Integrating Fuzzy FMEA and RAM Analysis for Evaluating Modernization Strategies in an LNG Plant Pumping and Vaporization Facility

Abstract

In today’s competitive industrial landscape, Reliability Engineering plays a vital role in minimizing costs and expenses in energy projects. The main focus of this paper is to propose the integration of a fuzzy-based FMECA process into a RAM analysis to assess modernization and reconfiguration strategies for LNG facilities. This approach estimates, through a systematic procedure, the system’s failure probabilities and gauges the impact of various maintenance and topological modification initiatives on the asset and the system’s availability as a driver of profitability. A methodology based on fuzzy-FMEA is proposed to collect and process imprecise data about reliability and maintainability of the components of the facility. Furthermore, Monte Carlo-based RAM experiments are performed. The selection of parameters for conducting Monte Carlo experiments is done after the defuzzification of MTBF and MTTR values defined in the FMEA stage. The proposed procedure allows for the prediction of the system’s reliability across hypothetical scenarios, incorporating design tweaks and potential improvements. As a case study, the proposed was applied to a Pumping and Vaporization facility in a Chilean LNG plant. Sensitivity analysis was performed on critical elements, leading to an optimization strategy for key components like Open Rack Vaporizers (ORV) and Submerged Combustion Vaporizers (SCV). The anticipated availability rate was found to be 99.95% over an 8760 h operating period. Final conclusions and managerial insights are discussed.

1. Introduction

As the global community pursues total decarbonization, the prominence of natural gas grows, owing to its minimal carbon emissions and vast reserves. However, such supply must be supported by industrial facilities and physical assets with high levels of reliability and availability. Given the relevance of operational continuity in LNG plants, several papers reveal the need to keep reliability parameters under control. According to the work of Arumuggam et al. [1], rigorous, adequate, and integrated maintenance approaches are essential to keep equipment running smoothly. Reliability indicates the probability that an asset or system will operate without failures, fulfilling its intended purpose regarding a given level of confidence. According to Kececioglu [2], reliability is considered as the best measure of the integrity of a system. He further notes that, “No industry in any country can progress effectively without the knowledge and implementation of reliability engineering” [2]. Therefore, reliability analysis is considered a critical aspect in the design and operation of Natural Gas Liquefaction (LNG) plants, and it plays a crucial role in ensuring safety and the efficient operation of these types of facilities [3]. It helps to evaluate the ability of plant assets and systems to perform their intended functions and the likelihood of failures or unplanned shutdowns. In addition, reliability analysis can be used to improve design and optimize maintenance strategies. As Calixto (2019) states, “RAM analysis is the basis for complex system performance analysis. To demonstrate such a methodology, the RAM analysis steps, such as scope definition, lifetime data analysis, modeling, simulation, critical analysis, sensitivity analysis, and conclusions, will be discussed” [4]. The proposed approach allows for the implementation of RAM analysis based on incomplete information and fuzzy modeling, which we believe adds value to our proposal. It is important to note that reliability analysis is an ongoing process that needs to be repeated regularly to keep up with changes in plant design and operating conditions, ensuring that the plant continues to operate at maximum efficiency and reliability. One of the most widely used tools to ensure reliability in LNG plants is Reliability Centered Maintenance (RCM), through the identification of critical components and their failure modes and critical effects [5]. RAM analysis is a term that refers to Reliability, Availability and Maintainability analysis [6,7]. It is a technique widely used in engineering, especially in the field of system design, to evaluate the parameters in a given system. RAM analysis involves assessing those three factors in order to identify and mitigate potential issues that could impact the performance of a system or a physical asset [8]. As systems become increasingly complex, it is more difficult to compute or estimate reliability, maintainability, and availability parameters in an analytical manner [9]. As computers have advanced in processing speed and memory capacity, the use of Monte Carlo methods has expanded and gained acceptance among maintenance practitioners and researchers. Some cases of Monte Carlo experiments applied in maintenance and reliability analysis can be found in [10,11]. However, various steps in the application of RAM analysis are based on semi-quantitative information, incomplete data, or estimates derived from manuals. To address the challenges associated with semi-quantitative information, incomplete data, or estimates derived from expert judgements, this work is intended to propose a novel procedure based on a Fuzzy-FMEA integrated into a RAM analysis framework to analyze and optimize the structure, operation, and maintenance of an engineered system. In addition, the proposed framework aims to address uncertainty by incorporating Monte Carlo simulation experiments.

Subsequent sections of this paper are in Section 2; the literature background is discussed. Next, in Section 3, the proposed methodology is described. In Section 4, a case study based on an actual LNG plant located in central Chile is presented to validate the proposal. That section presents a set of three optimization experiments to demonstrate the usefulness of the proposed methodology. Finally, conclusions, limitations and additional research directions are discussed in Section 5.

2. Literature Background

RAM analysis is a term that refers to Reliability, Availability, and Maintainability analysis [12]. It is a technique widely used in engineering, especially in the field of system design, to evaluate the parameters in a given system. RAM analysis involves assessing those three factors in order to identify and mitigate potential issues that could impact the performance of a system or a physical asset [13]. As commented above, the use of Monte Carlo methods has expanded and gained acceptance among maintenance practitioners and researchers. Some cases of Monte Carlo experiments applied in maintenance and reliability analysis can be found in [14,15,16]. Several RAM models can be used during the design phase to optimize or modify system configuration, or during the operational phase to identify areas for improvement or assign resources to preventive maintenance or take other actions, such as decommissioning or dismantling part of or an entire system.

RAM analysis usually involves the following steps [17]: identifying critical components, establishing failure modes and consequences, the assessment of reliability of each component, and the overall reliability of the plant. Once these steps have been conducted through mathematical models and simulations, the optimization may take place. Therefore, results from those stages can be used to optimize the design and maintenance strategies of plants, minimizing downtime and improving overall reliability.

Most of the time, RAM analysis is preceded by an FMECA-type analysis; that is, the main failure modes and their effects are mapped and analyzed [18]. Based on this identification, the levels of criticality and the corresponding priorities are defined. Frequently, this analysis is performed using the failure records of the system. However, in many cases, this analysis is based on subjective values or simple estimates of mean time between failures (MTBF) and mean time to repair (MTTR) using approximations or ranges of values.

Accurately determining the probability of failures is often challenging, as many evaluations are based on non-existent or incomplete information, or are expressed in qualitative terms such as “probable” or “very high”, among others [19]. Additionally, components and systems typically degrade over time, introducing multiple states that are difficult to objectively assess using traditional FMEA. Furthermore, conventional FMEA heavily relies on the diversity and expertise of the team of specialists, who may not always be available. Moreover, the sharing of experiences among various industrial practitioners is complex, thereby limiting the broader application of FMEA.

In the last decade, numerous efforts have been made to enhance the performance of FMEA. Approaches have been proposed to express interdependencies between causes and effects, and a method for causal reasoning using the FMEA language has been developed. Recently, techniques employing membership functions to describe the characteristics of a component or asset in fuzzy terms have been introduced. Additionally, methods based on max–min inference and defuzzification have been applied in criticality analysis. Other techniques rely on probability distribution theories to address uncertainties and the existence of multiple failure modes. The gas industry is no exception to these considerations. Criticalities are high, and many installations operate under demanding conditions and with very high utilization levels.

The study by Sesini et al. [5] highlights the need for further research on the reliability and value of gas storage to enhance energy security. Ismail, F.B., et al. [20] analyze the role of operational factors in an LNG plant, such as plant design and equipment performance, in determining the effectiveness of maintenance activities. They also investigate the impact of manpower management strategies, such as training and staffing, on maintenance effectiveness, along with exploring different approaches to control and optimize maintenance productivity, such as process improvement, performance metrics, and resource allocation. In Pereira et al. [14], multiple flow-control valve-stem packing failures in an LNG plant are investigated. Through a root cause analysis (RCA), they analyzed historical failures’ data series and maintenance records. The work of Wakman and Sudiarto [15] presents a reliability analysis of the emergency switching system of an LNG plant comparing the existing configuration and the proposed new configuration. The analysis uses software modeling based on a fault-tree diagram. The proposed design concept improves the reliability of the emergency system by reducing unavailability. Pereira et al. [14] present a case study where the failure of the primary seals of the swing joint (SW) of the loading arms is studied. The incident of loading-arm primary seals deformation is critically evaluated using the RCA to identify the failure and determine the maintenance needs for the LNG ship-to-ship loading reliability improvement procedure. The main conclusion of that work, based on a cost analysis of the seal failure replacement with dual redundancy, is a modification in the facility design.

In the paper by Rahmadhanty et al. [17], the functions, causes, and effects are pinpointed, and the updated maintenance tasks are defined. In the same line, and aiming at the efficiency of maintenance operations, the paper seeks to identify the most influential factors that impact the Wrench Time (WT) of labor productivity, identifying causes to achieve a clear vision of how management can allocate the necessary resources to eliminate such impacts. Random sampling of field observations was used for this purpose. For data collection, the Day in Life Of (DILO) approach was used as an observation method involving the supervisor’s participation with the technicians throughout the workday. To validate the methodology, a case study was conducted based on one of the largest LNG plants in the Middle East.

Risk analysis is also an important aspect in the operation of LNG plants [19]. Despite this, the body of work on risk-analysis model classifications for LNG facilities is notably sparse [19]. Animah and Shafiee [21] conducted a systematic review of the current state of the literature on LNG risk analysis with the aim of mapping the risk analysis of LNG installations. The major contribution of this work aims to help regulators, policy makers and LNG facility operators to Identify the risk analysis models that align with their specific needs. Viana et al. [22] propose a decision model to select a set of risk-based maintenance actions in gas pipelines. The model focuses on sustainability aspects, oriented towards the Triple Bottom Line approach (environmental, economic, and human). Additionally, the model integrates the multicriteria PROMETHEE method to select the maintenance actions. Gonzalez-Prida et al. [23] also use a multicriteria method (AHP) to aid in defining the best maintenance strategy. Furthermore, as a way to reduce the effects of subjectivity in the aforementioned method, it is complemented with the execution of Monte Carlo experiments. Finally, the feasibility of the proposed framework was assessed by examining a well-control system in an actual oilfield [24]. The article by Yu, W.C., et al. [25] proposes a methodology to evaluate the gas supply reliability of natural gas transmission pipeline systems. Using Monte Carlo experiments, an indicator quantifying gas supply reliability is obtained. Finally, in a case study focused on an actual gas transmission pipeline system, the average gas supply reliability is obtained. In addition, the effects of uncertainties in supply capacity and market demand on gas supply reliability are examined. In addition, recommendations for enhancing gas supply dependability are put forward. Other computational tools and methods have been developed to facilitate the reliability calculation of a complex system, as is the case of the UltraSAN software of the University of Illinois (1995), which uses the Monte Carlo technique and has been reported by Gedam and Beaudet [26] as a highly sophisticated simulation modeling tool.

New trends in data processing have also begun to be used in the analysis of LNG facilities. The article by Yu, W.C., et al. [25] develops a data-driven methodology for reliability analysis of natural gas compressor units. The study focuses mainly on historical failure data (catastrophic and degradation) as well as performance data. The techniques used are regression models and support vector machines. Based on this, the reliability of the compressor unit is assessed and forecasted by combining the reliability functions of both catastrophic and degradation failures. Moreover, the formulated approach is tested on a real compressor unit to validate its practicality, and the unit’s reliability is then estimated. The evaluation results highlight the influence of operating conditions on the precise prediction of performance operational parameters.

The economic dimension is not less important in such analyses [27]. In this respect, it is strongly related to the aspect of reliability and quality assurance in LNG plants. In Orme and Venturini [28], the application of a risk-assessment methodology is presented which provides information on the use of risk indicators such as PML (Probable Maximum Loss) and MFL (Maximum Foreseeable Loss). Based on both technical literature and operational data extracted from a typical large natural gas liquefaction facility, the common sources of risk are considered. The result of that work constitutes a good approximation of the economic loss derived from the risk in two hypothetical natural gas liquefaction plants. Additionally, the life-cycle costs analysis of LNG facilities and assets allows the characterization of the behavior of costs over the useful life including aspects such as asset’s health, reliability, and systemic availability (Durán et al. [29]).

A recent trend in the gas industry is the use of artificial intelligence tools integrating cloud, big data, internet of things, computer simulation, and information security, which will become a reliable technical support to the process of operation, optimization, and continuous improvement in the plants for obtaining and processing gas [30]. Thus, AI tools have been incorporated into the decision-making process in LNG plants, such as the work of Hameed, A., et al. [31], which strives to formulate a tool to assist decision-makers in risk-oriented maintenance scheduling within an LNG sweetening facility. The tool considers two competing objectives: total maintenance cost and reliability. The model is developed by integrating a genetic algorithm and simulation-based optimization to find the optimal maintenance schedules. In the article by Gabbar, H.A. [32], a technique based on semantic fault networks (FSN) is used. Through the use of previously mentioned techniques, a forecasting algorithm to pinpoint and estimate safety measures for each operation step and process was developed. Then, the proposed solution was validated using a process-state approach regarding events that may stop operation in LNG plants. As can be seen, computational tools are emerging to support decision-making processes in LNG plants and their maintenance [33].

3. Proposed Methodology

This proposed work was developed using two primary data sources. First, historical data was utilized to approximate failure frequency and probability distributions. Second, severity and detection criteria were assessed by industry experts. In certain instances, the OREDA handbook served as a foundational reference. By integrating these diverse data sources with the effectiveness of a fuzzy approach, the study easily addresses uncertainty and imprecision in failure and repair data, delivering a more robust and reliable evaluation [34].

Regarding the choice of triangular fuzzy numbers, this was motivated by their ability to efficiently handle imprecision and uncertainty in system parameters [35]. Triangular fuzzy numbers were selected for their simplicity in modeling vague or incomplete data, making them particularly useful in environments where exact failure and repair data are not always available. Although other fuzzy number types exist, such as trapezoidal or Gaussian fuzzy numbers, triangular fuzzy numbers offer a practical balance between computational simplicity and adequate representation of uncertainty [36].

A procedure is proposed that employs fuzzy terms to complement an FMECA analysis, thereby facilitating the use of imprecise or incomplete information regarding the reliability and maintainability values of the identified failure modes. The methodology proposed in this paper is illustrated in the diagram shown in Figure 1. This figure will provide the reader with a comprehensive understanding of the proposed methodology and the sequence of analysis. Additionally, the following paragraphs elaborate on the elements that constitute the methodological development, which contribute to the objectives outlined for this study.

The diagram depicted in Figure 1 shows the methodological proposal. At the first stage, the operation and system’s taxonomy are described. The information is obtained for each piece of equipment, and their corresponding drawings and additional technical information regarding the assets are compiled. With this, a descriptive scheme of the stages of the operational process is made. Once the functional and topological relationships between the system components have been identified and mapped, the Reliability Block Diagram (RBD) is drawn up, where each of the subsystems is established according to its given logical configuration (series, parallel, redundancy, etc.) [37].

An RBD constitutes a graphical representation for assessing the reliability of a system [38]. It shows the logical connections of the components involved in the system which are necessary for the success of the system. Since it represents the logical relationships necessary for the operation of the system, an RBD does not necessarily represent how the elements are physically connected in the system, although this is considered as far as possible (European Committee for Electrotechnical Standardization, 2006). In addition, such diagrams incorporate the behavior of the reliability and maintainability of each piece of equipment through the values of the Mean Time Between Failures (MTBF) and Mean Time to Repair (MTTR). This constitutes the basis for the quantification of the influence of each piece of equipment and subsystem on the reliability and availability at a systemic level thanks to the so-called RAM (Reliability, Availability, and Maintainability) analysis [39].

Subsequently, the use of a fuzzy logic-based FMEA approach is proposed [40,41], which extends the criticality analysis method to FMEA and constructs a fuzzy evaluation system to generate inputs for the RAM analysis experiments. This methodological stage will be analyzed in detail in the following section. Fuzzy logic allows for handling imprecise data and does not assume complete independence of the combined evidence or ideas, facilitating the qualitative evaluation of the relationships between failure modes and their effects. The incorporation of fuzzy logic allows for the handling of information recorded in natural language and built upon the expertise of professionals [34,42]. It also facilitates the treatment of multiple states of components and systems and the combination of qualitative assessments in a natural and coherent manner. The next step is to select the critical equipment in the system under analysis. This stage is mainly based on FMEA results. Critical equipment should be considered as that which causes the plant to stop in the event of a failure, as well as that which forms an essential part of the plant’s operation. In conjunction with this selection criterion, alternatively, for each piece of equipment, the failure mode or modes that produce the longest recovery times to its nominal operating state (critical failure mode) are prioritized.

Bearing in mind the previous steps, a series of Monte Carlo simulation experiments are executed with the objective of obtaining probabilistic distributions to represent the behavior corresponding to reliability, maintainability, and availability of each one of the assets. For this purpose, the data previously extracted from the FMECA report and the incident log are considered, and the most representative probability distributions for each system element are analyzed.

The analysis of reliability and risk prioritization in industrial systems is essential for enhancing efficiency and minimizing failures. In their article, Sharma and Gupta (2023) present an integrated approach combining fuzzy FMECA and AHP for risk prioritization in vertical mills, highlighting the accuracy in assessing critical failures [42]. Similarly, Kumar et al. (2024) employ a comparable method to evaluate failures in mining trucks, demonstrating that the fuzzy approach effectively manages uncertainty and ambiguity better than traditional methods [43]. Collectively, these studies underscore the necessity of adopting innovative, data-driven approaches for risk management and reliability optimization across various industrial applications [4,41,42,43,44].

3.1. Fuzzy Logic Principles

This section presents the fundamental definitions and principles of fuzzy logic, in contrast to “crisp” sets. The latter are defined by strict membership criteria, where an element either fully belongs to a set or does not. In contrast, fuzzy logic allows the value of a variable to be described through degrees of membership to a concept, using a continuous scale from 0 to 1.

There are various types of membership functions, including triangular, trapezoidal, gamma, and rectangular, among others. Triangular Membership Functions (TMF) are particularly popular due to their simplicity and effectiveness in modeling imprecise data. For instance, TMFs are well-suited for representing vague or incomplete information. A typical example is describing a mean time to repair as “approximately 1.5 h” or “somewhere between 1 and 2 h”, where exact precision is either unavailable or unnecessary.

Triangular fuzzy numbers are defined by three values: (m₁, m₂, m₃). Along with their respective α-cuts, this variable is expressed as M_α = [m₁(α), m₃(α)]. TMFs not only capture the behavior of various system parameters but also accurately reflect data dispersion. This dispersion accounts for both the inherent variations of any process and the vagueness of the system. As a result, the decision-making process becomes more intuitive for engineers, even when dealing with imperfect information.

Imprecisely defined events are often described using linguistic terms such as “low”, “very low”, “high”, or “very high”. These linguistic variables are employed to model and understand such events by leveraging fuzzy membership functions. In the context of this study, terms like low, medium, high, and very high are used to characterize the probability of occurrence or frequency of a given failure mode, its severity, and, consequently, the associated level of difficulty or ease in its recovery or repair. These linguistic terms are integral to expressing the expert knowledge underlying the decision-making process, forming the basis of what is known as a fuzzy inference system.

Fuzzy inference systems derive output fuzzy sets based on rules (combinations) and input variables, often expressed in an “If–Then” format: “If x is Mi, then y is Ni”, where xx is the input linguistic variable, Mi represents antecedent linguistic constants, y is the output linguistic variable, and Ni refers to consequent linguistic constants. The two most common types of inference methods are the max–min inference method (Mamdani implication) and the max–prod inference method (Larsen implication). In this study, the Mamdani max–min inference method is used.

To make decisions regarding RAM analysis experiments, the fuzzy outputs must be converted into crisp values. This requires a defuzzification process. Several defuzzification techniques exist, such as the centroid, bisector, middle of maximum, and weighted-average methods. The most used method is the centroid method, due to its computational simplicity and plausible results. This process is represented as follows:

$$Defuzzyfied Value={\displaystyle \frac{\int y \cdot m_{B0}\left(y\right) dy}{\int m_{B0}\left(y\right) dy}}$$

3.2. Fuzzy FMEA Implementation

Once the main elements of a system have been identified, an FMEA analysis is performed. For this purpose, a simplified variant of FMEA is proposed. The objective of this phase is to characterize the criticality of each previously identified failure mode by obtaining MTBF and MTTR values. Through the Fuzzy FMEA process, critical failure modes will be identified by determining the RPN (Risk Priority Number) derived from the fuzzy inference process, which is explained in the following paragraphs.

To conduct Monte Carlo experiments during RAM experiments, it is essential to select parameters that reflect the ambiguity of MTBF and MTTR values, which are usually defined in the FMEA stage. In the absence of detailed probabilistic functions that explain the behavior of these parameters, this is achieved through estimation based on expert judgment, which derives the distribution parameters that capture, according to their assessment, the inherent variability. Furthermore, the FMEA likelihood ratings can be used to define MTBF ranges, such as when a failure is rated as “likely within a year”, which indicates a lower MTBF compared to a “rare” failure. This approach allows for a more accurate representation of the uncertainty in simulation parameters.

The structure of the format for the FMEA analysis is shown in Figure 2.

The table contains the following headers and their respective descriptions:

Equipment: The name of the equipment or component being evaluated.

Tag No.: The tag number or identification of the specific equipment.

Arrangement: The type of arrangement or configuration of the equipment.

Failure Mode Description: The description of the failure mode that may occur in the equipment.

FMEA Workshop—2011: Information obtained from the FMEA workshop in 2011, including the values of MTTF (Mean Time To Failure) and MTTR (Mean Time To Repair) in years and hours respectively, along with their minimum and maximum values.

FMEA GNLQ Review 2011: Data from the FMEA GNLQ review in 2011, including the values of MTTF and MTTR with their minimum and maximum values.

FMEA Workshop—2014: Information obtained from the FMEA workshop in 2014, including the values of MTTF and MTTR in years and hours respectively, along with their minimum, median, and maximum values.

Data Source and Comments (2014): Data sources and relevant comments from 2014 that provide additional context or clarifications about the presented data.

In this structure, the relevant information about the FMEA (Failure Modes and Effects Analysis) for different components and their failure modes is captured, facilitating the evaluation of the reliability and maintainability of the equipment. The MTTF and MTTR values are recorded using the triangular fuzzy numbers approach. This method facilitates the collection of the data required for the FMEA, allowing for variability throughout the asset lifecycle, as well as accommodating uncertainty or lack of complete knowledge about them. Once these fuzzy numbers are collected, inference rules are applied to generate crisp values for both parameters and an RPN value. This RPN value enables the prioritization of failure modes, which will be selected for further analysis in the RAM stage. These values can then be used as parameters for executing the subsequent RAM analysis.

The RPN (Risk Priority Number) is the fundamental criterion for determining the priorities of failure modes. It is essential to calculate the RPN with precision and clarity. This indicator is determined as the product of three factors: the occurrence, which estimates how often failures may occur; the severity, which assesses the impact of these failures on the system; and the detection, which measures the likelihood of identifying the failure before it occurs. However, this definition is often laden with subjectivity and uncertainty.

For the calculation of the RPN, an adapted process of that suggested by [36] was used. A fuzzy inference model based on rules for determining a fuzzy representation of the RPN was implemented. This approach enables the identification of criticalities and the prioritization of failure modes under analysis. The terms related to the degrees of occurrence, severity, and detectability have been transformed into a fuzzy scale using triangular fuzzy numbers. Additionally, a rule base has been defined to calculate the fuzzy RPN. These rules were implemented using MATALB fuzzy toolbox and are shown in Figure 3.

A graphical representation of the fuzzy rules is shown in Figure 4. Once the key maintenance parameters that reflect the behavior of each piece of equipment within the system have been obtained, probability distribution curves for these parameters are generated based on actual records or estimates. These data enable the RAM analysis through which the analyst can evaluate various scenarios, such as the addition or modification of equipment, changes in behavior due to new strategies, or alterations in system topology. This allows for the measurement of the impact of these modifications on the overall performance of the system.

If improper handling of bias and outliers is detected during the execution of the procedure, a type-2 fuzzy logic approach could eventually be utilized. This method offers a more advanced framework for addressing uncertainties and variations in the data, thereby improving the robustness and accuracy of the results. Type-2 fuzzy logic extends the capabilities of traditional fuzzy logic by incorporating an additional layer of uncertainty, which allows for better handling of imprecise and ambiguous information [43]. This approach has been shown to be effective in various applications, such as improving the reliability of control systems and enhancing the performance of pattern recognition tasks [45]. By using type-2 fuzzy logic, systems can achieve higher levels of accuracy and robustness, particularly in environments where data is noisy or incomplete [46].

In the next section we show the application of the proposed procedure using real data from an LNG plant located in central Chile.

4. Case Study

This section aims to validate the proposed model by developing a case study. This section is divided into concomitant parts with the methodological design described in the previous section.

4.1. System Description

This case study is based on an LNG plant which operates in Central Chile. Figure 5 deploys the main phases of the entire process.

In such plants there are 4 fundamental areas responsible for the operation, among which we can mention:

• Unloading area: This section is where the LNG is unloaded from the ship. This is carried out by means of five arms located on a pier. From here, the unloaded LNG is sent to the storage tanks and to the vaporization and pumping area. In addition, return gases to the methane are sent to the tanker/ship to maintain a pressure balance in the storage tanks. This dock has the capacity to receive ships with LNG storage of up to 265,000 cubic meters.
• Storage area: LNG is pumped to three storage tanks, two of which have a storage capacity of 160 thousand cubic meters each. The third of these tanks has a storage capacity of 14,000 cubic meters of LNG. The total storage capacity of the LNG plant is 334,000 cubic meters.
• Vaporization and pumping zone: in general terms, at this stage the gas in its liquid state is pumped from the storage tanks to the vaporization zone where the LNG is transformed into natural gas. Since this stage is the focus of our case study, both zones will be described in detail below:

  a.

  Pumping Zone: It is composed of five high-pressure pumps which operate in partial redundancy configuration (model K/N: 3/5).

  b.

  Vaporization Zone: It is made up of three open-rack vaporizers (ORV) and one Submerged Combustion Vaporizer (SCV), each contributing 33% of the systemic load arranged according to a K/N:3/4 configuration.

• Tanker truck loading facility: The remaining fraction of LNG that does not pass through the vaporizers goes directly to the truck loading facility which is composed of four independent loading islands that store the LNG in tank trucks. These are responsible for supplying both industries and cities that are not connected to the pipeline network where it is regasified locally.

4.2. Failure Modes and Effects Analysis

The FMEA of the systems and subsystems of the LNG plant has been prepared in order to compile historical data on failures in each of the plant’s system components and subsystems. This aims at defining the criticalities that allow, subsequently, to move forward with the study. It should be noted that this text does not provide historical details, dates, or frequency of failure or repair times. On the other hand, and in order to simplify the study and its description, average values of MTBF and MTTR of each component are provided.

• Critical Process Failure Modes and Critical Equipment Selection

For the purposes of this study, critical equipment are those components whose failures or stoppages could cause or contribute to a decrease in the reliability and availability of the main production line. Among these failure modes and given that certain components have MTBFs that are too long, causing a minimal impact on the RAM analysis, some of them were not considered in this study.

Table 1. Selection of critical failure modes of the process.

Equip.	Tag	Systemic Load	Failure Mode	MTBF (Years)	MTTR (h)
Open Vaporizer ORV	300-E-102 A/B/C	3 × 33%	Short Repair	0.5	8
Closed Vaporizer SCV	300-E-103	1 × 33%	Short Repair	0.5	10
HP Pumps	300-P-102 A/B/C/D/E	5 × 33%	Short Repair	1	28
SW Pumps	400-P-101 A/B/C/D/E	4 × 33%	Spurious Failure	2.5	4
Pipeline Emergency Valves	XZV-03018/3026	2 × 100%	Short Repair	4	4
Gas Measurement Package	300-X-104 A/B/C	3 × 50%	Gas Leak at Flange	5	-

shows the equipment selected and defined as critical.

• Analysis of Vaporization and Pumping Zone Plans

The technical information of the vaporization and pumping zones was analyzed in order to obtain a detailed representation of the process-flow diagram of the plant under study, providing the possibility of constructing the Reliability Block Diagram, as follows.

• Elaboration of Reliability Block Diagram (RBD)

The data obtained from the FMEA, the existing maintenance plans of the pumping and vaporization zones, and the selection of critical equipment within the system with its most frequent failure mode (previous stages) have been taken into consideration for the elaboration of the RBD. Figure 6 shows the RBD diagram of the pumping and vaporization plant.

• System Reliability, Maintainability, and Availability Calculation Procedure

To make all this representation and the calculations necessary to carry out the RAM analysis feasible, a spreadsheet-based calculation platform was developed (supported by specific macros), which constitutes the materiality of the methodology proposed in this work. The procedure adopted and the work it was based on [23] is summarized below.

Once the reliability function R(t) has been obtained for each of the 18 pieces of equipment that make up the system, the reliability of the existing subsystems is calculated. Thus, the formulation applied for the resolution of the reliability calculation of each configuration present in the subsystems (series, K/N and fractionation) is expressed below:

▪

Subsystem 1, HP pumps arranged in K/N configuration: 3/5:

$$R\left(t\right)=K_1+K_2+K_3$$

(1)

where K₁ represents the probability of failure of two pieces of equipment simultaneously among the five total pieces of equipment that make up the system, expressed by the following:

$$K_1=P_{f12}+P_{f13}+P_{f14}+P_{f15}+P_{f23}+P_{f24}+P_{f25}+P_{f34}+P_{f35}+P_{f45}$$

(2)

Taking into consideration the first term:

P_f12: Probability of failure of equipments 1 and 2 simultaneously.

In this way, all the probabilities resulting from Equation (2) are added together for each P_fxy

Where x and y are the numerical designation of the equipment involved for each term corresponding to the probability of failure belonging to Equation (2), by means of the following expressions:

$$P_{f12}=(1-R_1)\cdot (1-R_2){\cdot R}_3\cdot R_4\cdot R_5$$

(3)

$$P_{f13}=(1-R_1)\cdot R_2\cdot (1-R_3)\cdot R_4\cdot R_5$$

(4)

$$P_{f14}=(1-R_1)\cdot R_2\cdot R_3\cdot (1-R_4)\cdot R_5$$

(5)

$$P_{f15}=(1-R_1)\cdot R_2\cdot R_3\cdot R_4\cdot (1-R_5)$$

(6)

$$P_{f23}=R_1\cdot (1-R_2)\cdot (1-R_3)\cdot R_4\cdot R_5$$

(7)

$$P_{f24}=R_1\cdot (1-R_2)\cdot R_3\cdot (1-R_4)\cdot R_5$$

(8)

$$P_{f25}=R_1\cdot (1-R_2)\cdot R_3\cdot R_4\cdot (1-R_5)$$

(9)

$$P_{f34}=R_1\cdot R_2\cdot (1-R_3)\cdot (1-R_4)\cdot R_5$$

(10)

$$P_{f35}=R_1\cdot R_2\cdot (1-R_3)\cdot R_4\cdot (1-R_5)$$

(11)

$$P_{f45}=R_1\cdot R_2\cdot R_3\cdot (1-R_4)\cdot (1-R_5)$$

(12)

Thus, now for the K₂ term, the probability of failure of one piece of equipment among the five total that make up the system is represented as follows:

$$K_2=P_{f1}+P_{f2}+P_{f3}+P_{f4}+P_{f5}$$

(13)

Taking into consideration the first term:

P_f1: Probability of equipment failure 1

In this way, all the probabilities resulting from formula 13 are added together for each P_fx, where x is the numerical designation of the equipment involved for each term corresponding to the probability of failure pertaining to formula 13 by means of the following expressions:

$$P_{f1}=(1-R_1)\cdot R_2\cdot R_3\cdot R_4\cdot R_5$$

(14)

$$P_{f2}=R_1\cdot (1-R_2)\cdot R_3\cdot R_4\cdot R_5$$

(15)

$$P_{f3}=R_1\cdot R_2\cdot (1-R_3)\cdot R_4\cdot R_5$$

(16)

$$P_{f4}=R_1\cdot R_2\cdot R_3\cdot (1-R_4)\cdot R_5$$

(17)

$$P_{f5}=R_1\cdot R_2\cdot R_3\cdot R_4\cdot (1-R_5)$$

(18)

Finally, for the term K₃, we consider the probability of operation of the five pieces of equipment without failure; that is:

$$K_3=R_1\cdot R_2\cdot R_3\cdot R_4\cdot R_5$$

(19)

where:

R_i = R_i(t) = Reliability of Pump HP i at time t

▪

Subsystem 2, SW pumps arranged in a K/N: ¾ configuration:

$$R\left(t\right)=K_1+K_2$$

(20)

where K₁ and K₂ are the probability of one equipment failure and no failure, respectively. Thus, the expressions for K₁ and K₂ are as follows:

$$K_1=P_{f1}+P_{f2}+P_{f3}+P_{f4}$$

(21)

$$K_2=R_1\cdot R_2\cdot R_3\cdot R_4$$

(22)

Developing the terms of K₁, we have the following:

$$P_{f1}=(1-R_1)\cdot R_2\cdot R_3\cdot R_4$$

(23)

$$P_{f2}=R_1\cdot (1-R_2)\cdot R_3\cdot R_4$$

(24)

$$P_{f3}=R_1\cdot R_2\cdot (1-R_3)\cdot R_4$$

(25)

$$P_{f4}=R_1\cdot R_2\cdot R_3\cdot (1-R_4)$$

(26)

where:

R_i = R_i(t) = Reliability of SW Pump i at time t.

▪

Subsystem 3, ORV and SCV vaporizers arranged as a shared-load based redundancy configuration with 33% of load sharing fraction:

$$R\left(t\right)=I\cdot {\sum }_{i=1}^4{R}_i(t)+(1-4I)\cdot {\prod }_{i=1}^4{R}_i\left(t\right)$$

(27)

▪

Subsystem 4, GM gas meters arranged in a K/N: 2/3 configuration:

$$R\left(t\right)=K_1+K_2$$

(28)

where K₁ and K₂ are the probability of one equipment failure and no failure, respectively. Thus, the expressions for K₁ and K₂ are as follows:

$$K_1=P_{f1}+P_{f2}+P_{f3}$$

(29)

$$K_2=R_1\cdot R_2\cdot R_3$$

(30)

Developing the terms of K₁, we have:

$$P_{f1}=(1-R_1)\cdot R_2\cdot R_3$$

(31)

$$P_{f2}=R_1\cdot (1-R_2)\cdot R_3$$

(32)

$$P_{f3}=R_1\cdot R_2\cdot (1-R_3)$$

(33)

▪

Subsystem 5 Pipeline Emergency Valves

$${R\left(t\right)}_{S5}={R\left(t\right)}_{V1}\cdot {R\left(t\right)}_{V2}$$

(34)

The RBD initially proposed in Figure 7 is simplified to an equivalent system with a series configuration composed of the aforementioned five subsystems, resulting in the RBD shown below:

By means of the reliability calculation for a series system applied to the subsystems of the equivalent RBD shown above, the system reliability is depicted in Figure 8.

A drastic drop in reliability can be seen after approximately 3500 h. This is mainly due to the influence of the ORV and SCV vaporizers, which present an average of two failures per year, influencing or conditioning the drop in system reliability. For the simulation of maintainability, we have chosen to use the negative exponential probabilistic function, which consists of a single parameter µ that is equivalent to the inverse value of the MTTR obtained from the data provided by the FMEA.

• Approximation to estimate availability

Elsayed (2021) defines system availability as the ability of a system to be operating properly when it is required for use [47]. In this work, a tool capable of predicting the availability of the system according to a mission time is developed. According to Elsayed [47], it becomes complex to obtain the resulting mathematical expressions, so, the use of approximations or numerical solutions becomes the only alternative to obtain the A(t). One of the approximations developed by [36] was used to estimate A(t), which is based on the alternate renewal process, resulting in the equation presented below:

$$\overline{A}\left(t\right)={\displaystyle \frac{\lambda \left(t\right)}{\lambda \left(t\right)+\mu }}$$

(35)

where:

▪

$\overline{A}(t)$: Unavailability.

▪

t: Time.

▪

$\lambda \left(t\right)$: Failure rate at time t.

▪

$\mu$: Reparation rate (constant).

Which can be developed in the same way as shown in the following expression:

$$A\left(t\right)={\displaystyle \frac{\mu }{\lambda \left(t\right)+\mu }}$$

(36)

where:

▪

$A\left(t\right)$: Availability at time t.

This approximation is valid when the failure rate or repair rate is time-dependent and when the value of λ is much smaller than the value of µ, as is the case for each of the LNG system components described in the FMEA. Further details of the development of the resulting approximation given in Equation (36) can be found [36].

• Numerically obtained Availability A(t)

As previously mentioned, sometimes the use of approximations or numerical solutions becomes the only alternative to obtain A(t). Figure 9 depicts an extract of the results of A(t) for the case of Pump HP1.

Once the values of A(t) are obtained for each of the 18 pieces of equipment that make up the system, the availability of the existing subsystems is calculated using the formulation previously mentioned, considering that such equation is valid if the λ and µ are independent of each other. Then, with the values of A(t) for each subsystem, the system availability is calculated considering a serial configuration, as shown in Figure 7.

4.3. Optimization Experiments

Three experiments, considering three different scenarios, were put forward to demonstrate the applicability and feasibility of the proposed platform. With these experiments, the goal was to detect and measure the system’s availability behavior, concerning modifications in the system configuration or technology level within specific critical equipment. Such modifications were represented in the experiments by varying the frequency and timeliness of preventive interventions in critical assets and their effect on system reliability.

4.3.1. ORV Flow Measurement Technology Substitution

The proper operation of ORV vaporizers depends mostly on the flow of seawater entering the vaporizer. The function of the seawater is to carry out the work involved in the transformation of LNG into NG by means of a heat transfer process. In case of low seawater flow, the equipment is automatically protected and it stops. This causes the intermittent operation of the ORV vaporizers, a cause that is associated with the device that performs the flow measurement.

Data extracted from the FMEA shows that those events have a failure frequency in the ORVs equal to two events per year. The hypothesis is that by applying a change in the measurement technology, a drop in the failure frequency by half will be obtained (one event per year). For calculation purposes, the average time to failure value, µ, corresponds to 8760 h. Taking into consideration this improvement, and after applying the new value of µ to the simulation model, the frequency histogram and the reliability graphs were obtained (Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14).

4.3.2. Implementation of Retractable System for SCV Ignitors

One of the most frequent failure modes in the submerged combustion vaporizer (SCV) is due to failures of the ignitors. The cause of this problem is that when the ignition process is initiated, the ignitor gets wet due to the water present in the equipment, thus preventing the vaporizer from starting up. For this reason, the company proposed the implementation of a retractable system for the ignitor so that it enters the combustion area, generates the ignition, and then retracts. This protects the ignitor from problems related to the humidity present in the equipment and/or environment.

Therefore, after applying the retractable system in the LCS Ignitors, a decrease by half in the failure frequency is expected. This is equivalent to one failure per year. Thus, time to failure (µ) takes the value of 8760 h. Taking this improvement into consideration, and after applying the new value of “µ” in the simulation framework, the frequency histogram, reliability graph, and system availability were obtained and are shown in Figure 15, Figure 16 and Figure 17:

4.3.3. Improvements in Pipeline Emergency Valves

Another improvement that the company wished to test was the replacements of the actuators with the valve open. This replacement will facilitate the installation of a new actuator. In addition, the replacement of actuators is proposed, together with the installation of supports to avoid bending due to the weight of the component. With these improvements, the failures that affect the Pipeline Emergency Valves will tend to zero. A time of 10 years between failures is considered, and with this value, the new failure histogram is calculated. It is worth mentioning that as an analysis considering one year of simulation, the results will not largely affect the reliability and availability of the system.

For calculation purposes, this is reflected in the change of the average failure value “µ”, which takes the value of 87,600 h. Taking this improvement into consideration, and after applying the new value of “µ” in the Monte Carlo simulator, the frequency histogram and the reliability graph were obtained (Figure 18, Figure 19, Figure 20 and Figure 21).

For comparison purposes, the following

Table 2. Comparison of reliabilities between sensitivity studies conducted.

Reliability R (t)	Sensitivity Analysis #1	Sensitivity Analysis #2	Sensitivity Analysis #3
R (t = 1500 h)	100%	100%	100%
R (t = 3000 h)	99.9%	99.5%	99.2%
R (t = 4500 h)	99.0%	74.2%	57.7%
R (t = 6000 h)	93.2%	34.3%	4.3%
R (t = 7500 h)	68.4%	23.2%	0%
R (t = 8760 h)	24.7%	8.4%	0%

and

Table 3. Comparison of availabilities between sensitivity studies conducted.

Availability A (t)	Sensitivity Analysis #1	Sensitivity Analysis #2	Sensitivity Analysis #3
A (t = 1500 h)	100%	100%	100%
A (t = 3000 h)	100%	100%	100%
A (t = 4500 h)	100%	100%	100%
A (t = 6000 h)	100%	99.93%	99.87%
A (t = 7500 h)	99.97%	99.81%	99.72%
A (t = 8760 h)	99.94%	99.78%	99.61%

show reliability and availability values obtained for each experiment:

Taking into consideration the results of the sensitivity studies, through Monte Carlo experiments, it is demonstrated that the components with the greatest influence in terms of reliability and availability results are the ORV and SCV vaporizers. When applying the proposed improvement, the change of flow measurement system, it is estimated, through this tool, to have a reliability of 24.7% and an availability of 99.95% for the total time of 8760 h. This indicates that, in the case of suggesting and implementing an improvement in the plant based on the results obtained here, the most convenient improvement would be to maintain the focus on the vaporizers.

The proposed case study where sensitivity analysis and a series of Monte Carlo simulations within the computational framework were performed allows the managers to effectively evaluate the impact on system-level reliability. By representing the outcomes as probabilistic distributions, this approach enables decision-makers to gain a clear understanding of the contributions of each design improvement and the system topology to the overall reliability of the system.

5. Conclusions and Future Work

In this paper, a procedure for analyzing and optimizing a liquid natural gas vaporization system has been presented. This procedure is driven by an FMECA process that employs fuzzy numbers, enabling the management of imprecise and incomplete data regarding the performance parameters of each component in the system. This approach facilitates the identification of criticalities, which will inform the subsequent simulation experiments. Such an analysis-simulation tool based on the Reliability Block Diagram and Monte Carlo methodology allows the user to establish a series of scenarios to optimize some decision-making processes.

The integration of techniques such as fuzzy logic into FMECA analysis represents a breakthrough in reducing the gaps caused by poor-quality failure data. Fuzzy logic can reduce uncertainty, unlike the traditional approach that relies heavily on the accuracy of maintenance and operational activity records. This approach is particularly relevant in environments where data quality varies. It enables a more robust estimation of failure modes and their critical effects on the system, improving decision making and the reliability of physical assets.

The model serves as a decision-making instrument for managers. It assists in understanding the interconnections between maintenance and operational strategies, diverse system topologies, and views on disruptive events within sophisticated engineering systems. In addition, the defined model will serve as a simulation-based optimization tool, addressing real-world challenges and facilitating sensitivity evaluations. The primary challenges of this project are utilizing the proposed model to gauge system resilience behavior and derive optimized decisions for operations, maintenance, and structure. Therefore, availability, reliability, and maintainability metrics and uncertainty are pivotal factors of this research. No previous works have been devoted to the tentative mapping of the effects of different strategies on the availability of physical assets and systems in this type of facility.

The accuracy of parameter selection significantly impacts the reliability of Monte Carlo experimental results and RAM (Reliability, Availability, Maintainability) analysis. Accurate parameters ensure that the simulations and analyses reflect real-world conditions more closely, leading to more reliable and valid results. Conversely, inaccurate parameters can lead to misleading outcomes, compromising the integrity of the analysis and potentially resulting in poor decision-making.

Compared to previous works in the field of RAM analysis for LNG facilities, our study differentiates itself by integrating fuzzy FMEA to better handle imprecise failure and repair data, which are common in industrial environments. This fuzzy approach provides a novel way to quantify uncertainty in reliability assessments. Practically, the implementation of this methodology in an actual LNG facility demonstrates its effectiveness in optimizing system availability, particularly through targeted improvements in critical components like ORVs and SCVs. Our findings offer both theoretical advancements in the use of fuzzy logic in reliability assessments and practical insights for maintenance decision-making in complex systems [38,39].

As future projects, the multi-period modeling and multi-objective optimization will be addressed. A multi-objective decision problem is where trade-offs among maintenance and operational priorities must be considered and resolved. In addition, a multi-period approach will be incorporated into the model to portray the effects of decisions taken over the life cycle of the system.