitivity analysis was performed to investigate critical factors a ﬀ ecting the results. The investigated factors were failure rate, repair time, redundant equipment, and modiﬁed preventive maintenance schedule. The most critical factor was redundant equipment. It increased 0.486% availability.


Introduction
Various factors are considered in system design, such as efficiency, costs, safety, and environmental effect. Availability is also one of the important issues in the system design. The definition of the availability from BS4778-3.1 (British standards, quality vocabulary, availability, reliability, and maintainability terms.) Guide to concepts and related definitions is the ability of an item under the combined aspects of reliability, maintainability, and maintenance support to perform its required function at a specified instant or for a specified period [1]. The availability indicates that how much a system approaches ideal operation without production loss caused by equipment failures or undesired external events. Availability estimation is frequently performed in the oil and gas, chemical, and power plant industries to find the optimum design option, to predict the production level, and to evaluate maintenance and operating policies.
Many previous studies conducted the availability estimation for various systems to improve their designs. Basker and Martin [2] estimated the availability of production and electrical systems using the developed numerical method. They considered failure and repair rates following the non-exponential distribution. Keller and Stipho [3] conducted the availability estimation for two similar chlorine production plants which were located in different environmental conditions (Iraq and Switzerland).

Description of Target System
In this study, two systems in LNG-FPSO is selected as a target for the availability estimation. These are air compression and nitrogen generation systems in LNG-FPSO. LNG-FPSO is a huge facility for LNG production in offshore, and its concern has been increased because of the growing demand for LNG. LNG-FPSO is a floating unit for production, processing, storage, and offloading of LNG in remote offshore gas fields. Conventionally, the natural gas in an offshore field is transported by pipeline to onshore for processing. LNG-FPSO does not require the pipeline because it processes the natural gas itself in offshore. It is specialized for small scale gas field. Topside modules of the LNG-FPSO can be categorized into two: a processing module and a utility module. The processing module handles the primary hydrocarbon, whereas the utility module deals with utilities including energy, water, air, and diesel oil. The utility module provides utilities to the processing system for safe and stable operation. Some failure of the utility module can be critical because safety systems for preventing an accident are operated by the utility module.
The topside of LNG-FPSO can be divided into ten modules as shown in Figure 1. A produced feed gas come up through a turret, and it is transported to an inlet facility module. Slug in the feed gas is removed by a slug catcher, and liquid is separated by a separator. CO 2 , Hg, and H 2 O in the feed gas is removed in a pre-treatment module. The treated natural gas is liquefied by a liquefaction module, and a refrigeration module supplies the refrigerant to the liquefaction module. The heavier components than methane like ethane, butane, and propane are separated by a fractionation module. Some amounts of natural gas are transferred to a fuel gas compression system, and it is utilized for power generation. The liquefied natural gas is stored in storage tanks with LPG and condensate. A condensate stabilizer module separates the relatively light components for safe operation. Condensate is mainly composed of propane, butane, pentane, and heavier hydrocarbon. When condensate contains light components like methane and ethane, it can be vaporized and increase the pressure of a storage tank during storage. These light components should be separated before storage. A blowdown module treats combustion fluids in emergency situations. The utility module supplies various utilities to other modules for the operation.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 17 described. In Section 3, methodologies for the availability estimation are discussed. The results of the availability estimation and the sensitivity analysis are indicated in Section 4. Finally, the conclusions are presented.

Description of Target System
In this study, two systems in LNG-FPSO is selected as a target for the availability estimation. These are air compression and nitrogen generation systems in LNG-FPSO. LNG-FPSO is a huge facility for LNG production in offshore, and its concern has been increased because of the growing demand for LNG. LNG-FPSO is a floating unit for production, processing, storage, and offloading of LNG in remote offshore gas fields. Conventionally, the natural gas in an offshore field is transported by pipeline to onshore for processing. LNG-FPSO does not require the pipeline because it processes the natural gas itself in offshore. It is specialized for small scale gas field. Topside modules of the LNG-FPSO can be categorized into two: a processing module and a utility module. The processing module handles the primary hydrocarbon, whereas the utility module deals with utilities including energy, water, air, and diesel oil. The utility module provides utilities to the processing system for safe and stable operation. Some failure of the utility module can be critical because safety systems for preventing an accident are operated by the utility module.
The topside of LNG-FPSO can be divided into ten modules as shown in Figure 1. A produced feed gas come up through a turret, and it is transported to an inlet facility module. Slug in the feed gas is removed by a slug catcher, and liquid is separated by a separator. CO2, Hg, and H2O in the feed gas is removed in a pre-treatment module. The treated natural gas is liquefied by a liquefaction module, and a refrigeration module supplies the refrigerant to the liquefaction module. The heavier components than methane like ethane, butane, and propane are separated by a fractionation module. Some amounts of natural gas are transferred to a fuel gas compression system, and it is utilized for power generation. The liquefied natural gas is stored in storage tanks with LPG and condensate. A condensate stabilizer module separates the relatively light components for safe operation. Condensate is mainly composed of propane, butane, pentane, and heavier hydrocarbon. When condensate contains light components like methane and ethane, it can be vaporized and increase the pressure of a storage tank during storage. These light components should be separated before storage. A blowdown module treats combustion fluids in emergency situations. The utility module supplies various utilities to other modules for the operation. In this study, air compression and nitrogen generation systems are analyzed in the utility module because those are important systems for stable and safe operation. A general utility module In this study, air compression and nitrogen generation systems are analyzed in the utility module because those are important systems for stable and safe operation. A general utility module contains an instrument and service air system, a nitrogen generation system, a cooling water system, a seawater system, a hot oil system, a portable water system, a produced and wastewater system, and a diesel oil system. The instrument and service air system compresses the air up to approximately 10 bar for the usage of the instrument and others. The nitrogen generation system supplies nitrogen to the customers. The cooling water system is used to provide the cooling medium for all of the topside modules. The sea water system provides the seawater to various systems. The hot oil system increases the temperature of the oil within a specified range. It utilizes waste heat from flue gas using waste heat recovery units installed in a power generation system. The portable water system distributes water to topside eyewash and safety shower, and hot and cold water for personal usage. The produced and wastewater system removes the oil in the produced water from topside separators. The diesel oil system distributes the diesel oil to customers by transferring and purifying it. Figure 2 indicates the air compression and nitrogen generation systems. The systems mainly consist of three pieces of equipment; an air compressor, an air dryer, and a nitrogen generator. Air is compressed by the air compressor, and then the small amount of water in the compressed air is dehydrated by the air dryer. The dry air is sent to a customer requiring the instrument air and to the nitrogen generator. The nitrogen generator separates the nitrogen from the dry air. contains an instrument and service air system, a nitrogen generation system, a cooling water system, a seawater system, a hot oil system, a portable water system, a produced and wastewater system, and a diesel oil system. The instrument and service air system compresses the air up to approximately 10 bar for the usage of the instrument and others. The nitrogen generation system supplies nitrogen to the customers. The cooling water system is used to provide the cooling medium for all of the topside modules. The sea water system provides the seawater to various systems. The hot oil system increases the temperature of the oil within a specified range. It utilizes waste heat from flue gas using waste heat recovery units installed in a power generation system. The portable water system distributes water to topside eyewash and safety shower, and hot and cold water for personal usage. The produced and wastewater system removes the oil in the produced water from topside separators. The diesel oil system distributes the diesel oil to customers by transferring and purifying it. Figure 2 indicates the air compression and nitrogen generation systems. The systems mainly consist of three pieces of equipment; an air compressor, an air dryer, and a nitrogen generator. Air is compressed by the air compressor, and then the small amount of water in the compressed air is dehydrated by the air dryer. The dry air is sent to a customer requiring the instrument air and to the nitrogen generator. The nitrogen generator separates the nitrogen from the dry air.  includes not only the main equipment but also piping, instrumentation, and control devices. In this study, the piping information is not contained because it is unnecessary for the availability estimation.    Figure 3 is a process flow diagram (PFD) of the air compression and nitrogen generation systems. PFD shows the main equipment in the system. The preliminary process and instrument diagram (P&ID) is indicated in Figures 4 and 5. P&ID includes not only the main equipment but also piping, instrumentation, and control devices. In this study, the piping information is not contained because it is unnecessary for the availability estimation.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 17 contains an instrument and service air system, a nitrogen generation system, a cooling water system, a seawater system, a hot oil system, a portable water system, a produced and wastewater system, and a diesel oil system. The instrument and service air system compresses the air up to approximately 10 bar for the usage of the instrument and others. The nitrogen generation system supplies nitrogen to the customers. The cooling water system is used to provide the cooling medium for all of the topside modules. The sea water system provides the seawater to various systems. The hot oil system increases the temperature of the oil within a specified range. It utilizes waste heat from flue gas using waste heat recovery units installed in a power generation system. The portable water system distributes water to topside eyewash and safety shower, and hot and cold water for personal usage. The produced and wastewater system removes the oil in the produced water from topside separators. The diesel oil system distributes the diesel oil to customers by transferring and purifying it. Figure 2 indicates the air compression and nitrogen generation systems. The systems mainly consist of three pieces of equipment; an air compressor, an air dryer, and a nitrogen generator. Air is compressed by the air compressor, and then the small amount of water in the compressed air is dehydrated by the air dryer. The dry air is sent to a customer requiring the instrument air and to the nitrogen generator. The nitrogen generator separates the nitrogen from the dry air.  includes not only the main equipment but also piping, instrumentation, and control devices. In this study, the piping information is not contained because it is unnecessary for the availability estimation. The design stage considered in this study are three. The first stage is PFD and the second stage is the preliminary P&ID. The third stage is preliminary P&ID with the information on preventive maintenance.   The design stage considered in this study are three. The first stage is PFD and the second stage is the preliminary P&ID. The third stage is preliminary P&ID with the information on preventive maintenance.  The design stage considered in this study are three. The first stage is PFD and the second stage is the preliminary P&ID. The third stage is preliminary P&ID with the information on preventive maintenance.
Stage III-Preliminary P&ID + Information on Preventive Maintenance

Methodology
Several methods are available for the availability estimation: reliability block diagram (RBD), Markov model, and Monte Carlo simulation [17,18]. The former two are an analytical approach whereas the latter one is a simulation approach. The analytical approach calculates the availability using mathematical equations, while the simulation technique estimates it by generating scenarios. When the system is complex, the analytical approaches like RBD and Markov model are unrealistic. They are additionally difficult to apply to the system, which has nonconstant failure and repair rates. However, the Monte Carlo simulation approach can handle inconstant failure/repair rates and multi-state systems. One of the drawbacks of the Monte Carlo simulation is the long simulation time, but it can be overcome by the advanced simulation techniques. In this study, Monte Carlo simulation is employed for the availability estimation. Figure 6 shows the procedure for the availability estimation using Monte Carlo Simulation. First of all, the target system is analyzed, and then the reliability block diagram is drawn for the modeling of the system. The data for reliability and maintainability is collected from the data sources. The availability of the target system is estimated using the Monte Carlo Simulation. The followings are the details of each step.

Methodology
Several methods are available for the availability estimation: reliability block diagram (RBD), Markov model, and Monte Carlo simulation [17,18]. The former two are an analytical approach whereas the latter one is a simulation approach. The analytical approach calculates the availability using mathematical equations, while the simulation technique estimates it by generating scenarios. When the system is complex, the analytical approaches like RBD and Markov model are unrealistic. They are additionally difficult to apply to the system, which has nonconstant failure and repair rates. However, the Monte Carlo simulation approach can handle inconstant failure/repair rates and multistate systems. One of the drawbacks of the Monte Carlo simulation is the long simulation time, but it can be overcome by the advanced simulation techniques. In this study, Monte Carlo simulation is employed for the availability estimation. Figure 6 shows the procedure for the availability estimation using Monte Carlo Simulation. First of all, the target system is analyzed, and then the reliability block diagram is drawn for the modeling of the system. The data for reliability and maintainability is collected from the data sources. The availability of the target system is estimated using the Monte Carlo Simulation. The followings are the details of each step.

STEP 1 System Analysis
First, the information required for the availability estimation is gathered, and the system is analyzed. The boundary and a level of the system analysis determined in this step. The given operating conditions and assumptions for the availability estimation are determined. Those include the lifespan of the system, number of simulations, distribution function of failure, distribution function of repair time, unit of failure rate, and unit of repair time. Table 1 tabulates the information.

STEP 1 System Analysis
First, the information required for the availability estimation is gathered, and the system is analyzed. The boundary and a level of the system analysis determined in this step. The given operating conditions and assumptions for the availability estimation are determined. Those include the lifespan of the system, number of simulations, distribution function of failure, distribution function of repair time, unit of failure rate, and unit of repair time. Table 1 tabulates the information.

STEP 2 Determination of Reliability Block Diagram (RBD)
RBD is a block structure to show success logic of a system. The blocks represent equipment or components of the system to fulfill a specified function. Success path can be visually verified so that it can be easily understood. In this step, the RBD of the system is determined based on Step 1 s results. The followings indicate the RBD with the different design development states.
3.2.1. RBD at Stage I (PFD Stage) Figure 7 shows the RBD at Stage I. It is divided into three parts as shown in Figure 6: air compression, air dryer, and nitrogen generation parts. The configuration of the air compressor part is 3 × 50%. It means that three compressors are installed, and the capacity of each compressor is 50%. Two compressors are in operation, and one compressor is on standby for a failure of the operating compressors. The air dryer part has 2 × 100% configuration. One air dryer is redundancy. In the nitrogen generation part, the membrane has the 4 × 33% configuration. Three membranes are operated, and the remaining membrane stands by for a failure.

STEP 2 Determination of Reliability Block Diagram (RBD)
RBD is a block structure to show success logic of a system. The blocks represent equipment or components of the system to fulfill a specified function. Success path can be visually verified so that it can be easily understood. In this step, the RBD of the system is determined based on Step 1′s results. The followings indicate the RBD with the different design development states.
3.2.1. RBD at Stage I (PFD Stage) Figure 7 shows the RBD at Stage I. It is divided into three parts as shown in Figure 6: air compression, air dryer, and nitrogen generation parts. The configuration of the air compressor part is 3 × 50%. It means that three compressors are installed, and the capacity of each compressor is 50%. Two compressors are in operation, and one compressor is on standby for a failure of the operating compressors. The air dryer part has 2 × 100% configuration. One air dryer is redundancy. In the nitrogen generation part, the membrane has the 4 × 33% configuration. Three membranes are operated, and the remaining membrane stands by for a failure.

STEP 2 Determination of Reliability Block Diagram (RBD)
RBD is a block structure to show success logic of a system. The blocks represent equipment or components of the system to fulfill a specified function. Success path can be visually verified so that it can be easily understood. In this step, the RBD of the system is determined based on Step 1′s results. The followings indicate the RBD with the different design development states.
3.2.1. RBD at Stage I (PFD Stage) Figure 7 shows the RBD at Stage I. It is divided into three parts as shown in Figure 6: air compression, air dryer, and nitrogen generation parts. The configuration of the air compressor part is 3 × 50%. It means that three compressors are installed, and the capacity of each compressor is 50%. Two compressors are in operation, and one compressor is on standby for a failure of the operating compressors. The air dryer part has 2 × 100% configuration. One air dryer is redundancy. In the nitrogen generation part, the membrane has the 4 × 33% configuration. Three membranes are operated, and the remaining membrane stands by for a failure.

RBD at Stage III (Preliminary P&ID + Information on Preventive Maintenance)
RBD at Stage III is almost identical with that for stage II excepting the additional information on preventive maintenance. One block for the preventive maintenance is added for stage III.

RBD at Stage III (Preliminary P&ID + Information on Preventive Maintenance)
RBD at Stage III is almost identical with that for stage II excepting the additional information on preventive maintenance. One block for the preventive maintenance is added for stage III.

RBD at Stage III (Preliminary P&ID + Information on Preventive Maintenance)
RBD at Stage III is almost identical with that for stage II excepting the additional information on preventive maintenance. One block for the preventive maintenance is added for stage III.

Step 3 Data Collection
The reliability and maintenance data are required for the availability estimation. Since the results of the availability estimation are significantly influenced by the reliability and maintenance data, they are important. Reliability data is linked to the failure rate. The maintenance data is associated with the corrective maintenance time (repair time) and the preventive maintenance time. When the failure occurs, the corrective maintenance is conducted to a system. Preventive maintenance is performed on the basis of maintenance policies and strategies. The data can be categorized into three depending on the kinds of sources: Open data (from open books and reports), vendor data, and in-house data. This study uses the OREDA (Offshore and onshore reliability data) and vendor data. OREDA is offshore and onshore reliability data handbook sponsored by oil and gas companies. It is considered a unique data source in the offshore industry. OREDA is employed in this study because it is the most suitable for it [19,20]. Vendor data is taken from a manufacturer of air compression and nitrogen generation systems. Table 2 indicates the reliability and maintenance data employed in this study.  Table 3 indicates the information on the preventive maintenance. The preventive maintenance is conducted to prevent unexpected future failure. It is classified into four categories: age-based, clock-based, condition-based, and opportunity maintenance [18]. In the age-based maintenance, the preventive maintenance is performed at the defined age of the system (e.g., the number of take-offs/landings for an airplane). The clock-based maintenance is carried out at specified calendar time so that it is scheduled by administers. In the condition-based maintenance, the preventive maintenance is initiated by measuring condition variables. The opportunity maintenance is carried out when the system is stopped by the other failure. In this study, the clock-based maintenance is taken into account for the preventive maintenance, and the data is collected from the vendor of the air compression and nitrogen generation systems.

Step 4 Monte Carlo Simulation
Monte Carlo simulation is employed to estimate the availability. Figure 11 shows the flowchart of the Monte Carlo simulation [21]. First of all, components, their states, and their configuration are defined. Moreover, the next transition time for each component is estimated by the random number generation. The transition time is the time when the phase of a component in the system is changed from normal to failure. In this step, the generated random number is converted into a value of time using a conversion method at a cumulative distribution function. Figure 12 shows how the generated random number is transferred to the value of time by the conversion method. The cumulative distribution function for the exponential distribution is indicated in Equation (1).
where λ is the failure rate, and x is a value of time.
where R is the random number between 0 and 1. R* is a generated random number between 0 and 1.

Step 4 Monte Carlo Simulation
Monte Carlo simulation is employed to estimate the availability. Figure 11 shows the flowchart of the Monte Carlo simulation [21]. First of all, components, their states, and their configuration are defined. Moreover, the next transition time for each component is estimated by the random number generation. The transition time is the time when the phase of a component in the system is changed from normal to failure. In this step, the generated random number is converted into a value of time using a conversion method at a cumulative distribution function. Figure 12 shows how the generated random number is transferred to the value of time by the conversion method. The cumulative distribution function for the exponential distribution is indicated in Equation (1).
where λ is the failure rate, and x is a value of time. Figure 11. Procedure for availability estimation using Monte Carlo simulation [21]. Figure 11. Procedure for availability estimation using Monte Carlo simulation [21].
The shortest transition time is found among all of the predicted times, and then the system time is changed to the shortest transition time. If the time is shorter than the mission time, the transition times for all component are estimated again. The mission time is total operation time required to the system like lifespan. When the time is longer than the mission time, the system's availability is calculated. This process is just one simulation. If the number of simulations is lower than the desired number of simulations, the next simulation is repeatedly performed. The desired number of simulations is determined as referring the convergence of results. When a result converges sufficiently, the number of simulations is selected as the desired number of simulations. The desired number of simulations is determined as setting a sufficiently high number of simulations or determining the number of simulations after the initial simulation. When the number of simulations is the same as the desired number of simulations, the average system availability is calculated finally. The average system availability is the result after the last simulation, while the system availability is the result of each simulation.
where R is the random number between 0 and 1. R* is a generated random number between 0 and 1. The predicted time from the generated random number is shown in Equation (3).
The shortest transition time is found among all of the predicted times, and then the system time is changed to the shortest transition time. If the time is shorter than the mission time, the transition times for all component are estimated again. The mission time is total operation time required to the system like lifespan. When the time is longer than the mission time, the system's availability is calculated. This process is just one simulation. If the number of simulations is lower than the desired number of simulations, the next simulation is repeatedly performed. The desired number of simulations is determined as referring the convergence of results. When a result converges sufficiently, the number of simulations is selected as the desired number of simulations. The desired number of simulations is determined as setting a sufficiently high number of simulations or determining the number of simulations after the initial simulation. When the number of simulations is the same as the desired number of simulations, the average system availability is calculated finally. The average system availability is the result after the last simulation, while the system availability is the result of each simulation. Figure 13 shows the availability of the air compression and nitrogen generation systems depending on the design stages. The availability decreased with the increment of the design stages because the system in the late design stage was more complex than that in the early design stage. A complex system has more factors decreasing the availability of the system than a simple system. The availability is decreased by 0.331% when the design stage was changed from Stage I (PFD) to Stage II (P&ID). This meant that the instrument system occupies 0.331% of the system's availability. When the design stage was transferred from Stage II (P&ID) to Stage III, the availability was decreased by 0.103%. The preventive maintenance influenced about 0.103% of the availability. The availability difference between Stage I and Stage III was 0.434%. It showed that the availability in the early design stage was underestimated compared to the late design stage. The unavailability (1-availability) in the late design stage (0.972%) is approximately 1.8 times severe than that in the early design stage (0.535%). We can predict that the unavailability estimated in the late design stage is 1.8 times serious than that in the early design stage. The availability difference between early and late design stages The predicted time from the generated random number is shown in Equation (3). Figure 13 shows the availability of the air compression and nitrogen generation systems depending on the design stages. The availability decreased with the increment of the design stages because the system in the late design stage was more complex than that in the early design stage. A complex system has more factors decreasing the availability of the system than a simple system. The availability is decreased by 0.331% when the design stage was changed from Stage I (PFD) to Stage II (P&ID). This meant that the instrument system occupies 0.331% of the system's availability. When the design stage was transferred from Stage II (P&ID) to Stage III, the availability was decreased by 0.103%. The preventive maintenance influenced about 0.103% of the availability. The availability difference between Stage I and Stage III was 0.434%. It showed that the availability in the early design stage was underestimated compared to the late design stage. The unavailability (1-availability) in the late design stage (0.972%) is approximately 1.8 times severe than that in the early design stage (0.535%). We can predict that the unavailability estimated in the late design stage is 1.8 times serious than that in the early design stage. The availability difference between early and late design stages can be dissimilar with the target system. However, this result provides meaningful information to guess the actual availability in the early design stage. can be dissimilar with the target system. However, this result provides meaningful information to guess the actual availability in the early design stage.

Sensitivity Analysis
This study performed the sensitivity analysis to investigate the factors affecting the results. It is important to analyze the correlation between the factors and the results because the results can be changed depending on the variation of the factors. In this study, four factors are investigated for the sensitivity analysis: failure rate, repair time, redundant equipment, and modified preventive maintenance schedule. The reliability data used in this study are mainly from OREDA, and its mean value is utilized. The values can be different depending on the target conditions. OREDA predicts the failure rate with 90% confidence interval. The confidence interval describes the amount of

Sensitivity Analysis
This study performed the sensitivity analysis to investigate the factors affecting the results. It is important to analyze the correlation between the factors and the results because the results can be changed depending on the variation of the factors. In this study, four factors are investigated for the sensitivity analysis: failure rate, repair time, redundant equipment, and modified preventive maintenance schedule. The reliability data used in this study are mainly from OREDA, and its mean value is utilized. The values can be different depending on the target conditions. OREDA predicts the failure rate with 90% confidence interval. The confidence interval describes the amount of

Sensitivity Analysis
This study performed the sensitivity analysis to investigate the factors affecting the results. It is important to analyze the correlation between the factors and the results because the results can be changed depending on the variation of the factors. In this study, four factors are investigated for the sensitivity analysis: failure rate, repair time, redundant equipment, and modified preventive maintenance schedule. The reliability data used in this study are mainly from OREDA, and its mean value is utilized. The values can be different depending on the target conditions. OREDA predicts the failure rate with 90% confidence interval. The confidence interval describes the amount of uncertainty associated with a sample of a population. The sensitivity analysis was performed for the lower and upper limits of the failure rates. The repair times utilized in this study were also mostly from OREDA. The employed active repair time considers only the time when actual repair work is being done. It does not contain time to shut down the unit, issue the work order, wait for spare parts, start-up after repair. Some variation exists between the active repair time and the actual downtime. (The reason why OREDA only considers the active repair time is that the required time for the preparation and return to the normal operation are different depending on the location of the installation.) The additional repair time is taken into account. The availabilities with and without redundant equipment are estimated to examine its effect on the availability. Finally, the availability is calculated with different preventive maintenance schedules. Figure 15 indicates the availability depending on the design states with different failure rates: lower, mean, and upper failure rates. As the failure rate was increased from lower to upper, the availability was decreased. In the case of lower and mean failure rates, the availability was slightly decreased with the design stages. In contrast, the availability was significantly reduced in the case of upper failure rate. When the design stage was changed from Stage I (PFD) to Stage II (P&ID), the availability was dramatically decreased in the case of upper failure rate. This indicated that the instrument devices gave a critical impact on the availability. The availabilities are 99.506% (lower) and 97.819% (upper) at Stage III. The upper means that the result is derived using upper failure rate in Table 2, and the lower is the reverse. This meant that the most optimistic availability is 99.506% and the most pessimistic availability is 97.819%.

Lower amd Upper Failure Rates
installation.) The additional repair time is taken into account. The availabilities with and without redundant equipment are estimated to examine its effect on the availability. Finally, the availability is calculated with different preventive maintenance schedules. Figure 15 indicates the availability depending on the design states with different failure rates: lower, mean, and upper failure rates. As the failure rate was increased from lower to upper, the availability was decreased. In the case of lower and mean failure rates, the availability was slightly decreased with the design stages. In contrast, the availability was significantly reduced in the case of upper failure rate. When the design stage was changed from Stage I (PFD) to Stage II (P&ID), the availability was dramatically decreased in the case of upper failure rate. This indicated that the instrument devices gave a critical impact on the availability. The availabilities are 99.506% (lower) and 97.819% (upper) at Stage III. The upper means that the result is derived using upper failure rate in Table 2, and the lower is the reverse. This meant that the most optimistic availability is 99.506% and the most pessimistic availability is 97.819%.  Figure 16 shows the availability depending on the design stages with the additional repair time. Three additional repair times assumed in this study are 1, 3, and 5 h to investigate the impact of the delayed repair time. The availability decreased with the increment of the repair time. When additional 1, 3, and 5 h were considered at Stage III, the availabilities were 98.969%, 98.823%, and 98.701%, respectively. This result presented that one additional hour in the repair time decreased the availability by 0.065%.  Figure 16 shows the availability depending on the design stages with the additional repair time. Three additional repair times assumed in this study are 1, 3, and 5 h to investigate the impact of the delayed repair time. The availability decreased with the increment of the repair time. When additional 1, 3, and 5 h were considered at Stage III, the availabilities were 98.969%, 98.823%, and 98.701%, respectively. This result presented that one additional hour in the repair time decreased the availability by 0.065%.  Figure 17 presents the availability depending on the design stages with the installation of the redundant heater. As mentioned in Section 4.1, the most critical component in the availability was the heater regardless of the design stages. The availability was estimated depending on the installation of the redundant heater or not. The availability was considerably increased when the  Figure 17 presents the availability depending on the design stages with the installation of the redundant heater. As mentioned in Section 4.1, the most critical component in the availability was the heater regardless of the design stages. The availability was estimated depending on the installation of the redundant heater or not. The availability was considerably increased when the redundant heater is installed. The availability is 99.028% without the redundant heater at Stage III, whereas it is 99.514% with the redundant heater. That is, the redundant heater increased the availability by 0.486%. Although 0.486% availability seems to be low, it is not a negligible value in the system (LNG-FPSO).  Figure 17 presents the availability depending on the design stages with the installation of the redundant heater. As mentioned in Section 4.1, the most critical component in the availability was the heater regardless of the design stages. The availability was estimated depending on the installation of the redundant heater or not. The availability was considerably increased when the redundant heater is installed. The availability is 99.028% without the redundant heater at Stage III, whereas it is 99.514% with the redundant heater. That is, the redundant heater increased the availability by 0.486%. Although 0.486% availability seems to be low, it is not a negligible value in the system (LNG-FPSO).   Figure 18 shows the availability depending on the design stages with the modified preventive maintenance. As mentioned in Section 3, the preventive maintenance is conducted to prevent the critical failures. There are various activities for the preventive maintenance as indicated in Table 3. These activities are individually conducted depending on their inherent periodic. When the activities have different schedule, some activities can be merged to increase the availability. Although simultaneous preventive maintenance increases the availability, it requires new engineers to conduct the activities at the same time. Since all components have the same preventive maintenance schedule, different schedules were assumed in the modified schedule. The result showed that the availability was decreased by 0.076% through the modified preventive maintenance schedule. Since the preventive maintenance was not considered at Stages I and II, the values at those stages were unchanged.  Figure 18 shows the availability depending on the design stages with the modified preventive maintenance. As mentioned in Section 3, the preventive maintenance is conducted to prevent the critical failures. There are various activities for the preventive maintenance as indicated in Table 3. These activities are individually conducted depending on their inherent periodic. When the activities have different schedule, some activities can be merged to increase the availability. Although simultaneous preventive maintenance increases the availability, it requires new engineers to conduct the activities at the same time. Since all components have the same preventive maintenance schedule, different schedules were assumed in the modified schedule. The result showed that the availability was decreased by 0.076% through the modified preventive maintenance schedule. Since the preventive maintenance was not considered at Stages I and II, the values at those stages were unchanged.

Conclusions
This study estimated the availability of air and nitrogen systems depending on the design stages to analyze the gap between early and late design stages. Three design stages were considered: Stages I-III. Stage I was the process flow diagram (PFD) stage and Stage II was the piping and instrument