Identifying the Importance of Key Performance Indicators for Enhanced Maritime Decision-Making to Avoid Navigational Accidents

Abstract

Despite ongoing advances in maritime safety research, ship accidents persist, with significant consequences for human life, marine ecosystems, and port operations. Because many accidents occur in or near ports, assessing a vessel’s ability to enter or depart safely remains critical. Although ports apply local navigational rules, safety criteria could be strengthened by adopting more adaptive and data-informed approaches. This study presents a mathematical framework that links Key Performance Indicators (KPIs) to a Ship Risk Profile (SRP) for collision/contact/grounding risk indication. Expert-based KPI importance weights were derived using the Average Rank Transformation into Weight method in linear (ARTIW-L) and nonlinear (ARTIW-N) forms and aggregated into a nominal SRP. Using routinely monitored KPIs largely drawn from the Baltic and International Maritime Council and Port State Control/flag-related measures, the results indicate that critical equipment and systems failures and human/organisational factors—particularly occupational health and safety and human resource management deficiencies—are the most influential contributors to the normalised accident-risk index. The proposed framework provides port authorities and maritime stakeholders with an interpretable basis for more proactive risk-informed decision-making and targeted safety improvements.

1. Introduction

Throughout maritime history, ship casualties have had catastrophic impacts, affecting human life, societal wellbeing, and environmental integrity. In response to these severe events, the International Maritime Organization (IMO) introduced new regulations and updated existing rules aimed at enhancing maritime transport safety [1,2]. Historical records reveal an extensive and concerning list of maritime accidents, accompanied by substantial human casualties [3]. Data from the IMO indicate that approximately 20% of all maritime accidents involve ship collisions, resulting annually in notable economic damages, fatalities, environmental pollution, and other detrimental consequences [4].

The global increase in demand for raw materials and manufactured products has led to a rise in both the number and size of ships traversing international waters. Consequently, this trend creates denser maritime traffic and significantly escalates collision risk. The severity of consequences following marine accidents has also intensified, potentially reaching catastrophic scales [5]. Research on maritime accidents has evolved significantly, undergoing various fundamental transformations. Gaining insights into these developments allows maritime industry stakeholders to evaluate past actions critically, enhance future maritime safety measures, and substantially reduce risks associated with vessels, their crews, cargo, and marine ecosystems [6].

Maritime accidents present considerable risks to human safety, environmental sustainability, and the resilience of global supply chains [7,8]. Various types of maritime accidents such as collisions, contacts and groundings, each contribute differently to maritime casualty statistics. Collisions are noted as both the most common and severe type of accident, frequently caused by breaches of navigational regulations and human errors. Research by Uğurlu [9] highlights that human-related factors, especially errors in perception and manoeuvring, constitute the majority of collision accidents, underlining the importance of improved training programs and stricter adherence to safety protocols. Although groundings and fires occur less often, they can produce significant environmental damage and substantial economic losses [10,11]. The Ever Given grounding accident in the Suez Canal notably demonstrated how such accidents can severely disrupt global trade operations [12]. Furthermore, studies focusing on risks specific to ports, such as those conducted in Tianjin and Hong Kong, highlight how local operational practices and regulatory environments shape the nature and frequency of accidents [13,14].

Safe maritime operations remain essential for port functionality, with ship entry, mooring, and unmooring being particularly challenging processes [15]. Stakeholders, including port authorities, vessel owners, and ship operators, prioritise ensuring that risk levels remain acceptably low. Thus, there is a need for methodologies capable of swiftly and effectively assessing risks related to maritime operations, especially in confined and congested waters.

In the maritime industry, numerous risk assessment methodologies exist to analyse specific risks under defined constraints. However, a comprehensive evaluation of maritime safety necessitates the simultaneous consideration of multiple interconnected factors. To achieve detailed and reliable safety assessments for individual vessels or entire fleets, it is essential to adopt a unified method capable of integrating diverse data streams into a coherent analytical framework.

This paper proposes a model that estimates navigational-accident risk from maritime Key Performance Indicators (KPIs). Expert-elicited KPI ranks are transformed into weights using the Average Rank Transformation into Weights—linear (ARTIW-L) and nonlinear (ARTIW-N)—and aggregated into a Ship Risk Profile (SRP) that varies with observed KPI performance. While the Baltic and International Maritime Council (BIMCO) framework offers comprehensive KPIs for monitoring operational performance, their linkage to accident risk remains under-explored. By quantifying how degraded KPI scores shift the SRP, the model provides a tractable way to assess—and potentially reduce—navigational-accident risk for collisions, contacts, and groundings. The novelty of this study lies in operationalising an expert-weighted KPI-to-risk mapping that yields an interpretable nominal SRP and a ship-specific normalised accident-risk index suitable for proactive navigational decision support.

Following the introduction, Section 2 reviews navigational-accident statistics, common contributing factors, and established maritime risk-assessment approaches. Section 3 describes the methodology used to derive expert-based KPI weights using ARTIW-L/ARTIW-N and to construct the nominal SRP and the normalised accident-risk index $P$. Section 4 presents the results of the expert evaluation and the resulting KPI priorities and weights. Section 5 discusses the implications of the findings, links them to related evidence, and outlines limitations and directions for future research. Section 6 concludes the paper.

2. Literature Review

2.1. Accident Statistics: Scale, Types, and Locations

Whenever a significant maritime accident occurs, the international community typically responds by implementing new preventive measures. Consequently, the conventional method of enhancing maritime safety tends to be reactive instead of proactive [3]. It is crucial to carefully consider the existing information, explore how it can be practically applied, and identify gaps in knowledge that must be addressed to ultimately achieve the goal of entirely preventing maritime accidents. The ship accident-avoidance problem still exists, and Figure 1 illustrates the long-term pattern in the number of maritime accidents reported from 1978 to 2023.

As shown in Figure 1, the number of maritime accidents decreased from a peak of 3152 in 1979 to a low of 959 in 2001. However, it increased again in 2002, reaching a second peak in 2008. The third peak emerged in 2014 and has remained relatively high in recent years, with another maximum of 2388 accidents recorded in 2019. Over the past 46 years, the total number of maritime accidents is estimated at around 86.5 thousand, averaging approximately 1.9 thousand per year. About 2000 seafarers lose their lives annually [6].

According to the European Marine Casualty Information Platform (EMCIP) database—a data distribution system used to store information about marine casualties and incidents, operated by the European Commission, EU/EEA Member States, and EMSA—the distribution of navigational accidents is approximately 41.0% contacts, 30.3% collisions, and 28.7% groundings [17].

The accident sample comprises contacts, collisions, and groundings that occurred within port limits or other confined waters (Figure 2). Most accidents happened in port areas 54.0%, with a further 22.4% in internal or inland waters; only 19.1% occurred in the territorial sea and 4.5% in the open sea. This distribution indicates elevated risk in congested, spatially constrained settings, where traffic density, restricted manoeuvring space, proximity to port infrastructure, and frequent vessel interactions increase the likelihood of human error, miscommunication, or technical misjudgement.

2.2. Common Factors Leading to Ship Accidents

Navigational accidents often occur under adverse weather conditions, particularly when vessels lack sufficient power or manoeuvrability. A structured analysis of publicly available maritime accident reports revealed insightful patterns regarding vessel types involved in such accidents. Notably, General Cargo ships accounted for the highest percentage (31%) of these accidents, followed by Bulk Carriers (21%) and Ro-Ro Ferries (19%), underscoring significant differences in accident susceptibility across various ship categories [18].

The relationship between ship age and accident rates indicates that older vessels do not necessarily experience more accidents than newer ones; sometimes newer ships even show higher accident frequencies. Factors influencing accident likelihood include vessel type, quality standards during shipbuilding, maintenance practices, operational seamanship, timing of major class inspections, and vessel ownership changes [2]. Furthermore, accident and incident reports can effectively support evidence-based risk modelling, as demonstrated by introducing an updated version of the Human Factors Analysis and Classification System (HFACS). This approach identified operator errors as the primary cause of grounding, notably linked to poor bridge communication and cooperation [19].

The influence of port tugs on navigational safety has been widely discussed in recent research. Key risks within port areas include inadequate training of both ship crews and port personnel, insufficient maintenance and outdated equipment of port tugs, as well as ineffective communication during vessel arrivals. These issues were examined by Paulauskas [15], who also emphasized the importance of a strong safety culture in minimizing navigational risks. Channel and basin depths are particularly critical for safe manoeuvring in ports, which necessitates regular dredging and infrastructure maintenance. A related study [20] highlighted the importance of managing vessel speed within ports, both to enhance navigational safety and to reduce environmental impacts. Jensen [21] created a Bayesian Network (BN) model to evaluate collision risks in busy shipping lanes, considering vessel traffic information and environmental conditions. Their findings indicate that traffic density and vessel size significantly influence collision risk and should be considered in port and confined-water risk assessments.

Several studies have explored the underlying circumstances and contributing factors leading to ship accidents by applying systematic analysis of available data. In one study, researchers identified recurring patterns such as pilotage-related operations, failure to utilize navigational aids, inadequate navigational attention, lack of lookout, and the meeting of large vessels as common causal elements [22]. Complementing this approach, a qualitative analysis utilizing Automatic Identification System (AIS) data was conducted to investigate accident causation using parallel coordinates graphs—a method well-suited for identifying recurring parameter patterns such as vessel speed, type, size, weather conditions, and time of day [23]. This visualization technique revealed that vessel collisions frequently occurred when ships were moving at relatively low speeds compared to the average in similar situations, highlighting speed deviation as a notable risk factor. The integration of empirical data and advanced visualization techniques offers valuable insights for improving navigational safety and supporting evidence-based decision-making in maritime operations.

Aalberg [24] performed a statistical analysis of factors linked to navigation accidents using AIS data, vessel data from Information Handling Services, and accident databases. Their analysis aimed to support evidence-based risk modelling and identify indicators predicting navigation accidents. Employing both bivariate and multivariate statistical methods, they identified key characteristics associated with vessels involved in accidents, including vessel type, age, size, sailing distance, higher average speed, ship’s flag, MoU rating, and inclusion in the U.S. Coast Guard (USCG) target list. The ultimate goal was to develop a comprehensive risk-monitoring model tailored to Norwegian waters.

Additional inductive qualitative analysis by Yıldırım [25] using the HFACS framework reinforced the critical role of human factors in ship grounding and collision accidents. Their study pinpointed unsafe acts and human-related preconditions as principal causes of such accidents. Supporting these findings, collision accident data analysed by Ugurlu and Cicek [5] revealed that approximately 94% of collisions resulted from human error. Specifically, Yıldırım [25] highlighted decision errors, poor resource management, violations, communication failures, adverse mental states, inadequate planning, and skill-based mistakes as common collision factors. In the case of grounding accidents, the main factors identified included inadequate resource management, insufficient passage planning, poor internal bridge communication, and understaffed bridge operations. It is important to note that accident databases differ in terms of taxonomy and investigation depth, which may influence the attribution and categorization of causal factors. To ensure consistency and comparability, future research should aim to apply unified classification frameworks when analysing the multifactorial nature of maritime accidents—an example of such an approach can be seen in the EMSA accident investigation system.

Paulauskas [26] reports that many ship collisions and accidents arise from the human element alongside organisational, technical, environmental, and other contributing factors, and that mitigation remains challenging given small crew sizes, intensive work schedules, and operational constraints.

2.3. Methods for Maritime Risk Assessment

An accident model is defined as a simplified description of a system or process designed to assist the representation of accident occurrences based on an accident theory [3]. Various accident theories and models are recognized in this context, including Statistical analysis and theories, Risk analysis, Domino theory, Epidemiologic theory, and Control and system theoretic models. Statistical analysis aims to identify trends through computational methods, while risk analysis aids decision-makers by providing computed risk values paired with risk control options. Domino theory, Epidemiologic theory, and Control and system theoretic models focus primarily on subjective analysis, establishing chains of events leading to accidents and employing various techniques to control system behaviour and prevent unwanted accidents.

Maritime accident analysis employs probabilistic risk assessments, Bayesian Networks (BN), and Fault Tree Analysis (FTA), to assess the causes and impacts of accidents [5,27]. According to Dinis [28] most promising models to be applied to marine autonomous surface ships use BNs as the modelling method. FTA and BN, using EMCIP data, offer a robust framework for maritime risk assessment. FTA identifies human error pathways leading to accidents, while BN models dependencies among Risk Influencing Factors. According to Jovanović [29] this integrated approach enhances risk evaluation, pinpointing key contributors. By providing actionable insights, it strengthens risk management strategies, helping to mitigate human error and improve shipping safety.

Integrating fuzzy logic with Bayesian-network (BN)-based risk models can help address epistemic uncertainty and imprecision in maritime risk analysis, particularly when input data are incomplete or linguistically assessed. For example, Aydin et al. [30] applied a fuzzy Bayesian network approach to support collision-risk analysis in narrow waters, while Akyuz et al. [1] incorporated fuzzy logic into fault tree and event tree analysis for cargo liquefaction risk, improving robustness under limited precise data. In addition, advanced technologies such as machine learning and the Internet of Things (IoT) can enhance BN models by enabling the assimilation of real-time data streams and supporting predictive analytics [31,32,33]. Such integration has the potential to advance maritime safety by enabling more automated risk assessment and more dynamic decision support in operational settings [28].

Traditional models for analysing ship-grounding accidents often fall short in fully utilizing available evidence, relying instead on expert judgment and statistical records. To address this gap, a more evidence-based approach was developed by Bye and Aalberg [34], who integrated diverse data sources to construct scenarios that better reflect real-life maritime conditions. Automatic Identification System (AIS) data served as a core component in building indicators to represent ship activity at the time of the accident—such as vessel speed, number of port calls, hours since last port departure, course alterations, as well as general ship characteristics including category, age, flag, and nearby vessel traffic. The researchers combined chi-square statistic and correspondence analysis to explore significant associations between ship type and accident type. Their findings revealed a range of risk factors influencing ship safety at sea, particularly those related to vessel characteristics (speed, traffic density, equipment, port call frequency, registry, classification, size, Paris MoU status) and accident location. From the human factor perspective, key risk indicators included fatigue, automation challenges, situational awareness deficits, communication issues, poor decision-making, inadequate teamwork, stress, and health-related factors. Operational failures such as insufficient planning, non-compliance with the safety management system, and inadequate bridge manning were also highlighted. Additionally, environmental and contextual factors like adverse weather, wind speed, wave height, darkness, geographical location, seasonal conditions, and ice concentration were identified as significant contributors to maritime accidents.

Previous research confirms that the consequences of navigational accidents can be significant, and while numerous methods have been developed to analyse contributing factors, there is still a lack of a unified framework capable of integrating different types of data into a dynamic risk evaluation process. A key challenge is the fragmented nature of existing information: large volumes of data are collected across different sources, formats, and levels of granularity, often making it difficult to apply them consistently in real-time decision-making.

Safety, particularly in relation to unmanned ship operations, remains a significant concern, primarily achievable through the reduction of human-related maritime accidents [35]. To evaluate ship accidents, a safety assessment framework employing a two-step what-if analysis, supported by the Human Factors Analysis and Classification System for Marine Accidents method, has been developed alongside a straightforward consequence check. This analytical approach evaluates whether an accident might still occur in the absence of human presence and assesses if the consequences would vary without personnel intervention. The methodology enhances comprehension of accident risks and probabilities specific to unmanned vessels by eliminating common human errors such as poor situational awareness, inadequate mechanism supervision or maintenance, duty distractions, adherence to inappropriate passage plans, challenging visibility conditions, disregard for established safety procedures, and improper cargo stowage. Additionally, vessel classification, equipment integrity, and sensor reliability significantly impact overall maritime safety.

The ship risk profile, developed under the Paris Memorandum of Understanding (Paris MoU) on Port State Control (PSC) and supported by Directive 2009/16/EC, serves as a core tool in the risk-based inspection regime. The idea was first proposed by Sage [36], who argued that the establishment of criteria for identifying High-Risk Vessels within the Paris MoU region could assist coastal states in monitoring ship movements within their jurisdictional waters. The primary objective of the SRP, as defined by the Paris MoU, is “to reward quality shipping and to intensify control and sanctions on ships with poor performance” [37,38]. Under this regime, ships meeting defined safety and performance criteria are categorized as Low Risk Ships and benefit from extended inspection intervals of up to 36 months. Ships classified as Standard Risk Ships are subject to intervals of up to 12 months, while High Risk Ships—those with poor safety records—are subjected to mandatory expanded inspections every six months when calling at a Paris MoU member state port. This profiling system thus enables PSC authorities to prioritize inspections and allocate resources more effectively towards vessels that pose higher safety risks [28,36]. In doing so, coastal states gain greater awareness of potentially non-compliant vessels and are able to take proactive measures, ranging from enhanced monitoring to physical intervention, to ensure regulatory compliance and protect national interests.

Since risk consists of two fundamental parameters—the probability of occurrence and the severity of consequences—the probability of human error during critical shipboard operations becomes a key factor in determining the overall risk level. According to statistics about 80% of maritime accidents are attributed to human error [1,17,39,40,41]. Maritime authorities actively work to prevent the occurrence of such errors. Therefore, it is crucial to analyse the circumstances under which human errors are likely to occur in maritime operations [42]. The probability of human error is one of the core components of quantitative risk analysis, especially when calculating likelihood. Consequently, most risk analysis methods address the contribution of human error; however, it is worth noting that not all methods are capable of handling diverse types of input data—such as ship-specific performance indicators—which often require evaluation by maritime experts.

In order to move from a reactive to a proactive approach in maritime safety, the focus should be placed on data observation and the identification of causal links between specific data points and errors leading to ship accidents. SRP model developed by the Paris MoU demonstrates how structured criteria can be used to effectively monitor inspection resources and enhance safety outcomes. Building on this philosophy, there is a compelling rationale to explore additional observation-based data that could further improve risk identification. One of the most effective ways to manage risk is through continuous monitoring of critical operational areas using KPIs, which should be selected and evaluated by maritime experts. In this context, the Baltic and International Maritime Council (BIMCO)—one of the world’s largest international shipping associations representing ship-owners—plays a leading role and covers a wide range of areas, including compliance with environmental regulations; crew health, safety, and injury prevention; training, retention, and competence of personnel; navigational risks and accident prevention; operational efficiency; security performance; technical reliability and maintenance; and inspection outcomes, including Port State Control results [43,44].

Expert-based multi-criteria decision-making (MCDM) methods are widely used in transport and maritime research to support complex operational decisions when multiple technical, operational, and human-factor criteria must be balanced. In maritime operations, such approaches have been applied to decision-support problems in port and Vessel Traffic Service (VTS) contexts. For example, Shin and Song [45] developed a vessel-arrival priority determination model for VTS management in which evaluation factors were derived using the Delphi technique, while criterion weights were calculated using fuzzy and conventional Analytic Hierarchy Process (AHP); the resulting model was evaluated through scenario-based simulations involving experienced VTS officers. In transport research more broadly, expert-based MCDM methods built around Average Rank Transformation into Weights—linear (ARTIW-L) and non-linear (ARTIW-N)—have been developed to convert simple expert rankings of criteria into normalised subjective weights. In ARTIW-L, weights are linearly related to average ranks, while ARTIW-N applies a non-linear transformation that emphasises the most and least important criteria; in both cases, the input is an ordinal rank and the output is a cardinal weight vector that sums to one, with agreement of expert opinions assessed using Kendall’s coefficient of concordance and χ² tests [46,47,48,49]. These methods are attractive because they are transparent, computationally simple, and allow the combination of several expert-weighting algorithms (e.g., ARTIW-L, ARTIW-N, AHP) to be treated as a more robust estimate of underlying criterion importance.

ARTIW-based schemes can handle medium-to-large sets of criteria, integrate heterogeneous expert groups, and yield consistent priorities for safety, environmental, economic and service-quality indicators [46,47,48,49]. By analogy, the same approach can be used in maritime safety studies to transform expert rankings of KPIs or other risk factors into weights that quantify their relative contribution to navigational accident risk, provide a basis for concordance analysis between stakeholder groups (shipowners, masters, pilots, VTS, regulators), and supply a coherent set of input weights for subsequent probabilistic models, Bayesian networks or simulation-based risk assessments. This represents an untapped opportunity to build a more proactive maritime safety strategy. To the authors’ knowledge, however, ARTIW-based expert weighting has not yet been systematically applied to maritime KPI frameworks to derive a ship-level SRP and an associated normalised accident-risk index for collisions, contacts and groundings. The present study addresses this gap by combining expert-based KPI ranking with ARTIW-L/ARTIW-N weighting to construct a nominal SRP and an interpretable index P for navigational-accident risk indication.

While multiple maritime risk assessment frameworks exist—including probabilistic/causal models (e.g., BN, FTA, HFACS-based analyses, and MCDM-derived approaches) and inspection-based profiling such as the Paris MoU ship risk profile—their practical application typically relies either on detailed accident-causation variables or on compliance/inspection-related performance signals. The present study distinguishes itself by operationalising an expert-weighted mapping from a broader KPI set into a nominal Ship Risk Profile and a ship-specific normalised accident-risk index obtained by combining that nominal profile with the vessel’s observed KPI states. The KPI set deliberately combines operational, technical, human-factor, and regulatory-performance indicators (e.g., maintenance reliability, work–rest compliance, competence and organisational deficiencies, and PSC/flag-related measures) that can be monitored routinely and interpreted as performance signals relevant to navigational-accident avoidance. In this way, the proposed framework functions as an interpretable translation layer from KPI monitoring to risk-oriented screening and prioritisation, without presenting the normalised accident-risk index as an absolute accident probability.

3. Materials and Methods: KPI Ranking, ARTIW Weighting, and SRP Construction

In this study, expert assessments are used to derive normalised importance weights for maritime KPIs and to construct a nominal Ship Risk Profile (${SRP}^{nom}$) for navigational-accident risk indication. The workflow consists of: (i) collecting expert KPI importance assessments and converting them into a priority order, (ii) testing inter-expert agreement using Kendall’s coefficient of concordance [50], (iii) transforming aggregated KPI ranks into weights using the linear ARTIW-L and nonlinear ARTIW-N methods [46,47,48,49], and (iv) aggregating these weights into ${SRP}^{nom}$ and the normalised accident-risk index $P$. Research flowchart for constructing ${SRP}^{nom}$ and calculating the normalised accident-risk index $P$ is presented in Figure 3.

The ARTIW-L and ARTIW-N methods are well suited to the objectives of this study, as they operate directly on expert importance rankings and support explicit assignment of zero importance to indicators, allowing non-relevant KPIs to be excluded when full expert agreement is achieved. The combined use of linear and nonlinear transformations provides a weighting structure that simultaneously preserves proportional importance and emphasises the most and least influential KPIs. In contrast to pairwise-comparison-based approaches, such as AHP, ARTIW avoids pairwise comparisons between indicators, which makes it simpler to apply to a large set of indicators. Moreover, the ARTIW framework supports iterative development, enabling additional KPIs to be incorporated in future research through re-ranking and re-normalisation without altering the existing KPI structure.

Section 3.1 describes the KPI set, expert panel and questionnaire; Section 3.2 and Section 3.3 define the ARTIW-L and ARTIW-N weighting procedures; Section 3.4 presents the agreement (consistency) analysis; and Section 3.5 defines ${SRP}^{nom}$ and the calculation of the normalised accident-risk index $P$.

3.1. Expert Panel, KPIs and Questionnaire

The expert panel is designed as a group of navigational practitioners (experts). Panels of approximately 10–20 experts are commonly considered sufficient in expert-based multicriteria and safety assessments. In this methodology, the panel size is selected so that the total number of experts is not less than the half number of KPIs being evaluated, and the consistency of their judgements is subsequently assessed using concordance measures such as Kendall’s W. Experts are drawn from three professional categories—masters, chief mates and pilots—with at least five years of professional experience in the maritime sector. Where possible, the panel composition is balanced across these three groups; however, exact equality in category sizes is not critical, provided that all categories are represented and the overall panel remains sufficiently large and diverse for subsequent aggregation of rankings and consistency analysis. Such expert-driven qualitative evaluation is consistent with contemporary best practices in maritime safety assessments and risk management [51,52,53,54].

KPIs can be adopted from external sources such as BIMCO [44], or developed independently to characterise the technical condition of the ship, the organisation of shipboard operations and human-factor management.

Accident investigations provide detailed reports identifying the primary factors contributing to an accident. To examine the root causes of navigational accidents, these contributing factors—risk factors—can be related to maritime KPIs by experts. The questionnaire is designed to assess the relationship between each KPI and these risk factors, based on experts’ experience. Using their professional judgement, domain knowledge and operational experience, experts assess every KPI using a four-level importance scale from 0 to 3 in response to the question: How important is this KPI for assessing the ship’s and crew’s ability to avoid a collision, contact or grounding accident? The scale is defined as follows:

• 0—not important (no meaningful link with accident risk);
• 1—slightly important (limited link with accident risk);
• 2—important (clear but not critical link with accident risk);
• 3—very important (direct or critical link with accident risk).

These qualitative evaluations are used to select and prioritise the most relevant KPIs for further analysis and to provide the input data for the rank-based weighting procedures with the ARTIW-L and ARTIW-N methods.

3.2. ARTIW-L Weighting of KPIs

The ARTIW-L method converts expert ranks of the KPIs into a vector of normalised subjective weights. Let $m$ be the number of KPIs and $n$ the number of experts. Denote by $R_{ij}$ the rank assigned by the $j$-th expert $\left(j=1,2,\dots ,n\right)$ to the $i$-th KPI $\left(i=1,2,\dots ,m\right)$, where rank 1 corresponds to the most important KPI and rank $m$ to the least important one. For each KPI, the average rank is calculated as:

$${\overline{R}}_i={\displaystyle \frac{1}{n}}\sum _{j=1}^n{R}_{ij},$$

(1)

where ${\overline{R}}_i$ is the mean rank of the $i$-th KPI; $R_{ij}$ is the rank given to the $i$-th criterion by the $j$-th expert.

The ARTIW-L method then linearly transforms these average ranks into normalised weights [47,48]. The weight of the $i$-th KPI is calculated from the formula:

$${\omega }_i^L={\displaystyle \frac{\left(m+1\right)-{\overline{R}}_i}{\sum _{i=1}^m{\overline{R}}_i}},$$

(2)

where ${\omega }_i^L$ is the normalised subjective weight of KPI $i$ obtained by ARTIW-L.

By construction, ${\omega }_i^L\ge 0$ and $\sum _{i=1}^m{\omega }_i^L=1$. Smaller average ranks (higher expert priority) yield larger weights, and ${\omega }_i^L$ is in a strictly linear inverse functional relationship with $R_i$. This makes ARTIW-L a simple, transparent rank-based weighting scheme that preserves the ordinal priorities of the KPIs while producing a metric weight vector suitable for further quantitative analysis.

3.3. ARTIW-N Weighting of KPIs

The ARTIW-N method provides an alternative way of transforming average ranks into normalised subjective weights. In this case, the weights ${\omega }_i^N$ are related to the criteria average ranks ${\bar{R}}_i$ by a nonlinear inverse functional relationship [49]. As in Section 3.2, $m$ is the number of KPIs and $n$ is the number of experts, and the average rank ${\bar{R}}_i$ given to each criterion is calculated according to Equation (1).

Using the average ranks ${\bar{R}}_i$ of all $m$ criteria, the ARTIW-N method first calculates an intermediate value $u_i$ for each KPI as the ratio between the minimum average rank and the average rank of KPI $i$:

$$u_i={\displaystyle \frac{\underset{i}{\mathrm{m}\mathrm{i}\mathrm{n}}{\bar{R}}_i}{{\bar{R}}_i}},$$

(3)

These intermediate values are then normalised to obtain the ARTIW-N weights, calculated from the formula:

$${\omega }_i^N={\displaystyle \frac{u_i}{\sum _{i=1}^m{u}_i}}.$$

(4)

By construction, ${\omega }_i^N\ge 0$ and $\sum _{i=1}^m{\omega }_i^N=1$. The weights ${\omega }_i^N$ are in a nonlinear inverse relationship with the average ranks ${\bar{R}}_i$: KPIs with very low average ranks receive relatively higher weights than under a purely linear transformation, while mid-ranked KPIs are slightly down-weighted. This nonlinear transformation “amplifies” the significance of the most important and the least important criteria by reducing the relative significance of criteria with medium importance, while preserving the same priority order of criteria as the ARTIW-L method [47].

Together, ARTIW-L and ARTIW-N provide two complementary rank-based weighting schemes: ARTIW-L maintains a strictly linear inverse relationship between ${\bar{R}}_i$ and the weights, whereas ARTIW-N emphasises the extremes of expert rankings, which can be useful in risk assessment when the most and least important KPIs are of particular interest.

3.4. Consistency of Expert Rankings

The averages of expert ranks and the corresponding ARTIW-based weights can be used as reliable results only if the experts’ opinions are sufficiently consistent and non-contradictory. The degree of consistency of the expert group is expressed by Kendall’s coefficient of concordance $W$, which takes values in the interval $\left[\mathrm{0,1}\right]$: $W\approx 1$ indicates strong agreement, whereas $W\approx 0$ indicates that expert rankings are essentially random. When tied ranks occur in the experts’ rankings, the coefficient $W$ is adjusted by applying the standard tie-correction factor as recommended by Kendall and Gibbons [50]. The coefficient of concordance $W$ is calculated from the formula:

$$W={\displaystyle \frac{12\sum _{i=1}^m{\left[\sum _{j=1}^n{R}_{ij}-\frac{n\left(m+1\right)}{2}\right]}^2}{n^{2}m\left(m^2-1\right)-n\sum _{j=1}^n{T}_j}},$$

(5)

where $m$ is the number of KPIs, $n$ is the number of experts, and $R_{ij}$ is the rank given to the $i$-th criterion by the $j$-th expert. The correction factor $T_j$ accounts for tied ranks in the ratings of the $j$-th expert and is calculated from the groups of identical ranks assigned by that expert.

The correction factor $T_j$ accounts for tied ranks within the ratings given by the $j$-th expert and is calculated as:

$$T_j=\sum _{k=1}^g\left(t_{kj}^3-t_{kj}\right),$$

(6)

where $t_{kj}$ is the size of the $k$-th group of identical ranks (ties) assigned by the $j$-th expert, and $g$ is the number of such groups in that expert’s ranking. When there are no ties, all $T_j=0$ and the denominator in Equation (5) reduces to the standard form $n^{2}m\left(m^2-1\right)$.

The calculated value $W$ is compared with its minimum value $W_{\mathrm{m}\mathrm{i}\mathrm{n}}$, which depends on the chosen significance level $\alpha$ (typically $\alpha =0.05$ or, more stringently, $\alpha =0.01$) and the number of degrees of freedom $v=m-1$ [46,47,48,49]:

$$W_{\mathrm{m}\mathrm{i}\mathrm{n}}={\displaystyle \frac{{\chi }_{\alpha ,v}^2}{n\left(m-1\right)}},$$

(7)

where ${\chi }_{\alpha ,v}^2$ is the critical value of the Pearson’s chi-square statistic with $v=m-1$ degrees of freedom. If $W\ge W_{\mathrm{m}\mathrm{i}\mathrm{n}}$, the experts’ judgements are considered to be in agreement.

The same consistency condition can be expressed in terms of the chi-square statistic. Under the null hypothesis of no agreement between experts, the random variable is calculated as:

$${\chi }^2=W\hspace{0.17em}n\hspace{0.17em}\left(m-1\right),$$

(8)

where ${\chi }^2$ approximately follows a chi-square distribution with $v=m-1$ degrees of freedom. For the chosen significance level $\alpha$, the critical value ${\chi }_{\alpha ,v}^2$ is taken from the chi-square distribution table. The requirement $W\ge W_{\mathrm{m}\mathrm{i}\mathrm{n}}$ is then equivalent to ${\chi }^2\ge {\chi }_{\alpha ,v}^2$. If the value of ${\chi }^2$ calculated according to Equation (8) is greater than or equal to ${\chi }_{\alpha ,v}^2$, the experts’ judgements are considered to be in agreement.

For additional interpretation, the consistency coefficient $k_C$ is used:

$$k_C={\displaystyle \frac{W}{W_{\mathrm{m}\mathrm{i}\mathrm{n}}}}={\displaystyle \frac{{\chi }^2}{{\chi }_{\alpha ,v}^2}}.$$

(9)

This coefficient shows how many times the calculated concordance coefficient $W$ is greater than its minimum value $W_{\mathrm{m}\mathrm{i}\mathrm{n}}$, and equivalently how many times ${\chi }^2$ exceeds its critical value ${\chi }_{\alpha ,v}^2$. When the opinions expressed by the experts are in sufficient agreement, $k_C>1$; otherwise $\left(k_C<1\right)$, the opinions differ significantly and the average ranks and derived weights are not considered reliable.

3.5. Construction of the Nominal Ship Risk Profile

To construct the nominal ship risk profile, which summarises the expert-based importance of all KPIs in the form of a normalised weight vector, the methodology combines the linear and nonlinear transformations by calculating the final weight of KPI $i$ as the arithmetic mean of the ARTIW-L and ARTIW-N weights:

$${\omega }_i={\displaystyle \frac{{\omega }_i^L+{\omega }_i^N}{2}},$$

(10)

where ${\omega }_i^L$ and ${\omega }_i^N$ are the normalised weights obtained from the formulas in Section 3.2 and Section 3.3. The resulting weights remain normalised, ${\omega }_i\ge 0$, $\sum _{i=1}^m{\omega }_i=1$ and preserve the same priority order of KPIs as in the original expert rankings, while integrating the sensitivity characteristics of both ARTIW variants [46,47,48,49]. In this way, the influence of the most and least important KPIs is “amplified” relative to criteria of medium importance through the ARTIW-N component, while the ARTIW-L component maintains a strictly linear response to changes in average ranks.

Since neither of these transformations has a clear theoretical advantage in the present context, and both preserve the original priority order of the KPIs, the final average weight of each KPI is additionally characterised by a simple measure of deviation that reflects the difference between the two ARTIW variants. This method-based deviation is defined as half of the absolute difference between the ARTIW-L and ARTIW-N weights:

$${\delta }_i={\displaystyle \frac{|{\omega }_i^N-{\omega }_i^L|}{2}}.$$

(11)

For each KPI, the interval ${\omega }_i\pm {\delta }_i=[{\omega }_i-{\delta }_i,{\omega }_i+{\delta }_i]$ defines a plausible range of weight values across the considered weighting methods. Thus, ${\omega }_i$ represents the average estimate of KPI importance, while ${\delta }_i$ quantifies the associated variability. This variability enables context-dependent selection of more extreme weights when required (e.g., emphasizing the most and least important KPIs).

The nominal ship risk profile is then defined as the vector of these final KPI weights:

$${SRP}^{nom}=\left({\omega }_1,{\omega }_2,\dots ,{\omega }_m\right).$$

(12)

Each component ${\omega }_i$ represents the relative contribution of the corresponding KPI to the accident-risk index under the assumption that all KPIs are in a very unfavourable (worst) state.

For a given ship or time period, let $x_i\in \left[\mathrm{0,1}\right]$ denote the normalised “risk level” of KPI $i$, where $x_i=1$ corresponds to a very bad (critical) KPI state and $x_i=0$ corresponds to a fully satisfactory state. Where a KPI is originally measured on a different scale, its observed value is first normalised to $x_i\in \left[\mathrm{0,1}\right]$, with higher $x_i$ indicating worse performance. A normalised accident-risk index is then defined as:

$$P=\sum _{i=1}^m{\omega }_i\hspace{0.17em}{x}_i,$$

(13)

where $m$ is the total number of KPIs and $i=1,2,\dots ,m$ indexes the KPIs.

A deviation of the normalised accident-risk index can be obtained by propagating the deviations ${\delta }_i$:

$$\Delta P=\sum _{i=1}^m{\delta }_i\hspace{0.17em}{x}_i.$$

(14)

When all KPIs take their worst-performance state (that is, $x_i=1$ for all $i=1,2,\dots ,m$), the index reaches its maximum value $P_{\mathrm{m}\mathrm{a}\mathrm{x}}=1$, and the weights ${\omega }_i$ directly represent each KPI’s share of the total accident-risk index. For observed KPI profiles, the index $P$ provides a normalised accident-risk level (a probability proxy) conditional on the current KPI performance profile.

4. Results

This section presents the empirical results of the expert evaluation and the derived nominal Ship Risk Profile. Section 4.1 describes the composition of the expert panel and the final KPI set retained for analysis. Section 4.2 examines the consistency of expert judgements using Kendall’s coefficient of concordance. Section 4.3 reports the relative importance of individual KPIs obtained by applying the ARTIW-L and ARTIW-N weighting procedures. Section 4.4 defines and interprets the nominal Ship Risk Profile ${SRP}^{nom}$ and the normalised accident-risk index $P$ constructed on the basis of these weights.

4.1. Expert Panel and KPI Set

The expert evaluation was conducted with 33 navigational practitioners (masters, chief mates, and pilots), each with at least five years of professional experience in maritime operations. The panel was formed to ensure that the judgements reflect accumulated navigational experience and direct responsibility for ship safety. The panel size exceeds the number of criteria retained for analysis (29 KPIs), consistent with the criterion stated in Section 3.1 that the expert group should not be smaller than half the number of evaluated KPIs.

The starting point of the study was a candidate set of 37 KPIs. Of these, 36 indicators were adopted from the BIMCO KPI framework [44], which covers areas such as compliance with environmental regulations; crew health, safety and injury prevention; training, retention and competence of personnel; navigational risks and accident prevention; operational efficiency; security performance; technical reliability and maintenance; and inspection outcomes, including Port State Control results. In addition, one KPI—Flag State rating indicator—was added based on the Paris MoU Ship Risk Profile and its Black–Grey–White lists, as scientific literature supports the relevance of flag performance for inspection outcomes and casualty risk [24,28,34,38].

All 37 KPIs were set out in a structured questionnaire. For each indicator, the experts were provided with a short description and were asked to assess, using their professional judgement and operational experience, how important the KPI is for assessing the ship’s and crew’s ability to avoid a collision, contact or grounding accident. The responses were given on the four-level importance scale from 0 to 3 defined in Section 3.1 (0—not important, 3—very important), indicating the perceived strength of the link between each KPI and navigational accident risk.

Indicators that were consistently judged to have no meaningful connection with navigational accident probability were removed before further analysis. For eight KPIs, all experts assigned an importance level of 0, and these indicators were therefore excluded. The subsequent concordance analysis and ARTIW-based weighting procedures are based on the remaining 29 KPIs, which constitute the final KPI set for constructing the nominal Ship Risk Profile: KPI-01 Budget performance indicator, KPI-02 Ship dry-docking planning accuracy indicator, KPI-03 CO₂ efficiency indicator, KPI-04 Operational deficiencies indicator, KPI-05 Navigational deficiencies indicator, KPI-06 Security deficiencies indicator, KPI-07 Cargo incidents indicator, KPI-08 Navigational accidents indicator, KPI-09 Crew experience indicator, KPI-10 Crew training days indicator, KPI-11 Number of cadets indicator, KPI-12 Crew turnover indicator, KPI-13 Frequency of crew disciplinary offences indicator, KPI-14 Crew work–rest hour violations indicator, KPI-15 Human resource management deficiencies indicator, KPI-16 Occupational health and safety violations indicator, KPI-17 Frequency of crew accidents and illnesses indicator, KPI-18 Passenger injury indicator, KPI-19 Overdue planned maintenance tasks indicator, KPI-20 Critical equipment and systems failures indicator, KPI-21 Classification society conditions indicator, KPI-22 Ship operational time indicator, KPI-23 Fires and explosions indicator, KPI-24 Port State Control performance indicator, KPI-25 Port State Control deficiencies indicator, KPI-26 Port State Control detentions indicator, KPI-27 Flag State rating indicator, KPI-28 Environmental regulations violations indicator, KPI-29 Pollutant spills indicator.

The excluded KPIs are NOx efficiency, SOx efficiency, Ballast water management violations, Releases of substances, Vetting deficiencies, Lost Time Injury Frequency, Lost Time Sickness Frequency, and Total Recordable Case Frequency. According to the expert panel, their exclusion reflects both limited relevance to collision/contact/grounding avoidance and conceptual overlap with retained indicators. NOx efficiency and SOx efficiency were considered not relevant to navigational-accident risk, as they primarily describe emission performance. Ballast water management violations are captured within the Environmental regulations violations indicator (KPI-28), while Releases of substances are encompassed by the Pollutant spills indicator (KPI-29). Vetting deficiencies overlap with Port State Control performance and Port State Control deficiencies. Lost Time Injury Frequency, Lost Time Sickness Frequency, and Total Recordable Case Frequency were excluded because they represent closely related occupational safety measures, where Total Recordable Case Frequency including first-aid cases already aggregates injury, sickness, and first-aid events. The expert panel therefore considered it difficult to differentiate their relative importance for navigational-accident avoidance and recommended relying on the aggregated Frequency of crew accidents and illnesses indicator (KPI-17).

4.2. Consistency of Expert Opinions

Before transforming expert rankings into KPI weights, the internal consistency of expert opinions was assessed according to the procedure described in Section 3.4. Kendall’s coefficient of concordance $W$ was calculated using the tie-corrected formula given in Equation (5), for $m=29$ KPIs and $n=33$ experts. The resulting value of the concordance coefficient for the full expert panel is $W=0.5304.$

The minimum threshold value of the concordance coefficient $W_{\mathrm{m}\mathrm{i}\mathrm{n}}$, at which the expert opinions may still be considered consistent at the adopted significance level $\alpha =0.05$, was obtained from Equation (7). Using $\nu =m-1=28$ degrees of freedom and the critical value of Pearson’s chi-square statistic ${\chi }_{\nu ,\alpha }^2=41.34$, the corresponding minimum concordance is $W_{\mathrm{m}\mathrm{i}\mathrm{n}}=0.0447.$

The empirical value of Pearson’s chi-square statistic was then calculated from Equation (8), which relates $W$ to ${\chi }^2$. For the present data, this gives ${\chi }^2=490.09,$ which is much larger than the critical value ${\chi }_{\nu ,\alpha }^2=41.34$. Therefore, at the significance level $\alpha =0.05$, the null hypothesis of mutually independent, random rankings is rejected, and the consistency of the experts’ rankings is considered statistically sufficient.

The consistency coefficient $k_c$, defined in Equation (9) as the ratio between the actual and minimum concordance, is equal to $k_c=11.86.$

Because $W>W_{\mathrm{m}\mathrm{i}\mathrm{n}}$, ${\chi }^2>{\chi }_{\nu ,\alpha }^2$ and $k_c>1$, the rankings provided by the 33 experts can be regarded as mutually consistent and non-contradictory. Consequently, the average ranks and the ARTIW-based transformations derived from them can be used as a reliable aggregated representation of expert judgement in the subsequent KPI weighting.

4.3. KPI Ranking, Priorities and Weights

After the consistency of the expert judgements had been established, their rankings were converted into KPI weights using the ARTIW-L and ARTIW-N methods. For each KPI $i$, the mean rank ${\bar{R}}_i$ was first calculated from the expert assessments in accordance with Equation (1). These mean ranks were then transformed into normalised weights ${\omega }_i^L$ and ${\omega }_i^N$ by applying the linear and nonlinear transformations specified in Equations (2) and (4), respectively. Both transformations use the same input ${\bar{R}}_i$ and preserve the original ordering of KPI priorities, but they differ in how they allocate relative importance to the highest- and lowest-ranked indicators.

The distribution of the average ranks ${\bar{R}}_i$ and the resulting KPI priorities is presented in Figure 4. Figure 5 shows the bar diagrams of the calculated normalised weights ${\omega }_i^L$ and ${\omega }_i^N$, illustrating the differences between the linear and nonlinear transformations for each KPI.

The ranking and weighting results are summarised in Table 1 in Section 4.4. For each of the 29 KPIs, the table presents the average rank ${\bar{R}}_i$, the normalised ARTIW-L weight ${\omega }_i^L$, the ARTIW-N weight ${\omega }_i^N$, and the resulting priority of each KPI.

4.4. Nominal Ship Risk Profile and Normalised Accident-Risk Index

To define the ship-specific normalised accident-risk index $P$ according to Equation (13), the nominal Ship Risk Profile $SR{P}^{nom}$ is used as the core set of KPI weights and is combined with the actual KPI values $x_i$ for the selected ship. The vector $SR{P}^{nom}$ is constructed from the average weights ${\omega }_i$, calculated using Equation (10), while the deviations ${\delta }_i$ are determined according to Equation (11). Each component ${\omega }_i$, as defined in Equation (12), $SR{P}^{nom}=\left({\omega }_1,{\omega }_2,\dots ,{\omega }_m\right),$ where $m=29$ is the total number of KPIs, represents the relative share of the total accident-risk index attributed to KPI $i$ under the hypothetical assumption that all KPIs are in a highly unfavourable state. For graphical presentation, the components of $SR{P}^{nom}$ are ordered based on KPI priority and expressed as percentages in Figure 6, along with the deviations ${\delta }_i$, which illustrate the variation in weights. For all 29 KPIs, the values of ${\omega }_i$ and ${\delta }_i$ are summarised in Table 1.

The normalised accident-risk index $P$ can be calculated together with its deviation $\Delta P$ using Equation (14), which defines the sensitivity of the index and indicates the range from $P_{\mathrm{m}\mathrm{i}\mathrm{n}}=P-\Delta P$ to $P_{\mathrm{m}\mathrm{a}\mathrm{x}}=P+\Delta P$. When all KPIs are in a very poor state (i.e., $x_i=1$ for all $i=1,2,\dots ,m$), the index reaches its maximum value $P_{\mathrm{m}\mathrm{a}\mathrm{x}}=1$. In this case, the weights ${\omega }_i$ directly reflect the share of the total accident-risk index attributed to each KPI and are equal to the components of $SR{P}^{nom}$, as presented in Figure 6.

Due to data protection and confidentiality constraints, the calculation of $P$ is demonstrated using anonymised KPI values for a representative vessel, here referred to as Ship A. If the ship’s KPI vector is X = (0.3, 0.2, 0.5, 0.1, 0.1, 0.1, 0.3, 0.2, 0.4, 0.1, 0.2, 0.7, 0.2, 0.4, 0.5, 0.1, 0.8, 0.4, 0.6, 0.5, 0.3, 0.9, 0.7, 0.4, 0.5, 0.6, 0.2, 0.6, 0.4), where the components correspond to KPI-01 through KPI-29 in sequential order, then the normalised accident-risk index is $P=0.3750$ (37.50%), with a deviation $\Delta P$ corresponding to a range from $P_{\mathrm{m}\mathrm{i}\mathrm{n}}=0.3057$ (30.57%) to $P_{\mathrm{m}\mathrm{a}\mathrm{x}}=0.4442$ (44.42%).

Table 1. Summary of KPI average ranks, weights and nominal ship risk profile values with method-based deviations.

KPI No.	${\overline{\mathit{R}}}_{\mathit{i}}$	${\mathit{\omega }}_{\mathit{i}}^{\mathit{L}}$	${\mathit{\omega }}_{\mathit{i}}^{\mathit{N}}$	${\mathit{\omega }}_{\mathit{i}}$	$\mathit{S}\mathit{R}{\mathit{P}}^{\mathit{n}\mathit{o}\mathit{m}}$, %	${\mathit{\delta }}_{\mathit{i}}$, %	Priority
KPI-01	20.439	0.0220	0.0216	0.0218	2.18%	0.02%	23rd
KPI-02	21.727	0.0190	0.0203	0.0197	1.97%	0.07%	25th
KPI-03	27.045	0.0068	0.0163	0.0116	1.16%	0.48%	29th
KPI-04	11.333	0.0429	0.0390	0.0409	4.09%	0.20%	9th
KPI-05	7.045	0.0528	0.0627	0.0577	5.77%	0.50%	3rd
KPI-06	15.273	0.0339	0.0289	0.0314	3.14%	0.25%	18th
KPI-07	21.591	0.0193	0.0205	0.0199	1.99%	0.06%	24th
KPI-08	11.515	0.0425	0.0384	0.0404	4.04%	0.21%	10th
KPI-09	11.758	0.0419	0.0376	0.0398	3.98%	0.22%	11th
KPI-10	9.470	0.0472	0.0466	0.0469	4.69%	0.03%	6th
KPI-11	23.758	0.0144	0.0186	0.0165	1.65%	0.21%	27th
KPI-12	17.030	0.0298	0.0259	0.0279	2.79%	0.19%	21st
KPI-13	13.364	0.0382	0.0331	0.0357	3.57%	0.26%	13th
KPI-14	6.955	0.0530	0.0635	0.0582	5.82%	0.53%	2nd
KPI-15	8.894	0.0485	0.0497	0.0491	4.91%	0.06%	5th
KPI-16	11.212	0.0432	0.0394	0.0413	4.13%	0.19%	8th
KPI-17	13.273	0.0385	0.0333	0.0359	3.59%	0.26%	12th
KPI-18	24.818	0.0119	0.0178	0.0149	1.49%	0.29%	28th
KPI-19	15.121	0.0342	0.0292	0.0317	3.17%	0.25%	17th
KPI-20	6.288	0.0545	0.0703	0.0624	6.24%	0.79%	1st
KPI-21	7.788	0.0511	0.0567	0.0539	5.39%	0.28%	4th
KPI-22	23.667	0.0146	0.0187	0.0166	1.66%	0.21%	26th
KPI-23	16.682	0.0306	0.0265	0.0285	2.85%	0.21%	20th
KPI-24	15.394	0.0336	0.0287	0.0311	3.11%	0.24%	19th
KPI-25	14.833	0.0349	0.0298	0.0323	3.23%	0.25%	16th
KPI-26	10.470	0.0449	0.0422	0.0435	4.35%	0.14%	7th
KPI-27	20.152	0.0226	0.0219	0.0223	2.23%	0.04%	22nd
KPI-28	14.182	0.0364	0.0311	0.0338	3.38%	0.26%	15th
KPI-29	13.924	0.0370	0.0317	0.0343	3.43%	0.26%	14th

Table 1. Summary of KPI average ranks, weights and nominal ship risk profile values with method-based deviations.

KPI No.	${\overline{\mathit{R}}}_{\mathit{i}}$	${\mathit{\omega }}_{\mathit{i}}^{\mathit{L}}$	${\mathit{\omega }}_{\mathit{i}}^{\mathit{N}}$	${\mathit{\omega }}_{\mathit{i}}$	$\mathit{S}\mathit{R}{\mathit{P}}^{\mathit{n}\mathit{o}\mathit{m}}$, %	${\mathit{\delta }}_{\mathit{i}}$, %	Priority
KPI-01	20.439	0.0220	0.0216	0.0218	2.18%	0.02%	23rd
KPI-02	21.727	0.0190	0.0203	0.0197	1.97%	0.07%	25th
KPI-03	27.045	0.0068	0.0163	0.0116	1.16%	0.48%	29th
KPI-04	11.333	0.0429	0.0390	0.0409	4.09%	0.20%	9th
KPI-05	7.045	0.0528	0.0627	0.0577	5.77%	0.50%	3rd
KPI-06	15.273	0.0339	0.0289	0.0314	3.14%	0.25%	18th
KPI-07	21.591	0.0193	0.0205	0.0199	1.99%	0.06%	24th
KPI-08	11.515	0.0425	0.0384	0.0404	4.04%	0.21%	10th
KPI-09	11.758	0.0419	0.0376	0.0398	3.98%	0.22%	11th
KPI-10	9.470	0.0472	0.0466	0.0469	4.69%	0.03%	6th
KPI-11	23.758	0.0144	0.0186	0.0165	1.65%	0.21%	27th
KPI-12	17.030	0.0298	0.0259	0.0279	2.79%	0.19%	21st
KPI-13	13.364	0.0382	0.0331	0.0357	3.57%	0.26%	13th
KPI-14	6.955	0.0530	0.0635	0.0582	5.82%	0.53%	2nd
KPI-15	8.894	0.0485	0.0497	0.0491	4.91%	0.06%	5th
KPI-16	11.212	0.0432	0.0394	0.0413	4.13%	0.19%	8th
KPI-17	13.273	0.0385	0.0333	0.0359	3.59%	0.26%	12th
KPI-18	24.818	0.0119	0.0178	0.0149	1.49%	0.29%	28th
KPI-19	15.121	0.0342	0.0292	0.0317	3.17%	0.25%	17th
KPI-20	6.288	0.0545	0.0703	0.0624	6.24%	0.79%	1st
KPI-21	7.788	0.0511	0.0567	0.0539	5.39%	0.28%	4th
KPI-22	23.667	0.0146	0.0187	0.0166	1.66%	0.21%	26th
KPI-23	16.682	0.0306	0.0265	0.0285	2.85%	0.21%	20th
KPI-24	15.394	0.0336	0.0287	0.0311	3.11%	0.24%	19th
KPI-25	14.833	0.0349	0.0298	0.0323	3.23%	0.25%	16th
KPI-26	10.470	0.0449	0.0422	0.0435	4.35%	0.14%	7th
KPI-27	20.152	0.0226	0.0219	0.0223	2.23%	0.04%	22nd
KPI-28	14.182	0.0364	0.0311	0.0338	3.38%	0.26%	15th
KPI-29	13.924	0.0370	0.0317	0.0343	3.43%	0.26%	14th

5. Discussion

Ship accidents—particularly collisions, groundings, and contacts—continue to occur despite substantial advances in maritime safety research, with severe consequences for human life, marine ecosystems, and port operations. The literature review identified more than 80 risk factors reported for these accident types, indicating fragmentation across existing studies in both risk-factor definitions and methodological approaches. In parallel, EMSA has published an extensive analysis of EMCIP navigation-accident data, identifying 1,637 contributing factors [17], which highlights the significant yet underutilized potential of EMSA data for predictive maritime safety modelling. In this context, KPIs can help interpret patterns in these contributing factors and link observed accident mechanisms to measurable operational and organizational conditions, thereby supporting more proactive navigational-accident risk management.

This study presents a practical route for linking operational KPIs to navigational-accident risk by converting expert priorities into a weighted $SR{P}^{nom}$ and combining it with observed, ship-specific KPI states to produce a normalised accident-risk index $P$ for collision/contact/grounding avoidance (noting that $P$ is a normalised index rather than a calibrated absolute probability). The expert panel—masters, chief mates, and pilots—evaluated an initial set of 37 KPIs; eight indicators were subsequently excluded because all experts assigned an importance level of 0, indicating no meaningful link to navigational-accident risk. This filtering step is informative, as it suggests that not all performance indicators commonly used in shipping operations are perceived as relevant for accident avoidance, and it helps keep the SRP focused on mechanisms that practitioners associate with navigational failures.

The resulting $SR{P}^{nom}$ (Figure 6) represents a compact “importance map” across the 29 retained KPIs, where each weight corresponds to that KPI’s share of the maximum index under the (hypothetical) worst-performance state for all indicators. The weights are not dominated by a single KPI (the largest individual share is 6.24%), supporting the view that navigational-accident risk is multifactorial rather than attributable to one isolated deficiency. Methodologically, ARTIW-L and ARTIW-N provide a transparent means to transform ordinal expert rankings into a cardinal weight vector while explicitly characterising structural uncertainty associated with the choice of transformation: the linear form preserves proportional differences in average ranks, whereas the nonlinear form places relatively greater emphasis on the most and least important KPIs [46,47,48,49]. The weight analysis is also supported by adequate agreement among the 33 experts: Kendall’s coefficient of concordance is $W=0.5304$, with ${\chi }^2=490.09$ exceeding the critical value ${\chi }_{(\nu =28,\alpha =0.05}^2=41.34$, and the consistency coefficient is $k_c=11.86>1$; therefore, the aggregated ranking can be treated as mutually consistent for constructing a single $SR{P}^{nom}$ vector.

The constructed $SR{P}^{nom}$ is conceptually aligned with the SRP applied in the Paris MoU regime, where ships are classified as low-risk, standard-risk, or high-risk based on PSC inspection results [28,36,37,38]. The present framework extends this concept in two respects. First, it is built on a broader set of 29 KPIs spanning operational, technical, human-factor, and regulatory dimensions. Second, it enables integration of the risk profile with time-varying KPI states through the index $P$, allowing a quantitative assessment of how changes in KPI performance affect the index $P$ (i.e., modelled navigational-accident risk level). In this way, the framework bridges traditional inspection-based profiling and more dynamic, performance-driven risk monitoring.

The KPI priorities derived from the expert panel mainly highlight determinants of human performance, bridge-team effectiveness, and the technical and organizational conditions that influence decision-making under workload. In the $SR{P}^{nom}$ model, the ten highest-weight indicators are: critical equipment and systems failures (KPI-20; 6.24%); crew work–rest hour violations (KPI-14; 5.82%); navigational deficiencies (KPI-05; 5.77%); classification society conditions (KPI-21; 5.39%); human resource management deficiencies (KPI-15; 4.91%); crew training days (KPI-10; 4.69%); Port State Control detentions (KPI-26; 4.35%); occupational health and safety violations (KPI-16; 4.13%); operational deficiencies (KPI-04; 4.09%); and navigational accidents (KPI-08; 4.04%). Collectively, these indicators account for 49.45% of the total $SR{P}^{nom}$ weight, indicating that—by model construction—almost half of the maximum accident index is driven by a relatively small set of predominantly human/organizational and technical-condition KPIs.

A similar concentration also appears in EMSA’s safety analysis using EMCIP navigation-accident data: the ten most frequent safety-issue families (bridge resource management coordination; use of electronic navigation equipment; work methods and supervision; bridge resource availability; external communications; coordination with third parties; resources for plans and procedures; safety culture and climate; safety awareness; and external environmental impact) jointly represent about 46.43% of all contributing factors reported in the analysis [17]. When the top ten $SR{P}^{nom}$ KPIs are compared with the top ten EMCIP safety-issue families at the domain level, clear thematic alignment is observed: navigational deficiencies (KPI-05) and operational deficiencies (KPI-04) correspond closely to families related to bridge coordination and work methods/supervision; critical equipment and systems failures (KPI-20) align with equipment-related issues; and crew work–rest hour violations (KPI-14), crew training days (KPI-10), and human resource management deficiencies (KPI-15) reflect fatigue, competence, and resource-availability mechanisms frequently emphasized in accident investigations. The similarity in these aggregate shares should be interpreted as a descriptive concentration pattern rather than a statistical validation; however, it supports the plausibility that a limited set of human/organizational and technical-condition themes dominates both investigation-derived factor frequencies and KPI-based risk attribution. This pattern is consistent with the wider literature, which attributes a large share of navigational accidents to human error and related mechanisms while emphasising organisational, procedural, and technological context effects [1,17,25,36,39,40,41,42]. Overall, this domain-level alignment supports the paper’s central premise that existing KPI frameworks can capture a substantial portion of the information relevant for proactive navigational-accident risk indication, even before introducing new KPIs.

The practical value of $SR{P}^{nom}$ is illustrated in Figure 6, because it enables a broad-perspective interpretation of how different KPI groups can drive the accident-risk index under deteriorating performance. Under the model definition, the $SR{P}^{nom}$ weights describe the maximum share of the index attributable to each KPI. As KPI values improve from poor to satisfactory states, the index declines according to the SRP weights, providing a transparent mechanism to estimate how targeted performance improvements may reduce the initial maximum risk. The demonstration with anonymised values for Ship A ($P=37.50\%$, range 30.57–44.42%) provides an illustrative example of how the SRP-based calculation can be used as an interpretable risk profile rather than an unstructured collection of raw KPI values [38,44,55]; for conservative operational decision support, the upper-bound estimate may be used as a precautionary risk level.

From an operational perspective, the SRP approach can support decision-making by multiple stakeholders in constrained and congested port environments. Port authorities, pilots, Port State Control inspectors, and ship operators often need to judge whether a vessel can safely transit port entrances or narrow channels and whether berthing and unberthing can be conducted safely under unfavourable conditions—phases repeatedly identified as high-consequence and coordination-intensive [15,17,56]. This perspective is consistent with port-operational research highlighting entry, mooring, and unmooring as particularly high-risk phases requiring proactive mitigation [15,26]. Because the framework relies on KPIs that are already collected (or can be collected) routinely—including BIMCO indicators and PSC/flag-related measures—it offers a feasible pathway for implementation without requiring immediate access to detailed accident-investigation variables [37,38,44]. The same structured SRP output may also be valuable for insurers and cargo stakeholders by enabling more transparent risk differentiation across vessels and by incentivising improvements in the highest-weight operational and human-factor KPIs [14,53,54].

In practice, the normalised accident-risk index $P$ can support pre-arrival screening and prioritisation by converting routinely monitored KPI states into a single, traceable risk indication. Ports and pilots could use elevated index values as a trigger for enhanced control measures, such as assigning a more experienced pilot team, requiring tug assistance or escort, deferring transit or berthing until conditions are within locally defined operational limits (e.g., visibility and wind/current limits), or requesting additional bridge-team resources. Ship operators can use the same output internally to prioritise corrective actions (maintenance reliability, work–rest compliance, competence/training, procedural deficiencies) by targeting the KPI terms that contribute most to the current index. Where used by control authorities, the index can inform risk-oriented prioritisation (screening/inspection focus) while remaining interpretable through the underlying KPI contributions.

Several limitations indicate priorities for future work. First, $SR{P}^{nom}$ weights are expert-elicited and should be interpreted as prioritisation rather than an empirically calibrated causal model; validation against KPI time series linked to independent accident outcomes is required to assess empirical validity and recalibrate weights where appropriate. Second, the framework focuses on ship- and crew-related KPIs and does not explicitly represent external operational context (e.g., hydrometeorology, traffic complexity, tug availability, port infrastructure constraints, and regional practices); future iterations should incorporate context correction factors and/or a parallel port risk profile to improve realism and transferability. More generally, dynamic and context-aware risk assessment could incorporate traffic density, environmental conditions, AIS-derived encounter dynamics, and port-specific constraints as modifiers of the $SR{P}^{nom}$-based index, particularly because navigational-accident risk is highly context dependent in confined waters. Third, the current scope is limited to collisions, contacts, and groundings; extension to other accident classes would require KPI additions and revised indicator–accident mappings. Fourth, $P$ is a normalised accident-risk index rather than a calibrated absolute probability; empirical calibration is therefore needed before interpreting $P$ as a probability in an absolute sense. For operational use, SRP outputs should also be communicated in simplified forms (e.g., Low/Standard/High categories or dashboards) while preserving traceability to underlying KPIs and weights.

The nominal $SR{P}^{nom}$ weights reflect structured expert judgement and therefore inherit limitations typical of elicitation studies: (i) potential panel-composition effects (experience domain, operational background, and regional practice), (ii) cognitive and framing biases when ranking a relatively large KPI set, and (iii) the possibility that perceived importance does not match observed accident outcomes under specific operating contexts. Future work should therefore validate and, if necessary, recalibrate the weighting structure using ship-level KPI time series linked to independent accident outcomes. A practical validation route is a retrospective design in which KPI vectors are paired with subsequent collision/contact/grounding events, enabling outcome-association assessment and calibration of the normalised accident-risk index. A complementary prospective design is to compute the index continuously for a monitored fleet and evaluate whether elevated index values precede adverse outcomes over a defined follow-up window, with periodic re-estimation of weights to improve transferability across ship types, trades, and regions.

The proposed workflow is KPI-set agnostic and can be applied in other regions by adapting the KPI set and re-estimating weights to reflect local conditions, operational traditions, and port-specific characteristics. Because maritime KPIs are broadly understood across stakeholder groups, the framework can be piloted in different countries or ports either by applying the current weight structure as an initial benchmark or by repeating the expert-weighting stage to recalibrate prioritisation to the local operational context, while preserving the SRP framework, index structure, and interpretability. Outside the BIMCO/Paris MoU setting, operational, technical, and human-factor indicators are expected to remain directly transferable, while regulatory-performance components (e.g., PSC- and flag-related measures) can be substituted with locally applicable inspection regimes and flag-performance classifications. For different ship types, $SR{P}^{nom}$ can be re-estimated using expert panels stratified by ship type and/or empirically recalibrated using outcome-linked data to yield ship-type-specific profiles without changing the underlying framework.

These findings support the view that $SR{P}^{nom}$ can function as a scientifically grounded “translation layer” between accident-investigation knowledge and proactive performance monitoring. The concentration of weight in human/organizational and technical-condition KPIs aligns with major safety-investigation findings and highlights actionable levers for reducing navigational-accident risk through targeted improvements in bridge-team performance conditions, competence development, maintenance reliability, and compliance oversight. The results indicate what can be extracted from existing KPIs and help identify where additional indicators may be required, thereby providing direction for future KPI development and competence-building efforts in data-driven operating environments [29,56,57,58,59,60].

6. Conclusions

This study proposed a practical framework to link maritime KPIs with navigational-accident risk and to support proactive decision-making in ports and other confined waters. The work is based on the proposition that routinely monitored operational KPIs can be systematically mapped—via expert-derived weights—into an interpretable risk indicator for collision/contact/grounding avoidance. The novelty of the study lies in operationalising this linkage through an ARTIW-based weighting of a comprehensive KPI set to form a nominal Ship Risk Profile, $SR{P}^{nom}$, and a transparent, ship-specific normalised accident-risk index $P$ suitable for decision support.

Expert judgements were transformed into KPI weights using the ARTIW-L and ARTIW-N rank-to-weight methods and aggregated into $SR{P}^{nom}$; observed KPI states were then used to compute $P$. From an initial set of 37 candidate KPIs, 29 were retained for the construction of $SR{P}^{nom}$, while eight were excluded because all experts assessed them as not relevant for navigational-accident risk indication. Expert agreement was sufficient for aggregation (Kendall’s $W=0.5304$, consistency $k_c=11.86>1$). The resulting $SR{P}^{nom}$ indicates that navigational-accident risk attribution is multifactorial; however, the ten highest-weight KPIs represent 49.45% of the total weight. The leading contributors were critical equipment and systems failures (KPI-20; 6.24%), crew work–rest hour violations (KPI-14; 5.82%), navigational deficiencies (KPI-05; 5.77%), classification society conditions (KPI-21; 5.39%), and human resource management deficiencies (KPI-15; 4.91%). An illustrative calculation using anonymised KPI values for Ship A produced $P=0.3750$ (37.50%), with a deviation range from 30.57% to 44.42%, demonstrating how the framework can translate routine KPI monitoring into an interpretable risk indication and highlight where targeted performance improvements may yield the largest reduction in the index.

The proposed index $P$ is a normalised accident-risk indicator (a probability proxy) and is not an empirically calibrated absolute probability. Future work should therefore focus on empirical validation and calibration using ship-level KPI time series linked to independent accident outcomes. In addition, incorporating external operational context (e.g., hydrometeorology, traffic complexity, tug availability, and port infrastructure constraints) through correction factors and/or a parallel port risk profile would improve realism and transferability. Extending the approach to additional accident categories beyond collisions, contacts, and groundings will require revised KPI sets and indicator–accident mappings. Overall, the framework provides an interpretable and implementable pathway for translating expert-weighted KPIs into proactive navigational risk indication to support maritime stakeholders’ safety decisions.