Decision Framework for Asset Criticality and Maintenance Planning in Complex Systems: An Offshore Corrosion Management Case

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A decision support system for optimizing maintenance portfolio selection in offshore oil and gas assets through integrating Reliability-Centered Maintenance principles, fuzzy logic-enhanced FMEA, group Analytical Hierarchy Process with expert systems, and mixed-integer programming optimization considering asset criticality, uncertainty modelling, and risk-informed cost-effectiveness constraints.

Abstract

Asset maintenance management is critical in industries such as petrochemicals and oil and gas (O&G), where complex, interdependent systems heighten failure risks. Maintenance costs represent a significant portion of operational expenditures, emphasizing the need for effective risk-based strategies. A considerable gap exists in integrating uncertainty modelling into both criticality assessment and maintenance planning. Existing approaches often neglect combining expert-driven assessments with optimization models, limiting their applicability in real-world scenarios where cost-effective and risk-informed decision-making is crucial. Maintenance inefficiencies due to suboptimal asset selection result in substantial financial and safety-related consequences in asset-intensive industries. This study presents a framework integrating Reliability-Centered Maintenance (RCM) principles with fuzzy logic and decision-support methodologies to optimise maintenance portfolios for offshore O&G assets, particularly focusing on corrosion management. The framework evaluates asset criticality through comprehensive FMEA, employing MCDM and fuzzy logic to enhance maintenance planning and extend asset lifespan. A case study on offshore asset corrosion management demonstrates the framework’s effectiveness, selecting 60% of highly critical assets for maintenance, compared to 10% by current industry practices. This highlights the potential risk reduction and prevention of critical failures that might otherwise go unnoticed, providing actionable insights for asset integrity managers in the O&G sector.

1. Introduction

The assets mobilized in these types of industries are complex in nature, as they have many diverse elements that interact dynamically [1]. Therefore, their interactions create an environment favorable to failure propagation due to the established relationship of interdependence among the elements [2]. Assets of this nature necessitate the assessment of various types of data, rendering the analysis non-trivial in most cases [3]. These industries typically rely on many continuously operating equipment working in concert to fulfill their objectives [4,5]. This scenario heightens the probability of encountering extreme, uncommon, and disruptive events [6,7]. Consequently, ensuring the integrity of these assets through well-executed maintenance routines is paramount [8,9,10]. Maintenance and inspection costs represent a significant portion of operational expenditures, ranging from 28% to 52% [11], with maintenance alone accounting for up to 40% of total costs in the oil and gas sector, much of it due to poorly planned activities [12]. This has led to a growing emphasis on risk-based maintenance strategies to optimize operations. In offshore contexts, assets are particularly vulnerable to corrosive processes in the marine environment [13], which negatively impact performance, safety, and lifespan [14]. The impact of ineffective maintenance strategies is evident in major offshore platform incidents, many of which were linked to corrosion-related failures. In 2022, the FPSO Cidade de Vitória was shut down by the Brazilian National Petroleum Agency (ANP) due to severe corrosion in pipelines, leading to an estimated loss of $1.1 million per day, given its average production of 9360 barrels per day at an oil price of $120 per barrel [15]. More critically, in 2015, the FPSO Cidade de São Mateus suffered a catastrophic explosion, caused among other factors by gas leakage from corroded pipelines, leading to nine fatalities and significant financial losses [16]. These cases underscore the substantial economic and safety risks posed by inadequate maintenance planning, highlighting the necessity of structured methodologies that integrate risk analysis, asset criticality assessment, and maintenance optimization to prevent such costly failures.

Contemporary methods for maintenance planning encompass Risk-Based Inspection (RBI) and RCM [1]. Risk-Based Inspection (RBI) is a strategic approach for predictive maintenance that defines a detailed inspection plan based on each component’s failure risk. Its primary purpose is to apply risk analysis to identify potential degradation mechanisms that threaten equipment integrity, assess the consequences of such failures, and evaluate the associated risks [17]. The RBI process involves a comprehensive risk assessment to prioritize mitigation actions by combining the severity of potential effects with the likelihood of their occurrence [18]. This assessment is typically conducted using a risk matrix that correlates probability with consequence, thereby ranking hazards and guiding inspection efforts [19].

RCM includes scheduled maintenance, reliability, frequency of maintenance actions, and safety [20,21,22]. RCM has gained prominence due to sector-specific regulations and guidelines, systematically addressing the mitigation of failure risks and prioritizing components or units based on their failure potential and consequences [23,24,25,26,27,28]. The effectiveness of RCM combined with FMEA is well-documented across many industries, including chemical, oil and gas, power distribution, and manufacturing [23,29]. FMEA is a safety and reliability technique used to identify, track, and mitigate potential issues [30]. Despite their widespread use, FMEA has notable shortcomings: (i) difficulty in obtaining accurate Risk Priority Numbers (RPNs) due to limited expert knowledge; (ii) failure to consider the weights of risk factors, leading to potentially flawed prioritization; (iii) criticized mathematical formulation of RPN, resulting in non-continuous values and difficulty in risk prioritization [31].

To address these drawbacks, Chemweno et al. [32] have introduced a methodology leveraging Bayesian hierarchical theory and Monte Carlo simulations for a more dynamic asset risk evaluation, incorporating failure likelihood and associated costs to classify assets by criticality for optimal maintenance strategy identification. Concurrently, Gupta et al. [28] have integrated RCM program principles with fuzzy logic for a detailed analysis of criticality parameters (severity, occurrence, and detection) through the RPN algorithm across various alpha levels. Both research endeavors, subsequent to risk evaluation, classify assets on a criticality scale, thereby facilitating the determination of the most suitable maintenance strategy. Selim et al. [33] furthered this by employing MCDM techniques and fuzzy logic for formulating economically viable maintenance strategies, considering both technical and cost criteria for asset criticality. Gao et al. [34] innovated the FMEA tool to enable reliability analysis of complex mechanical systems, addressing failure propagation and offering a holistic asset assessment. Daneshvar et al. [30] proposed an integrated fuzzy smart FMEA framework that combines the Analytical Hierarchy Process (AHP) and Data Envelopment Analysis (DEA) to enhance risk assessment reliability, demonstrated through an aircraft landing system example. Chakhrit et al. [26] introduced a novel fuzzy resilience-based RPN model to enhance the FMEA method, overcoming traditional limitations by including additional factors impacting cost, sustainability, and safety, and employed an assessment approach integrating three MCDM methods (fuzzy AHP, grey relation analysis, and entropy method) validated through a gas turbine case study.

Although previous studies have employed MCDM-based FMEA to select critical assets [31,35], there are still gaps regarding uncertainties in expert assessments [30,35] and data scarcity [35], and there is a significant gap in approaches that combine criticality analysis from FMEA with a comprehensive maintenance optimization plan [29]. While it is possible to identify proposals in the literature [28,32,33,34] that innovate in reliability analysis, developing a new framework for evaluating the criticality of complex assets related to the Offshore domain, which optimizes selection to compose maintenance plans, is scarce. In this vein, empirically validated frameworks that combine MCDM methods under uncertainty with optimization models for optimal maintenance planning are lacking [31,36,37]. Thus, there is a need for a structured methodology to define a maintenance plan based on the RCM program, whose application not only prioritizes assets but also provides a feasible plan with real business constraints for the user.

Therefore, the objective of this research is to propose an integrated framework that addresses the aforementioned gaps by combining fuzzy logic-based FMEA, group AHP, and mixed-integer programming. Specifically, this study aims to handle uncertainties in expert assessments and data limitations through the fuzzy rule-based RPN, systematically aggregate expert judgments using group AHP, and optimize maintenance planning via a resource-constrained MIP model. By doing so, we seek to deliver both an accurate prioritization of critical offshore assets and feasible maintenance planning, ultimately contributing to improved asset integrity and operational decision-making in complex industrial environments.

The contribution of this paper is threefold: theoretical, practical, and methodological. First, an improved fuzzy FMEA approach, aggregating experts’ judgment with α-cut and considering the weights through a group aggregation technique for AHP, has been proposed, which handles ambiguous data and integrates expert evaluations more flexibly. Thus, from the theoretical point of view, the innovation is provided by presenting a robust method that integrates the use of the innovative Risk Priority Number algorithm with group AHP, expert systems, and mixed integer programming to optimize maintenance portfolios for offshore oil and gas assets, particularly focusing on corrosion management. Second, an expert system following if-then rules is proposed and validated (applied in the Oil & Gas domain) to measure RPN’s dimensions based on degradation factors that affect the systems (previously identified in the literature and by experts). In this context, we changed the risk estimated from the classical FMEA technique with a fuzzy FMEA evaluated through an automated, rule-based system and assigned weights through a multi-personal decision-making method. Hence, from a practical perspective, this method offers technical decision support elements for managers responsible for asset integrity in various other domains. To verify the model’s effectiveness, a case study application is provided for maintaining assets within the Oil & Gas industry that are susceptible to corrosion. Third, the criticality of the complex systems is combined with resource parameters in mixed-integer programming (MIP) to define optimal maintenance planning that considers resource allocation to maintenance teams. Therefore, by combining a comprehensive literature review, expert interviews, and data analysis, a novel FMEA methodology is provided for group decision-making on asset criticality and optimal maintenance planning in complex systems.

The remainder of this paper is structured as follows: Section 2 provides preliminaries and gaps of FMEA and criticality analysis. Section 3 presents the proposed method, including the mathematical modelling and the framework. An application case is presented in Section 4. Next, a discussion and analysis of the case and its implications are described in Section 5. Finally, Section 6 presents the conclusions and suggestions for further research.

2. Literature Review

Several maintenance strategies address asset operability within technical and financial constraints, ranging from basic to advanced approaches. Corrective maintenance is the simplest but costly method after system failure, resulting in expensive repairs and lost production [38]. Preventive maintenance, the most widely used approach, involves scheduled actions based on long-term experience, reducing downtime costs with proper planning [39].

Predictive maintenance hinges on real-time component conditions rather than fixed schedules, relying on diagnostic data from sensors and inspections. A key method in predictive maintenance is RCM, emphasizing the functional importance of components and their failure history through a structured approach. Failure modes are analyzed for each component, based on causes, effects, and consequences, to determine preventive tasks [38]. Endrenyi et al. [39] present an overview of maintenance approaches and detail the RCM as a predictive maintenance strategy based on condition monitoring and analyzing needs and priorities.

RCM is a systematic approach to preserving equipment functionality, aiding in the optimization of maintenance strategies tailored to specific circumstances, including corrective, preventive, condition-based, and proactive maintenance [28]. RCM offers significant advantages, such as defining effective maintenance actions, reducing the severity of failure impacts, financial savings in terms of time and repair costs, and enhanced facility reliability [40]. According to Gupta et al. [41], the RCM methodology can be divided into six main steps, namely (i) system selection and data collection, (ii) system division and identification of the functionally significant item (FSI), (iii) determination of FMEA, (iv) criticality analysis, (v) RCM logical decision, and (vi) selection of maintenance action.

The primary goal of RCM is to ensure equipment functionality. Its initial steps focus on identifying the critical components essential for the equipment or structure to function, distinguishing RCM from conventional maintenance approaches [42]. Preserving asset reliability hinges on the continued operation of key components [22]. In the RCM process, the subsequent step involves performing an FMEA, where various failure modes for each component are identified, their impact and consequences are assessed, and they are ranked based on RPN, a crucial tool that guides maintenance actions to prevent critical flaws [28].

$$\mathrm{R}\mathrm{P}\mathrm{N}=\mathrm{S}\times \mathrm{O}\times \mathrm{D}$$

(1)

In this case, (S) is the severity, related to the effect of failure; (O) is the occurrence, related to the likelihood; and (D) is for detection, related to the difficulty in detecting the damage. Nevertheless, some authors criticized the RPN model’s simplicity as it may not adequately address real-world issues [43]. Gupta et al. [41] and Ouyang et al. [44] note that this calculation is limited to analyzing only three dimensions and doesn’t consider their interrelationships. Lo et al. [45] contend that this method oversimplifies the influence of severity, occurrence, and detection on failure urgency, relying on subjective values over objective criteria, which could result in inaccurate conclusions.

Moreover, failures in complex systems disrupt the production process, causing considerable downtime and financial losses. Consequently, investigating the degradation mechanisms of these systems has become a growing area of research [37]. Existing studies often categorize system failures into hard and soft types. While optimizing maintenance strategies based on system degradation information is both valuable and effective, there is limited research in this domain [36].

Although RCM provides a structured approach to mitigating failure risks through scheduled maintenance, reliability analysis, and safety prioritization, existing methods often fall short in addressing the inherent uncertainties and limitations of traditional FMEA [26] Specifically, traditional FMEA struggles with accurately determining RPNs due to the limited knowledge of experts, failure to consider the weights of risk factors and a simplistic mathematical formulation that complicates risk prioritization [24]. Furthermore, subjectivity in fuzzy rules remains a persistent issue [31].

To address these challenges and limitations, the literature proposes alternatives involving RCM combined with FMEA models based on expert opinions [25,26,27,30,33]. These approaches often combine fuzzy logic with MCDM methods [28]. For example, Fang et al. [46] employed a fuzzy FMEA and AHP approach within the RCM framework to enhance maintenance decisions for metro door systems. Shamayleh et al. [47] applied a conventional RCM process focusing on equipment priority determination for medical equipment, utilizing FMEA and a simple risk-based decision logic. Alrifaey et al. [48] developed a hybrid RCM model for electrical gas turbine generators, combining analytic network process and hybrid linguistic FMEA with optimization models. Catelani et al. [49] customized RCM procedures for yaw systems in wind turbines, using optimization and decision diagrams. Patil and Bewoor [50] developed a comprehensive RCM framework for steam boiler systems in the textile industry, incorporating step-by-step RCM procedures, FMEA, and decision tree logic. These diverse applications demonstrate the flexibility and effectiveness of integrating RCM with FMEA across various industries and contexts [29]. However, while there are innovative proposals in the literature for reliability analysis, there is a notable scarcity of frameworks designed to evaluate the criticality of complex assets in the offshore domain and optimize their selection for maintenance plans. Thus, there is a pressing need for a structured methodology that defines a maintenance plan based on the RCM program, which prioritizes assets and provides a feasible plan within real business constraints.

3. The Proposed Method

3.1. Preliminaries

To develop the framework, this study analyzed the corrosion management practices of a leading O&G company that operates multiple units. Each unit is allowed to adopt specific maintenance strategies within the company’s overarching guidelines. The diverse operational experiences across these units provided valuable insights into identifying the best approach to optimize resource allocation for regular maintenance and address the corrosion management challenge effectively. This research employed four data collection methods, as summarized in Figure 1.

First, two secondary data collection methods were used: literature review and document analysis. This approach aimed to contextualize corrosion management in the O&G industry, survey asset prioritization criteria, and identify possible classification rules. The literature review also helped determine the MCDM and optimization methods used in the framework, which were revisited whenever clarification was needed.

The second method involved participant observation, which was used to gain a holistic understanding of the system and capture real-world conditions more accurately [51]. For instance, one of the authors participated in two maintenance campaigns on offshore platforms, closely following the day-to-day work of a painting inspector. This hands-on approach provided primary data, supplemented by interactions with painting inspectors, equipment inspectors, and coordinators. During this time, the researchers visited most of the facilities involved in the maintenance plan, further enriching the practical insights gained from the literature.

The third method was a survey conducted with 16 professionals from diverse backgrounds within the company (

Table 1. Demographic profile of questionnaire respondents.

Experience with External Corrosion Management
None	1	6%
Less than 5 years	2	13%
5 to 10 years	5	31%
More than 10 years	8	50%
Experience with Inspection Activities
None	6	38%
Less than 5 years	1	6%
5 to 10 years	2	13%
More than 10 years	7	44%
Experience with Maintenance Activities
None	2	13%
Less than 5 years	4	25%
5 to 10 years	4	25%
More than 10 years	6	38%

). The survey, titled “Proposal of Methodology for External Corrosion Evaluation Based on Risk Analysis”, aimed to gauge the respondents’ level of agreement regarding the proposed methodology for asset prioritization and determine weights of failure parameters.

The fourth and final method involved conducting structured interviews with eight experts, representing four operating units of the company (

Table 2. Profile of experts interviewed.

Expert	Operating Unit	Position	Experience
1	1	Senior technician	Experience in corrosion inspection
2	4	Senior level	Experience in corrosion management
3	3	Senior level	Experience in corrosion research and corrosion management
4	1	Production engineer	Maintenance team leader
5	3	Master technician	Experience in corrosion inspection
6	Corporate	Master level	Experience in asset integrity
7	2	Senior level	Experience in corrosion management
8	4	Master technician	Experience in corrosion inspection

). The group was composed of four experts with a planning profile and four with an inspection profile, ensuring the inclusion of both managerial and operational perspectives in the assessment. The number of participants was defined to balance diversity of knowledge with the manageability and reliability of the evaluation process, following recommendations from expert-based decision-making methods. Moreover, practical constraints related to the accessibility and availability of qualified specialists made the inclusion of a larger number of experts unfeasible.

These interviews had three main objectives: to validate corrosion factors obtained from the literature, to rank the importance of these factors, and to validate the criticality analysis rules for each factor. The interviews were conducted in Portuguese, with each respondent providing their inputs via an Excel sheet, ensuring consistency in capturing the data.

3.2. Mathematical Model Formulation

3.2.1. AHP-Group Decision-Making Method

Decision-making theory suggests that MCDM methods are instrumental in solving complex problems, as they allow viewing a variety of criteria when evaluating available alternatives [52]. To ensure unbiased decisions, these criteria must be selected and analyzed systematically [53]. Rezaei [54] highlights that there are numerous MCDM methods exist in the literature, with the Analytic Hierarchy Process being one of the most widely applied. The AHP, introduced by Saaty [52], is particularly useful for complex decision processes, capable of synthesizing numerous factors and structuring them hierarchically [55,56]. This model is widely used when expert opinions need to be considered [56].

Saaty [52] defined six iterative macro steps that comprise the process that constitutes the AHP process:

(i)

define the problem and clarify the domain of knowledge;

(ii)

design the decision structure from a top-down perspective, considering the objective, criteria, and set of available alternatives;

(iii)

construct pairwise comparison matrices for each level and its subsequent lower level. The matrix values designate relative weights;

(iv)

weight each level (criteria and sub-criteria) based on priority values from previous steps;

(v)

perform hierarchical synthesis using eigenvectors and criterion weights; and

(vi)

determine the consistency of comparison matrices using the eigenvalue method to calculate the consistency index (CI).

The relative weights mentioned in step 3 are predefined on a numerical scale (1—equal importance to 9—extreme importance), known as the fundamental scale. This scale allows for the comparison of each alternative according to its importance relative to the criteria [52].

Considering the previously mentioned steps, it is noteworthy that steps 3 to 6 encompass the AHP analysis phase. In step 3, the pairwise comparison matrix (denoted as matrix $A$) is constructed using data obtained from interviews. The principal right eigenvector of the matrix A is computed as w. If the equality ${\mathrm{a}}_{ik}\times {\mathrm{a}}_{kj}={\mathrm{a}}_{ij}$ is not confirmed for all k, j, and i, the Eigenvector method is selected. If the matrix is incompatible or presents incomplete inconsistencies, column normalization to obtain W_i cannot be used in the pairwise comparison matrix [57].

In the context of group decision-making, addressing inconsistencies in pairwise comparisons is essential to achieving convergence in responses. When inconsistencies are detected, two common approaches can be employed: (i) resubmitting the questionnaire to respondents to refine their judgments [54,55] or (ii) eliminating inconsistent responses to maintain the integrity of the decision matrix [56]. This ensures that the final weight assignments are reliable and align with the expected decision-making framework. Once an acceptable consistency level is achieved, the following equations are utilized to convert the raw data into meaningful absolute values and normalize the weights w = ($w_1$, $w_2$, $w_3$, …, $w_n$), where A is the pairwise comparison, w is the normalized weight vector, ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum eigenvalue of matrix A, and ${\mathrm{a}}_{ij}$: numerical comparison between the values i and j.

$$Aw={\mathsf{\lambda }}_{\max }\mathrm{W},\hspace{1em}\hspace{1em}{\mathsf{\lambda }}_{\max }\ge \mathrm{n}$$

(2)

$${\mathsf{\lambda }}_{\max }={\displaystyle \frac{1}{n}}\sum _{i=1}^n{\displaystyle \frac{\left[Aw\right]}{w_i}}$$

$$\mathrm{A}=\left\{{\mathrm{a}}_{ij}\right\}\hspace{1em}\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\hspace{1em}{\mathrm{a}}_{ij}=1/{\mathrm{a}}_{ji}$$

(3)

To verify the outcomes of the AHP, the consistency ratio (CR) is determined by the formula CR = CI/RI. The consistency index (CI) is then evaluated using:

$$\mathrm{C}\mathrm{I}={\displaystyle \frac{\left({\mathsf{\lambda }}_{\max 1}-\mathrm{n}\right)}{\left(\mathrm{n}-1\right)}}$$

(4)

The value of RI is related to the dimension of the matrix and will be extracted from the study by Golden et al. [58]. It should be noted that a consistency ratio lower than 0.10 verifies that the results of the comparison are acceptable.

3.2.2. Algorithm of Risk Priority Number

RPN measures the failure modes with multiple S, O, and D in traditional FMEA. To avoid the dilution phenomenon, a risk-space diagram is applied according to the risk assessment on aviation safety management [59]. This methodology allows for allocating different weights for each of the RPN axes. Therefore, the Risk Space diagram, Figure 2, is created to define the RPN value further.

The fuzzy alpha-cut method is recommended for selecting finite subsets that are semantically distinct, considering the relevance of their respective degrees of membership [60] The application of this method allows for a more detailed analysis of each dimension (S, O, and D) based on their respective levels (l, m, or r) since the algebraic operations of a-cuts can offer more accurate results [61]. The proposition of the alpha-cut method begins with the definition of alpha values (

Table 3. Alpha-cut method.

${\mathbf{\alpha }}_1$	SL SR	${\mathbf{\alpha }}_2$	SL SR	${\mathbf{\alpha }}_3$	SL SR
	OL OR		OL OR		OL OR
	DL DR		DL DR		DL DR

).

Si, Oi, and Di values are defined according to the following equations, where ${\mathrm{S}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}$ and ${\mathrm{S}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}$ represent the value to the left and right of the S interval of the i-th Failure Mode by the α-level. [${\mathrm{O}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}$, ${\mathrm{O}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}$] e [${\mathrm{O}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}$, ${\mathrm{O}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}$] represent the range O e D, respectively [28,59].

The α parameter is a sensitivity variable applied to the RPN, representing the uncertainty level in the risk assessment. It defines the range within which the Risk Priority Number (RPN) can vary, accounting for imprecision in expert evaluations. The α-level is bounded by 0.0 < α ≤ 1.0, where higher α values reduce the uncertainty range, and lower values allow for greater variability [28,62,63].

$${\mathrm{S}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}={\mathrm{S}}_{\mathrm{i}\mathrm{l}}+\mathsf{\alpha }\left({\mathrm{S}}_{\mathrm{i}\mathrm{M}}-{\mathrm{S}}_{\mathrm{i}\mathrm{R}}\right)$$

(5)

$${\mathrm{S}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}={\mathrm{S}}_{\mathrm{i}\mathrm{l}}-\mathsf{\alpha }\left({\mathrm{S}}_{\mathrm{i}\mathrm{L}}+{\mathrm{S}}_{\mathrm{i}\mathrm{M}}\right)$$

(6)

$${\mathrm{O}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}={\mathrm{O}}_{\mathrm{i}\mathrm{l}}+\mathsf{\alpha }\left({\mathrm{O}}_{\mathrm{i}\mathrm{M}}-{\mathrm{O}}_{\mathrm{i}\mathrm{R}}\right)$$

(7)

$${\mathrm{O}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}={\mathrm{O}}_{\mathrm{i}\mathrm{l}}-\mathsf{\alpha }\left({\mathrm{O}}_{\mathrm{i}\mathrm{L}}+{\mathrm{O}}_{\mathrm{i}\mathrm{M}}\right)$$

(8)

$${\mathrm{D}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}={\mathrm{D}}_{\mathrm{i}\mathrm{l}}+\mathsf{\alpha }\left({\mathrm{D}}_{\mathrm{i}\mathrm{M}}-{\mathrm{D}}_{\mathrm{i}\mathrm{R}}\right)$$

(9)

$${\mathrm{D}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}={\mathrm{D}}_{\mathrm{i}\mathrm{l}}-\mathsf{\alpha }\left({\mathrm{D}}_{\mathrm{i}\mathrm{L}}+{\mathrm{D}}_{\mathrm{i}\mathrm{M}}\right)$$

(10)

Subsequently, the weighted Euclidean distance formula is employed to induce ${\mathrm{R}\mathrm{P}\mathrm{N}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}$ and ${\mathrm{R}\mathrm{P}\mathrm{N}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}$ according to the relationship in RSD. Considering the discrepancy of the risk factors, importance weights are indicated to calculate of RPN. According to the research on weighting Euclidean distance, RPNi is expressed in a multiplicative weighted format, given by:

$${\mathrm{R}\mathrm{P}\mathrm{N}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}={\displaystyle \frac{\sqrt{\sum _{\mathrm{x}}{{\mathrm{w}}_{\mathrm{x}}}^2{\left({\mathrm{x}}_{\mathrm{i}\mathrm{L}}^{\mathsf{\alpha }}-{\mathrm{x}}_{\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathsf{\alpha }}\right)}^2}}{\sum _{\mathrm{x}}{{\mathrm{w}}_{\mathrm{x}}}^2}}$$

(11)

$${\mathrm{R}\mathrm{P}\mathrm{N}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}={\displaystyle \frac{\sqrt{\sum _{\mathrm{x}}{{\mathrm{w}}_{\mathrm{x}}}^2{\left({\mathrm{x}}_{\mathrm{i}\mathrm{R}}^{\mathsf{\alpha }}-{\mathrm{x}}_{\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{n}}^{\mathsf{\alpha }}\right)}^2}}{\sum _{\mathrm{x}}{{\mathrm{w}}_{\mathrm{x}}}^2}}$$

(12)

3.2.3. Optimization Model

According to Biondi [64], optimization problems can be classified in terms of discrete or continuous variables. Most continuous optimization problems encompass linear programming (LP) and nonlinear programming (NLP) [64]. LP primarily aims to find the best solutions (e.g., a region or a single value) for problems whose models are represented by linear equations and generally operates in situations involving labor, raw materials, capital, among other criteria [65]. Discrete optimization problems, on the other hand, can be classified into mixed-integer linear programming (MILP), mixed-integer nonlinear programming (MINLP), or integer programming, where all variables are integers [66]. The problem at hand can be transcribed as a discrete, mixed-integer problem based on the nature of the variables selected for the study. Various approaches exist in the literature to solve problems of this nature, and we have chosen the method that best fits the asset selection problem for the context analyzed: the transportation problem.

The transportation problem can be illustrated by the following scenario: there are m origins producing homogeneous products that must be transported to n destinations. Each origin has a maximum supply limit, and each destination has a maximum absorption limit of the production. The supply from origin i to destination j represents a route with an associated cost. This type of problem aims to minimize the total cost of established routes [67], ensuring that each destination is serviced and that each origin operates according to its capacity [68]. The classic transportation problem, whose main objective is to minimize costs, is mathematically described in the form presented in:

$$\sum _{i=1}^{\mathrm{m}}\sum _{j=1}^{\mathrm{n}}{\mathrm{c}}_{ij}{\mathrm{x}}_{ij}$$

(13)

Here, ${\mathrm{c}}_{ij}$ represents the cost associated with transporting goods from origin i to destination j, and ${\mathrm{x}}_{ij}$ represents the decision variable, indicating the volume transported between i and j.

The first constraint, expressed in the following equation, ensures that the total volume of products transported across all possible arcs will be equal to the maximum supply limit associated with the origin. Therefore, in this formulation, the parameter ${\mathrm{a}}_i$ represents the total volume of products originating from the origins.

$$\sum _{j=1}^{\mathrm{n}}{\mathrm{x}}_{ij}={\mathrm{a}}_i,\hspace{1em}i=1,\dots ,\mathrm{m}$$

(14)

The second constraint ensures that the total volume of products transported across all possible arcs will be equal to the production absorption capacity of the respective destinations. Therefore, in this formulation, the parameter ${\mathrm{b}}_i$ represents the total volume of products requested by the destinations.

$$\sum _{i=1}^{\mathrm{m}}{\mathrm{x}}_{ij}={\mathrm{b}}_i,\hspace{1em}j=1,\dots ,\mathrm{n}$$

(15)

Notably, the variable ${\mathrm{x}}_{ij}$ must be greater than or equal to zero, indicating that if ${\mathrm{x}}_{ij}$ = 0, no transportation occurs along that specific route. This type of problem is one of the most significant applications in business, especially in the context of the physical distribution of goods [68].

3.3. Framework

In this section, we propose a practical framework developed for the selection of critical assets in the planning and execution of maintenance routines in complex structural systems. It is an adaptable tool that can be applied to other problems within the context of maintenance. The tool firstly guides the user in the systematic collection and classification of evaluative criteria. Secondly, the tool defines a hybrid approach considering multicriteria methods to prioritize and rank the analyzed assets. Lastly, it provides an optimization model to determine the maintenance portfolio.

In integrating Fuzzy FMEA, group AHP, and MIP within the same framework, one major challenge arises from the heterogeneity of data and expert judgments. While FMEA can effectively categorize failure modes, incorporating fuzzy sets becomes essential to address the subjectivity of linguistic scales [69], especially when dealing with corrosion-oriented risks and limited numerical data. However, integrating expert-based fuzzy models demands careful consideration of consistency in elicited opinions, which is managed through group AHP. By requiring each expert to perform pairwise comparisons, AHP facilitates the validation of consistency ratios, yet disagreements among experts can lead to re-evaluation and exclusion of certain inconsistent responses [58]. Furthermore, linking fuzzy metrics from the RPN model to an MIP optimization routine adds a layer of computational complexity: real-time adjustments in membership functions or alpha-cut thresholds can potentially affect solver performance, particularly in large-scale asset portfolios [60].

Despite these challenges, each method was chosen for its distinct advantages that collectively strengthen maintenance planning decisions. FMEA, enhanced with fuzzy logic, enables nuanced risk classification and compensates for the inherent subjectivity in severity, occurrence, and detection assessments. Group AHP, in turn, delivers a transparent and systematic weighting of risk factors, ensuring that the most influential dimensions receive appropriate emphasis. Finally, MIP provides an optimal allocation of resources under realistic constraints, converting prioritized assets into a feasible maintenance portfolio. Together, these methods form a comprehensive and adaptable decision-making tool, addressing not only the uncertainty in expert inputs but also the practical need for efficient resource planning in large-scale and complex industrial environments.

The framework proposed consists of five main steps, namely (i) criteria selection, (ii) criteria classification, (iii) determining performance at each failure parameter, (iv) obtaining the criticality index, and (v) defining the maintenance portfolio. The framework is presented in Figure 3 and is detailed in this section.

The first step involves collecting criteria that affect assets criticality. This step is conducted based on literature and documental analysis to define meaningful criteria that describe asset behavior. These criteria are then validated on two terms: firstly, considering practical application to the problem, in relation to the feasibility in terms of generalization to describe the asset characteristics, and the availability of data to analyze it. Secondly, considering their relevance, and for this analysis expert’s judgment is evaluated through structured interviews. To determine the relevance of each factor to the analysis, the method of relative frequencies [70] was used. If the consensus index exceeds 75%, the factor is considered relevant; otherwise, it is excluded [71]. The framework records the validated set and organizes factors under S, O, and D for the next steps.

The second step involves classifying the criticality level of the assets. Criteria for classification were selected according to information available on the main characteristics of the assets. The classification uses if-then rules, developed with experts through structured interviews, and also considering literature and document analysis. Therefore, the if-then rules results in a response matrix that associates a linguistic scale (Low, Average, or High) with each asset-criteria pair. These pairs are translated into triangular fuzzy numbers, where l, m, and r represent the lowest, medium, and highest values, respectively. This linguistic scale was adapted from Chen-yi et al. [69] (see

Table 4. Fuzzy linguistic scale: universe of discourse and triangular fuzzy numbers for corrosion assessment criteria, adapted from Chen-yi et al. [69].

Linguistic Variable	Universe of Discourse	Linguistic Values	Triangular Fuzzy Numbers
Corrosion assessment criteria	0–1	Low	(0; 0.25; 0.5)
		Average	(0.25; 0.5; 0.75)
		High	(0.5; 0.75; 1)

).

Step three assigns weights to each factor to ensure the order of importance of each factor within the RPN index. Experts, through structured interviews, define these weights. Factors are grouped by their dimensions in the RPN index, and experts assign a weight to each dimension, ranging from 0 to 1. The weights are normalized, and the arithmetic average of the normalized weights is used as an aggregation function to determine a consensus weight. Although geometric mean has been widely recommended in group AHP contexts to aggregate pairwise comparison matrices due to its ability to maintain reciprocal properties [72], the arithmetic mean is also a valid choice when aggregating normalized priority vectors, particularly in cases where decision-makers are considered equally reliable [56]. In such cases, the arithmetic mean provides a straightforward and interpretable representation of consensus by averaging final weights rather than intermediate judgments.

Step four involves calculating the criticality index after all the criteria are evaluated. First, the triangular fuzzy numbers for each level (l, m, and r) are aggregated. The sum operation is used to transform the multiple fuzzy sets associated with each S (severity), O (occurrence), and D (detectability) dimension into a set for each level. Next, these fuzzy sets are used to create the risk space diagram. Finally, RPN values are calculated based on the weighted Euclidean distance, as shown in (11) and (12). Expert knowledge is used solely to determine the weights of the failure parameters (S, O, D); all subsequent steps, namely aggregation, risk-space construction, distance calculation, and RPN computation, are executed automatically by the model.

This study adopts a structured approach in determining weight values through applying the AHP group aggregation approach. Within this methodological framework, the priority vector value (W_x) is derived through a collaborative decision-making process using the weighted geometric mean-aggregation of individual priorities (WGM-AIP) [73]. The primary aim is to translate the collective expertise of domain specialists, as expressed by the group of respondents, into quantifiable weightings. AIP excels in situations with conflicting objectives, preserving personal rankings [74], and its priority-based aggregation technique can handle multi-personal decision-making problems, making it suitable for both small and large groups [73].

The consistency of each judgment, measured in an individual comparison matrix, is measured by the consistency ratio, which should be less than 0.1 to be considered acceptable (a suitable indicator of rational decision-making). In this application, as shown in

Table 5. Importance evaluation and consistency ratio.

Expert	S_O	S_D	O_D	CR
1	3	4	2	0.02927491
2	2	3	1	0.02619547
3	4	4	4	0.35067212
4	4	3	4	0.49036376
5	3	2	1	0.02619547
6	2	2	4	0.24540649
7	2	4	0.5	0.33217336
8	4	3	3	0.34442475
9	4	4	4	0.35067212
10	4	4	2	0.09114386
11	4	3	3	0.34442475
12	3	2	4	0.47131007
13	4	3	4	0.49036376
14	4	2	4	0.70993915
15	4	4	4	0.35067212
16	3	2	4	0.47131007

, only 25% of the responses met the CR threshold, indicating that a significant portion of judgments were inconsistent. As a result, we decided to exclude inconsistent responses for reliable results.

The priority vector W_x = [S, O, D] was calculated from the consistent evaluations, as detailed in

Table 6. Comparison of evaluations with consistency ratio within the acceptable limit.

Expert 1
	S	O	D	Weights
S	1	3	4	0.6232
O	0.333	1	2	0.2395
D	0.25	0.5	1	0.1373
				CR = 0.0293
Expert 2
	S	O	D	Weights
S	1	2	3	0.5485
O	0.5	1	1	0.2409
D	0.333	1	1	0.2106
				CR = 0.0262
Expert 3
	S	O	D	Weights
S	1	2	3	0.5485
O	0.333	1	1	0.2106
D	0.5	1	1	0.2409
				CR = 0.0262
Expert 4
	S	O	D	Weights
S	1	4	4	0.6551
O	0.25	1	2	0.2114
D	0.25	0.5	1	0.1335
				CR = 0.0911
			Aggregated Weights
			S	0.5989
			O	0.2259
			D	0.1752
				CR = 0.1297

. The final resultant values are W_x = [0.5989, 0.2259, 0.1752] and a CR of 0.01297, signifying high reliability in the decision. Subsequently, the weightings are utilized to rank identified risks in descending order of significance. This hierarchical approach facilitates a comprehensive understanding and assessment of the problem domain.

Moreover, the centroid method is used to defuzzify the RPN score metric, translating it into a single value. The centroid calculation is given by the following equation, where the α-cut levels define different perspectives of uncertainty in the RPN evaluation. In this study, we follow the approach adapted from Gupta et al. [28], Chen et al. [63], and Ayag et al. [62], assuming values of α = 0 for lower bound, α = 0.5 for medium values, and α = 1.0 for upper bound, ensuring consistency in the sensitivity analysis of the RPN.

$$\mathrm{C}\mathrm{G}={\displaystyle \frac{1}{3}}\left({\mathrm{R}\mathrm{P}\mathrm{N}}^{\mathsf{\alpha }=0}+{\mathrm{R}\mathrm{P}\mathrm{N}}^{\mathsf{\alpha }=0.5}+{\mathrm{R}\mathrm{P}\mathrm{N}}^{\mathsf{\alpha }=1}\right)$$

(16)

Once the RPN value is defined for each Asset, the results are normalized by the minimum and maximum values possible for the RPN values, 0.25 and 0.75, respectively. In the initial round, the panel of experts reviewed and validated the RPN outputs, and their elicited weights were then fixed and embedded in the framework.

The entire decision model for criticality assessment is formally expressed as: Model = ⟨H, C, R, g, V, D⟩ where:

• H = M × S × Sys represents the complete three-tier asset hierarchy
• C = CS ∪ CO ∪ CD represents all 15 expert-validated criterion types
• R represents the complete set of expert-validated if-then rules
• g represents the fuzzy composition operator
• V = {Low, Average, High} represents the linguistic variable domain
• D represents the domain specifications for each attribute (as shown in the evaluation criteria table)

Moreover, the composition operator g: V × (V ∪ ∅) → V implements the MAX operator for combined criteria:

g(Low, Low) = Low

(17)

g(Low, High) = Average; g(High, Low) = Average

(18)

g(High, High) = High

(19)

g(V, ∅) = V (single criterion cases)

(20)

The final step in the framework involves defining the maintenance portfolio through an optimization model. The portfolio optimization model prioritizes systems based on their respective criticality indexes (normalized RPN). This approach is crucial for maintenance management as it ensures that systems critical to platform integrity remain in good operating condition, aligning with strategic objectives and industry standards.

In this case, a linear MIP optimization model is applied, considering an adaptation of the transportation problem. The assets are modeled as binary variables (${\mathrm{x}}_i$), where ${\mathrm{x}}_i=$1 if an asset is selected for maintenance and ${\mathrm{x}}_i=$0 if it is not. If an asset is selected, the model assumes it is restored to its original undamaged state.

The objective function (O.F.) maximizes the sum of the criticality indexes of the assets selected for maintenance. Given that each asset has a criticality index, the objective function prioritizes selecting systems with higher criticality levels over those with lower ones.

$$\mathrm{O}.\mathrm{F}.=\max \sum {RPN}_i{\mathrm{x}}_i$$

(21)

It is important to emphasize that systems with lower criticality should not be neglected. Therefore, the condition of the asset (determined through inspections) is included as a constraint on the objective function. Thus, besides prioritizing more critical items, the model will also promote an increase in the assets’ condition. This constraint (${\mathrm{R}}_1$) is expressed below, where ${\mathrm{D}}_i$ is the damage condition of asset ${\mathrm{x}}_i$, and $n$ is the total number of assets considered in the model (for selection and portfolio composition).

$${\mathrm{R}}_1={\mathrm{D}}_i\left({\displaystyle \frac{1-x_i}{\mathrm{n}}}\right)$$

(22)

Another important constraint relates to the resources available for performing maintenance activities. Including this constraint ensures that the portfolio generated is feasible. This constraint (R₂) is expressed in the following equation and designates to the model that the sum of resources required to execute activities in each portfolio must fit the total of available resources. In ${\mathrm{R}}_2$, ${\mathrm{R}\mathrm{S}}_i$ represents the required resources to perform a maintenance activity of asset i, and ${\mathrm{R}\mathrm{S}}_{\mathrm{a}\mathrm{v}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}}$ is the total resources made available by the company for maintenance activities execution.

$${\mathrm{R}}_2=\sum \left({RS}_i{x}_i\right)\le {\mathrm{R}\mathrm{S}}_{\mathrm{a}\mathrm{v}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}}$$

(23)

Finally, the framework operationalizes and embeds expert knowledge through the elicited rule base, the allocation and weighting of criteria, and the AHP-derived weights assigned to the failure parameters. After the initial calibration and validation round, execution is fully automated and requires no further expert participation. Because the framework is designed to adapt across applications and contexts, the same elicitation steps (for example, criteria definition, rule refinement, and weighting) can be repeated to reparameterize the model for a new asset class, dataset, or organizational objective. Once updated, the configuration again runs without ongoing expert involvement.

4. Application Case—An Offshore Corrosion Management Case

Corrosion is a major cause of equipment failure in the refining and petrochemical sectors, particularly due to the extensive use of equipment and piping systems that handle flammable hydrocarbons, toxic gases, and strong acids or caustics. In offshore installations, corrosion severely impacts asset longevity and reliability, accounting for up to 80% of total maintenance costs in the O&G exploration industry. Implementing effective corrosion management practices, such as inspection and prevention strategies, can reduce these costs by 20% to 30%. In the offshore industry, safety, reliability, and maintenance are critical priorities.

Coating is the primary method of external corrosion protection in offshore installations [75]. As a barrier, it shields materials from environmental exposure, particularly in the harsh conditions typical of marine environments. Visual inspection is the main method used to inspect these coatings [75] due to its simplicity and effectiveness. The outcome of a visual inspection is typically quantified as the percentage of the corroded area, which helps determine the severity of the damage. This corrosion percentage is compared against industry standards, such as ASTM D610-1 [76] and NBR/ISO 4628-3 [77], to assess the corrosion degree and guide maintenance decisions.

One of the major constraints in coating maintenance on offshore platforms is the limited availability of man hours (mh), the labor available for painting and other maintenance activities. Space and resources onboard are limited, making labor efficiency a critical factor. Painter productivity, measured in painted square meters per man hour (m²/mh), determines how much maintenance can be completed within the available time. Optimizing the use of man hours is crucial for effective corrosion management. Delays in coating maintenance, due to insufficient labor, can directly impact the platform’s operational efficiency and safety. Therefore, careful planning of maintenance activities, including the efficient allocation of labor resources, is vital to maintaining asset integrity.

A well-designed maintenance plan combines damage data with the engineering characteristics of equipment, such as material resistance, operating conditions, and stress distribution, to assess the probability of equipment failure [75]. While these engineering characteristics are established during the project phase, the damage information, such as corrosion levels, needs to be periodically updated through inspections. Regular updates ensure that the maintenance plan remains aligned with the actual condition of the assets, allowing for timely and accurate interventions. The main output is the annual painting plan for all platforms, including areas to paint next year, keeping total corrosion percentages within target limits. This plan serves as a productivity and integrity benchmark across platforms.

Figure 4 provides a comprehensive overview of the methodology used for periodic condition reassessment and maintenance planning. The process begins with asset identification, where components are grouped based on their function, location, and type within the platform’s modules. Following this, corrosion condition data is gathered for each asset, detailing their exposure and operational factors, such as location, elevation, and environmental conditions.

The FMEA procedure is applied using fuzzy logic and the AHP for group decision-making. This approach helps build a response matrix, which incorporates expert opinions to evaluate asset performance across different criteria. The matrix uses if-then rules and a triangular fuzzy evaluation (low, medium, high) to assess factors such as severity, occurrence, and detection of failure. These evaluations are then aggregated to generate a Risk Space Diagram (S, O, D), visually representing the risk factors for each failure mode, and the RPN is calculated using weighted Euclidean distance.

Expert participation is limited to setup and initial validation. A multidisciplinary panel defines the classification criteria, elicits the if–then rule base, and performs the pairwise comparisons used to derive the weights assigned to the failure parameters (S, O, D). The same panel reviews the first-round RPN results to confirm coherence with operational experience. After this validation, the elicited inputs are fixed and embedded in the framework. All subsequent steps, including aggregation of fuzzy evaluations, construction of the risk space diagram, computation and normalization of RPN values, and MIP-based portfolio optimization, are executed automatically. For new asset classes or operational contexts, the elicitation and validation steps can be repeated to reparameterize the model. Once updated, execution again proceeds without ongoing expert involvement.

Figure 4 also highlights how constraints such as resource availability (in terms of man hours) and degradation acceptance levels are fed into the MIP optimization model and provided as input parameters to the framework. The objective function (OF) aims to maximize the total RPN attended, ensuring that the highest-priority assets are addressed first while adhering to resource limitations and degradation goals. If the results are satisfactory, the methodology concludes with the definition of the maintenance portfolio, outlining which assets should be prioritized for intervention. However, if the results are not satisfactory, adjustments should be made to the constraints either by increasing available resources or modifying degradation goals to generate a revised prioritization that better meets the optimization targets. The process is iterative and continues until both resource limitations and degradation goals are satisfied.

The resultant maintenance plan is defined on a one-year horizon. After completing the proposed plan, the corrosion condition is reassessed in the next annual inspection cycle, and the framework is rerun with the updated condition to redefine the plan for the following year. This yearly reassessment ensures that the maintenance plan remains aligned with the evolving condition of the assets and the available resources.

A case study was conducted to evaluate this methodology, focusing on five modules of an oil rig. In total, 215 assets were analyzed. Figure 5 presents an overview of the selected items within the plant. The modules chosen for the study encompass a range of functions, including production, accommodation, and naval modules. Production modules were selected with and without gas processing and heat activity, providing insight into the effects of varying operational conditions. Additionally, the location of the modules across the FPSO (Floating Production Storage and Offloading unit) was considered to ensure comprehensive coverage of the platform, including both the center and the edges. Assets were distributed across a variety of components, exposure levels, and elevations to ensure a robust evaluation of the corrosion management approach.

4.1. Asset Identification

In this study, assets are defined as groups of components with similar characteristics. To classify and organize these assets for corrosion management, the platform’s components are divided into modules based on their location and operational function within petroleum processing. These modules are further divided into sectors, which provide more specific information about their location, particularly in relation to elevation and exposure to environmental conditions. Lastly, the assets are classified into systems, which offer a more detailed breakdown of their functional roles. By employing this module → sector → system hierarchy (Figure 6), components are grouped based on their corrosion behavior, allowing for targeted inspection and maintenance.

Additionally, asset characteristics are classified based on three key factors: operational function, location, and system function. Operational function refers to the overall role of the module within the platform, divided into three groups: production modules (related to O&G processing), naval modules (related to ship operations), and accommodation modules (for personnel transport and housing). Production modules were further categorized by specific activities like gas processing and heat operations, since these factors directly influence asset criticality. Location was defined by the plant layout, including port, starboard, bow, stern, and center areas, as well as elevation (classified into bottom, center, and top levels) and exposure to weather conditions (categorized as fully exposed or not exposed). Finally, system function classified components within each module according to their roles, such as ceiling, floor, primary or secondary structures, guardrails, staircases, and supports (electrical, piping, and equipment). These operational and physical characteristics are treated as fixed inputs for the framework and do not vary from year to year.

The asset hierarchy structure is formally defined as:

• Module Level (M): M = {Accommodation, Naval, Production, Cargo Area, Offloading, Pipe Rack, Pull In/Out, …}
• Sector Level (S): S = {Elevation × Exposure × Plant Location} where:

  ○

  Elevation ∈ {Bottom, Centre, Top}

  ○

  Exposure ∈ {Non-exposed(0), Exposed(1)}

  ○

  Plant Location ∈ {Starboard, Port, Bow, Stern, Centre}

• System Level (Sys): Sys = {Floor, Ceiling, Bulkhead, Staircase, Guardrail, Primary Structures, Secondary Structures, Piping Support, Equipment Support, Electrical Support}

This approach improves the efficiency and precision of corrosion management across the platform. The systems used in this study encompass critical structural and operational elements, including the ceiling, bulkhead, floor, primary structure, secondary structure, staircase, electrical support, piping support, equipment support, and guardrail.

4.2. Data Gathering

The damage data used for this study were gathered through visual inspections conducted in accordance with ASTM D610 [76], which was used to assess and quantify the corrosion percentage for each asset. Corrosion condition is reassessed annually following completion of the one-year maintenance plan, and the corrosion-percentage dataset is updated each cycle.

System-specific productivity (m² per mh) is also recorded as an input, varies by system type, and influences the effective resource cost per square meter.

Table 7. Sample input dataset (asset attributes and corrosion condition).

id	Area	Corrosion	Productivity	Components’ System	Modulus’ Function	Plant Location	Exposure	Elevation
0	491.86	10.00%	0.3	Floor	Accommodations	Stern	1	53,110
1	41.48	0.10%	0.15	Bulkhead	Accommodations	Stern	1	53,110
54	7.93	3.00%	0.1	Secondary Structures	Accommodations	Port	0	31,380
55	307.18	10.00%	0.3	Floor	Cargo Aerea	Starboard	1	35,920
56	32.12	0.10%	0.08	Piping Support	Cargo Aerea	Starboard	1	35,920
57	179.07	0.30%	0.15	Primary Structures	Cargo Aerea	Starboard	1	35,920
91	9.62	50.00%	0.1	Guardrail	Offloading	Centre	1	35,900
92	128.3	16.00%	0.08	Piping Support	Offloading	Centre	1	35,900
93	329.71	16.00%	0.15	Primary Structures	Offloading	Centre	1	35,900
129	109.97	33.00%	0.3	Floor	Pipe Rack	Centre	1	35,900
130	51.12	0.30%	0.1	Guardrail	Pipe Rack	Centre	1	35,900
131	237.06	10.00%	0.08	Piping Support	Pipe Rack	Centre	1	35,900
132	1881.02	16.00%	0.15	Primary Structures	Pipe Rack	Centre	1	35,900
172	185.14	16.00%	0.3	Floor	Pull In/Out	Centre	1	35,900
173	42.75	10.00%	0.1	Guardrail	Pull In/Out	Centre	1	35,900
174	295.31	1.00%	0.08	Piping Support	Pull In/Out	Centre	1	35,900

provides examples of the input data. Each input is detailed as:

• Quantitative Attributes:

  ○

  id: Unique asset identifier (integer)

  ○

  Area: Physical surface area in m² (continuous variable)

  ○

  Corrosion: Current corrosion level as percentage (0–100%)

  ○

  Productivity: Operational efficiency coefficient (0–1 scale)

• Categorical Attributes (Expert-Defined Domains):

  ○

  Components’ system ∈ {Floor, Bulkhead, Secondary Structures, Piping Support, Primary Structures, Guardrail, …}

  ○

  Module’s function ∈ {Accommodations, Cargo Area, Offloading, Pipe Rack, Pull In/Out, …}

  ○

  Plant Location ∈ {Stern, Port, Starboard, Center, …}

  ○

  Exposure ∈ {0 (Non-exposed), 1 (Exposed)}

  ○

  Elevation ∈ {Bottom, Centre, Top} (encoded as numerical values)

4.3. FMEA Analysis

4.3.1. Criteria Selection

The first step is to collect factors described as influential in analyzing the corrosive process of offshore assets under the marine atmosphere. For this purpose, a detailed literature review was conducted, from which 25 factors were identified, divided into six main categories, namely (i) influence of time, that presents factors related to periodicity and chronology; (ii) component information relates to data evaluated within the systems, such as geometry, temperature, and material; (iii) corrosive medium information presents factors associated with the atmosphere near the element’s surface; (iv) coating information is related to coating protection, such as the type of coating applied or the exposed surface area; (v) location information provides information about the exposure of the analyzed element and its influence on the surrounding environment; and (vi) cost information corresponds to the valuation of the component.

From the survey of factors that affect corrosion, a filter was applied to select feasible ones according to the proposed methodology, which groups the components into assets. Thus, an analysis was made to evaluate which characteristics are more representative of the evaluated factor. Regarding specific information about the components, a qualitative evaluation was made regarding the possibility of generalizing the information from one component to the group. If generalization is not possible, the factor is disregarded. In addition, a large part of the data is dispersed and in non-editable file formats, which makes accessing and extracting such information difficult. There are also cases of financial information that are not available for consultation. In these cases, even if the factors were feasible from a methodology point of view, they were disregarded due to the difficulty of accessing data to evaluate the proposed methodology.

Once the viable factors were defined, they were submitted to experts’ validation through structured interviews. The interviewees were presented with the list of eligible factors, for which they should inform if they considered the factor relevant to the criticality analysis. To determine the relevance of each factor to the analysis, the method of relative frequencies [70] was utilized. If the consensus index exceeds 75%, the factor is considered relevant; otherwise, it is disregarded [71].

In addition, interviewees were instructed to identify any relevant factors that were not listed in the previous questionnaire. It is worth noting that the methodology employed structured interviews, so any newly added factors by one interviewee were not shared with the others. For such cases, a qualitative analysis was conducted to determine if the proposed factor could be incorporated into the simplified FMEA method, and its relevance based on literature and documentary research. On such criterion, ‘risk of falling objects’, ‘surfaces in contact’ and ‘material’ were incorporated after expert deliberation.

A second analysis was conducted to determine to which axis of the RPN index they corresponded. The experts were instructed to define to which RPN axis the factor referred to, S (severity), O (occurrence) or D (detection). This analysis considered the relative frequency, except for the newly added factor suggested by the interviewees. For these factors, only the suggested respondents’ responses were considered, resulting in a 100% relative response for all selected factors. The resultant list of factors and their corresponding axis is presented in

Table 8. RPN dimension for each factor considered in the method.

		Dimension
Category	Factors	S	O	D
Location	Surrounding equipment	✔
	Risk of falls	✔
	Risk of falling objects	✔
	Wind exposure		✔
	Lighting conditions			✔
	Access to equipment			✔
Component information	Environmental impact	✔
	Risk of explosion	✔
	Production shutdown	✔
	Surfaces in contact		✔
	Material		✔
Corrosive medium information	Humidity		✔
	Atmospheric pollutants		✔
	Sun/ rain exposure		✔
	Environmental temperature		✔
Influence of time	Failure frequency		✔

.

Therefore, each evaluation criterion c is formally mapped to RPN axes based on expert validation:

• Severity Criteria (CS): {Environmental impact, Production shutdown, Risk of explosion, Risk of falls, Risk of falling objects}
• Occurrence Criteria (CO): {Frequency of failure, Humidity, Atmospheric pollutants, Environmental temperature, Material degradation}
• Detection Criteria (CD): {Access to equipment, Lighting conditions, Surfaces in contact}

4.3.2. Criteria Classification

The criteria classification aims to determine the criticality of assets for each factor, categorized as high, average, or low. For this purpose, “if-then” rules were defined to determine the criticality of an asset based solely on information that can be defined into three main pillars: (i) operational function, defined in terms of overall module’s function; (ii) location is defined as plant location, elevation concerning distance from water and exposure to weathering; (iii) the system is concerned with the components’ function within the module.

The authors proposed rules for each factor based on their perception of the operational routine, gathered from interviews and participant observations and combined with literature descriptions of each factor outlined in Section 4.1. In the second step, the proposed rules were presented to the experts as part of a structured interview for validation and improvement. During this stage, interviewees who proposed new factors also discussed the rules for each. The changes proposed by the experts are divided into three classes: (i) incremental improvement, where a criterion is added to the original rule; (ii) change in evaluation, where the same criteria are considered, but the expert proposes a change in the evaluation; (iii) definition of a new rule, where the respondent changes the proposed evaluation entirely.

The analysis conducted for consensus involved both quantitative and qualitative approaches. The quantitative analysis utilized the relative frequency method, which is similar to the method for validating factors. Consensus was reached when an agreement index of 75% or higher was achieved for a proposed rule [71]. However, if consensus was not reached, a qualitative analysis was conducted to assess the viability of the proposed rule based on the available information and its coverage. For example, if two interviewees proposed similar rules but with varying levels of detail, the more general rule was adopted.

The rules follow the structure proposed in Equations (17)–(20). Examples of formalized expert rules are:

• R1: IF (Module_function ∈ {Accommodation, Naval}) THEN (Surrounding_equipment_criticality = Low)
• R4: IF (Components_system ∈ {Guardrail}) AND (Elevation ∈ {Centre, Top}) THEN (Risk_of_falls_criticality = g(High, High) = High)
• R10: IF (Exposure = Non-exposed) AND (Plant_location ∈ {Port}) THEN (Wind_exposure_criticality = g(Low, High) = Average)

Table 9. Adopted if-then rules validated by experts.

Factor	Evaluation Criteria	If-Then Rule for Criticality Classification
Surrounding equipment	Module’s function	[Low] Accommodation modules; [Average] Naval modules; [High] Production modules.
Environmental impact	Components’ system	[Low] Floor/Ceiling/Bulkhead/Staircase/Guardrail; [Average] Electrical supports/Structures; [High] Piping supports/Equipment supports;
Risk of explosion	Module’s function	[Low] Accommodation and naval modules; [Average] Production modules without gas processing; [High] Production modules with gas processing.
Risk of falls	Components’ system Elevation	Components’ system: [Low] Systems different from Guardrail; [High] Guardrail Elevation: [Low] Bottom; [High] Centre, Top Combination: [Low] Elevation [Low] + Components’ system [Low]; [Average] Elevation [Low] + Components’ system [High] or Elevation [High] + Components’ system [Low]; [High] Elevation [High] + Components’ system [High]
Production shutdown	Module’s function Components’ system	Module’s function: [Low] Accommodation and Naval modules; [High] Production modules. Components’ system: [Low] Floor/Ceiling/Bulkhead/Staircase/Guardrail; [High] Structures/Supports. Combination: [Low] Module’s function [Low] + Components’ system [Low]; [Average] Module’s function [Low] + Components’ system [High] or Module’s function [High] + Components’ system [Low]; [High] Module’s function [High] + Components’ system [High]
Humidity	Exposure	[Low] Non exposed; [High] Exposed
Atmospheric pollutants	Elevation	[Low] Top; [Average] Centre; [High] Bottom
Frequency of failure	Components’ system	[Low] Piping Support/Equipment Support/Ceiling; [Average] Electrical support/Primary Structures/Secondary Structures; [High] Floor/Guardrail /Bulkhead/Staircase
Sun/rain exposure	Exposure	[Low] Non exposed; [High] Exposed
Wind exposure	Exposure Plant location	Exposure: [Low] Non exposed; [High] Exposed Plant location: [Low] Starboard, bow, stern, centre; [High] Port Combination: [Low] Exposure [Low] + Plant location [Low]; [Average] Exposure [Low] + Plant location [High] or Exposure [High] + Plant location [Low]; [High] Exposure [High] + Plant location [High]
Environmental temperature	Module’s function	[Low] Modules without heat activity; [High] Modules with heat activity
Lighting conditions	Exposure	[Low] Exposed; [High] Non-exposed
Access to equipment	Module’s function	[Low] All modules except the ones listed as high criticality; [High] Pipe Rack/Pump House/Automation and Electrical/Riser Pipe Rack/Fenders and bollards/Flare System/Engine Room/Bosun’s Store/Cranes/Essential equipment deck
Risk of falling objects	Components’ system Elevation	Components’ system: [Low] Systems different from Supports; [High] Supports Elevation: [Low] Bottom, Centre; [High] Top Combination: [Low] Elevation [Low] + Components’ system [Low]; [Average] Elevation [Low] + Component’s system [High] or Elevation [High] + Components’ system [Low]; [High] Elevation [High] + Components’ system [High]
Material	Components’ system	[Low] Guardrail; [Average] Primary structures/Floor/Ceiling/Bulkhead; [High] Secondary structures/Supports/Staircase
Surfaces in contact	Components’ system	[Low] Floor/Ceiling/Bulkhead/Staircase/Guardrail; [Average] Structures, Electrical support; [High] Piping and equipment supports

summarizes the adopted rule for each factor.

To delve deeper into the stages of the integrated methodology to calculate the criticality index, three assets located in separate modules and systems (see

Table 10. Profile of the assets selected for evaluation.

Assets	Components’ System	Modulus’ Function	Plant Location	Exposure	Elevation
1	Piping Support	Pipe Rack	Centre	1	Bottom
2	Secondary Structures	Cargo Area	Starboard	0	Bottom
3	Primary Structures	Offloading	Centre	1	Bottom

) were taken as examples in a comparative approach, each with significant differences in their respective criticality indices for comparison.

Table 11. Results of linguistic scale of criticality for each factor in linguistic scale.

	Factors	Asset 1	Asset 2	Asset 3
S	Surrounding equipment	High	Average	High
	Environmental impact	High	Average	Average
	Risk of explosion	High	Low	Average
	Risk of falls	Low	Low	Low
	Production shutdown	High	Average	High
	Risk of falling objects	Average	Low	Low
O	Atmospheric pollutants	High	High	High
	Wind exposure	Average	Low	Average
	Environmental temperature	High	Low	Low
	Humidity	High	Low	High
	Frequency of failure	Low	Average	Average
	Sun/rain exposure	High	Low	High
	Surfaces in contact	High	Average	Average
	Material	High	High	Average
D	Lighting conditions	Low	High	Low
	Access to equipment	High	Low	Low

presents the detailed response matrix for each asset. Once the linguistic response matrix is defined, triangular fuzzification is applied, and its degree is directly proportional to the system’s rating on the linguistic scale.

4.3.3. Performance at Each Failure Parameter

The factors were grouped by their dimensions in the RPN index, and experts were asked to assign a weight for each dimension, ranging from 0 to 1, where different factors could receive similar weights. Respondents’ weights were then normalized by summing up their specific dimension’s weights, considering only the factors deemed relevant by the experts. Normalization was necessary because the main objective of the analysis was to facilitate a comparative analysis of the factors considered, not the actual values, which might differ based on each expert’s perception of the hazard. The arithmetic average of the normalized weights was used as an aggregation function to determine a consensus weight among all the experts. Finally, a second normalization was performed so that all weights of each dimension sum one (

Table 12. Normalised weights and resultant aggregation.

RPN Dimension	Factor	Weights—Experts								Weight Aggregation
		Exp 1	Exp 2	Exp 3	Exp 4	Exp 5	Exp 6	Exp 7	Exp 8	Avg	Norm
S	Surrounding equipment	0.26	0.17	0.21	0.17	0.21	0.15	0.11	0.13	0.18	0.17
	Environmental impact	0.21	0.17	0.21	0.17	0.19	0.15	0.11	0.26	0.19	0.17
	Risk of explosion	0.26	0.17	0.13	0.17	0.10	0.31	0.22	0.26	0.20	0.19
	Risk of falls	0.13	0.17	0.21	0.17	0.21	0.31	0.22	0.26	0.21	0.20
	Production shutdown	0.13	0.14	0.13	0.14	0.10	0.08	0.11	0.08	0.11	0.11
	Risk of falling objects	-	0.17	0.11	0.17	0.19	-	0.22	-	0.17	0.16
O	Atmospheric pollutants	0.25	0.20	0.11	0.14	0.12	0.11	0.14	0.06	0.14	0.11
	Wind exposure	0.18	0.16	0.17	0.18	0.12	0.11	0.14	0.20	0.16	0.12
	Environmental temperature	0.13	0.10	0.22	0.16	0.12	0.11	0.14	0.10	0.13	0.10
	Humidity	0.08	0.20	0.06	0.18	0.12	0.22	0.14	0.16	0.14	0.11
	Frequency of failure	0.18	0.20	0.28	0.16	0.40	0.22	0.18	0.20	0.23	0.17
	Sun/rain exposure	0.20	0.16	0.17	0.18	0.12	0.22	0.14	0.20	0.17	0.13
	Surfaces in contact	-	-	-	-	-	-	0.14	-	0.14	0.10
	Material	-	-	-	-	-	-	-	0.20	0.20	0.15
D	Lighting conditions	0.58	0.44	0.33	0.47	-	0.50	0.33	0.50	0.45	0.43
	Access to equipment	0.42	0.56	0.67	0.53	1.00	0.50	0.67	0.50	0.60	0.57

).

4.3.4. Criticality Assessment

Once the factors have been analyzed by experts, it is necessary to determine the performance of each risk dimension (S, O, and D). For this, the first step is to aggregate the factors of each dimension, thus generating an aggregated triangular performance for S, O, and D.

The next step is to generate the Risk Space Diagram using the alpha-cut method, thereby facilitating the application of the weighted Euclidean distance. This method is crucial for determining the degrees of importance for the dimensions, distinguishing them as more or less significant.

Table 13. Results for RPN after weighted Euclidean distance, centroid method, and normalization.

		Asset 1	Asset 2	Asset 3
Alfa = 0	RPNiL	0.356	0.142	0.231
	RPNiR	0.833	0.611	0.739
Alfa = 0.5	RPNiL	0.480	0.264	0.351
	RPNiR	0.709	0.486	0.601
Alfa = 1	RPNiL	0.605	0.388	0.473
	RPNiR	0.586	0.363	0.466
RPN		0.595	0.376	0.477
Normalised RPN		0.690	0.251	0.453
Category		High	Low	Average

shows the final classification of assets obtained based on the aggregated and normalized metrics of the values calculated for each at the proposed alpha levels. This dynamic enables a more robust analysis of assets, promoting a better granulation of the analysis by distinguishing assets into three distinct classes.

The final RPN result for asset 2 is 0.25, while asset 1 scores 0.69. Asset 3 falls in between, with an average value of 0.45. This situation designates different classifications within the context of criticality assessment. Expanding this analysis to a larger data set, it appears that each asset receives a score that positions it as high, medium, or low criticality. From this, it is possible to carry out systematic analyzes to assist the decision-making process of selecting assets in an optimized manner.

Figure 7 presents a histogram illustrating the distribution of RPN results for the entire database considered in this study, encompassing 215 assets. The histogram shows a normal distribution pattern. Most assets fall within the vicinity of 50%. Notably, there are very few instances at the extremes, with 26% of the database belonging to the low priority class, 68% to the average priority class, and 10% to the high priority class.

To evaluate the robustness of the proposed criticality assessment and RPN model, a sensitivity analysis was conducted by varying the weights assigned to each risk dimension (Severity, Occurrence, and Detection). The sensitivity analysis involved adjusting the weights of these dimensions by 10% for each, redistributing the remaining weights of the other dimensions proportionally to maintain normalization. Specifically, scenarios were created where 10% more weight was given to Severity, Occurrence, and Detection, respectively, while comparing them to the original AHP-derived weights and a scenario where all dimensions were assigned equal weights. The results of the sensitivity analysis are presented in

Table 14. Sensitivity analysis results showing the correlation between RPN values with different weight adjustments for Severity (S), Occurrence (O), and Detection (D).

	AHP	Same Weights	10% More for S	10% More for O	10% More for D
AHP	1	0.9976	0.9931	0.9835	0.997
Same Weights	0.9976	1	0.9951	0.9843	0.9982
10% more for S	0.9931	0.9951	1	0.9817	0.9965
10% more for O	0.9835	0.9843	0.9817	1	0.9846
10% more for D	0.997	0.9982	0.9965	0.9846	1

, showing the correlation between each scenario and the original AHP weighting results.

4.4. Maintenance Portfolio Optimization

For the maintenance portfolio definition, the optimization model is applied. In this case, the objective function aims to maximize the sum of the RPN of the selected items. The restriction related to damage conditions analyzes the corrosion condition of the asset. The corrosion is measured as the average percentage of corroded area, defined as the corrosion rate, registered by inspectors according to the ASTM D610-1 guideline. The restriction is set to maintain an average corrosion rate of 10.0% for the entire set.

The main constraint regarding maintenance activity on offshore assets is the availability of man-hours (mh). Given the area of each asset and the productivity values per system (m²/mh), it is possible to calculate the mh required for each task. The productivity values vary according to the type of system, as presented in

Table 15. Standard productivity values (m²/mh) for different offshore systems.

Components’ System	Productivity (m2/mh)
Floor	0.3
Bulkhead	0.15
Staircase	0.1
Guardrail	0.1
Piping Support	0.08
Primary Structures	0.15
Electrical Support	0.1
Equipment Support	0.1
Secondary Structures	0.1
Ceiling	0.1

. This means that the cost of selecting a particular set of assets for maintenance is not only dependent on area size but also on the specific characteristics of the system, as some require more mh per square meter than others. For example, floor maintenance has the highest productivity (0.3 m²/mh), meaning it requires fewer mh per unit area compared to piping support (0.08 m²/mh), which is the least productive category. In this case study, the available resource considered was 69,500 mh, approximately 15% of the resources required to address the entire demand.

Table 16. Example of the input data for the optimization model.

id	mh	Corrosion	RPN
1	1553.50	16.00%	0.200
2	1373.00	1.00%	0.245
3	793.60	1.00%	0.376
4	4674.88	10.00%	0.266
5	366.59	33.00%	0.496
6	511.24	0.30%	0.555
7	2963.29	10.00%	0.690
8	12,540.15	16.00%	0.575

presents examples of the input data considered for the optimization model. Figure 8a presents the distribution of the dataset in terms of corrosion rate, where one can observe that assets considered of low criticality present the highest corrosion rate among all classes, while assets of high criticality present a low corrosion rate. Moreover, Figure 8b presents the distribution of mh required to conduct maintenance on the assets, where assets of average corrosion stand out, requiring most of mh, which is also a consequence of the concentration of the number of assets in this category.

When running the described optimization model, for a set of 215 assets, performance adherent to the proposed objective was observed. Out of the 215 assets, 132 were selected for painting activities execution, which represents 60% of assets with high criticality, 65% with average criticality, and 52% with low criticality. The final corrosion rate of the entire set is 7.3%.

The current portfolio definition applied by the company considers only the condition of the assets for optimization. When their model was applied to the same dataset, 10% of the assets with high criticality were selected for maintenance, while 48% of average criticality and 85% of low criticality were selected. In this case, the overall resultant corrosion rate was 4.57%.

Both models were executed under the same resource constraints, with identical available man-hours (mh) for both approaches. This ensures a fair comparison, as the total cost remains unchanged, with differences stemming exclusively from the asset selection strategy (Figure 9).

Figure 9 illustrates the distribution of mh across criticality classes in both models, revealing that the proposed model allocates twice as many mh to high-criticality assets compared to current industry practices.

5. Discussion and Analysis

The discussions stemming from the proposed integrated approach focus on two pillars: evaluating criticality and proposing an optimized portfolio. Regarding the criticality assessment, the findings indicate that experts do not consider the three RPN dimensions equally. The Severity dimension is consistently regarded as the most important by experts, therefore reaching a weight of 0.548, considerably higher than the other two dimensions, Occurrence, followed by Detection, which received weights close to 0.2.

Within the Severity dimension, factors concerning personnel safety, such as the risk of falls or explosions, take precedence. In contrast, considerations related to financial loss, such as production shutdown, hold less significance. Furthermore, in the Occurrence dimension, the frequency of failures, mainly linked to coating breakage, emerges as the most prominent factor, closely followed by exposure to weathering conditions. Within the Detection dimension, the ease of access takes greater precedence than lighting conditions.

Notably, assets situated in a production module with thermal activity and gas processing exhibit a notably high level of criticality for most severity-related factors. In contrast, assets located in naval modules registered comparatively lower to average values for these same factors. Environmental conditions primarily influence occurrences. Notably, assets located in exposed areas receive significantly higher criticality values for most of these factors than those in non-exposed areas.

The sensitivity analysis shows that the proposed criticality assessment model is robust, with high correlation values across all weighting scenarios. Even with a 10% increase in the weights for Severity, Occurrence, and Detection, the rankings of assets remained stable, with the lowest correlation observed being 0.9835 for the Occurrence dimension. This stability suggests that moderate changes in the importance assigned to each RPN dimension do not significantly impact the prioritization of critical assets, making the model resilient to variations in expert judgment. Therefore, the framework can be confidently applied across different contexts or expert groups without significantly altering the prioritization outcome. The consistency across different weightings ensures that the method can be confidently used for maintenance planning, allowing for different emphasis on risk dimensions without undermining the effectiveness of asset prioritization.

Moreover, the maintenance portfolio optimization proposed combines information of criticality with damage condition and considers the constraint of resources available. The current method applied by the company considers only information about the damage condition for the portfolio definition. Results show that 60% of the assets considered high criticality were selected for maintenance on the proposed method, while only 10% were selected on the current method.

However, an important trade-off was observed in this comparative scenario between the current and proposed methods: when there is an improvement in the percentage of selection of items with high criticality, the impact on the remaining data sets’ corrosion is low. The given scenario was evaluated based on the optimization achieved through the same operational resources. Now, when the impact on the remaining corrosion is considerable, the percentage of selected items with high criticality is lower. In this regard, the current method resulted in an average corrosion of 4.57%, while in the proposed method the observed average corrosion was 7.27%. This comparison between the performances of the methods makes it evident that the proposed method, based on asset criticality, should be prioritized over the current one, which is based solely on platform degradation, provided that the same minimum target percentage of corrosion (goal) is established for both methods, which was reached in both cases.

From a cost perspective, offshore maintenance contracts are typically structured based on man-hours (mh), making mh a direct reference for cost estimation. Since both models were executed under the same mh availability, the total cost remains identical. However, the allocation of these mh differs between approaches. In the current method, a larger portion of available mh is assigned to low-criticality assets, which generally have higher surface areas but lower maintenance urgency, leading to a more pronounced reduction in overall corrosion. Conversely, the proposed method directs more mh to high-criticality assets, doubling the allocation to critical components compared to the current practice. This ensures that structurally and operationally essential assets receive the necessary attention, even if the overall corrosion level is slightly higher.

This comparison of method performance reinforces that the proposed method, which prioritizes asset criticality, is preferable to the current industry practice, provided that the same minimum corrosion target (goal) is established for both approaches. Since the total mh and cost remain constant, adopting a criticality-based approach ensures a more strategic allocation of resources, focusing on the integrity and reliability of key structural components, rather than solely minimizing overall corrosion levels.

It is important to note that while the proposed optimization model is static in nature, it incorporates the corrosion percentage as a key factor that reflects the asset’s condition over time. Although the RPN is based on static information, which refers to characteristics that remain constant, such as the asset’s operational function and environmental exposure, the corrosion percentage is periodically updated. This periodic update allows for dynamic adjustments in the model. Specifically, the painting plan is recalculated annually, considering the variations in corrosion percentage, ensuring that the portfolio adapts to the evolving condition of the assets. Our method also emphasizes the need for regular reassessment, ensuring that the maintenance plan remains aligned with the actual state of degradation over time. This approach introduces adaptability into the decision-making process, allowing the maintenance strategy to evolve as asset conditions change.

6. Conclusions

This research proposed a framework rooted in RCM principles for asset management on offshore assets for prioritization and optimization of the maintenance portfolio. It was built based on a literature survey and experts’ opinions, and incorporates fuzzy logic and decision support methods to conduct a comprehensive FMEA analysis across complex systems. The results of the FMEA are input for an optimization method that considers constraints of damage condition and availability of resources, adherent to business demands to define a reliable maintenance portfolio. The novelty of the work lies in its integration of MCDM methods under uncertainty with integer programming to address real-world business demands, providing a more reliable maintenance portfolio than traditional approaches.

The methodology was applied in the context of offshore oil rigs and encompassed the key corrosion factors specific to the offshore asset environment, categorized components with similar characteristics, and assessed the leading elements of corrosion. It generated an RPN index for each component group. The components’ system prevailed as the most influential characteristic of the failure mode, followed by the modulus function. Moreover, factors that characterized the severity of the damage were ranked as most critical, followed by occurrence and detection.

Following this classification, the evaluated assets were subjected to an optimization model, aiming to facilitate an intelligent asset selection, prioritizing those with higher levels of criticality compared to others. The proposed method demonstrates a significant increase in prioritization of critical assets when compared to the predominant practice in the analyzed company. Our findings reveal a substantial discrepancy between the two methodologies. Specifically, the results indicate that the implementation of the proposed method resulted in the selection of 60% of assets categorized as highly critical for maintenance. In stark contrast, the current industry method exhibited significantly inferior performance, selecting only 10% of assets considered highly critical. This discrepancy is relevant because the company’s current method underestimates high-risk assets, potentially leading to unplanned failures and increased safety risks, which our method successfully captures and mitigates.

This conjuncture highlights not only the intricacies of practice but also the theoretical contribution of the research through the analysis of real business constraints and technical factors influencing the corrosion of offshore assets. These elements were carefully mapped in the literature and discussed with sector experts. The practical significance of the proposed methodology manifests in two key aspects: (a) the delineation of criticality levels for components and (b) the formulation of a corrosion maintenance plan based on condition assessment. Furthermore, applying this proposed framework enables the prevention of unplanned operational stoppages due to failures in the long-term planning horizon, as it generates optimized portfolios by prioritizing assets with high operational relevance.

Based on the findings of this study, several promising areas for future research could enhance corrosion management strategies and decision-making in the O&G industry. Regarding Maintenance Prioritization, researchers can develop a methodology for conducting a more detailed FMEA at the component level. This approach could aggregate the results into larger assets, providing a more granular understanding of maintenance priorities. Additionally, exploring alternative MCDM methods for combining criticality and degradation indexes is worthwhile, incorporating expert opinions. A comparative analysis of different MCDM approaches can enhance the robustness of maintenance prioritization. Hence, this study paves the way for future research to significantly advance maintenance management practices within the O&G industry. Moreover, future research could explore the potential application of this methodology to other asset-intensive industries (e.g., power plants, rail infrastructure, aerospace), assessing its adaptability and effectiveness in different operational contexts. By expanding its scope beyond the O&G sector, this approach could contribute to broader advancements in maintenance optimization across various domains.