Evaluating Maintainable Asset Criticality in Production Systems via a Network-Level, Consequence-Based Profitability Framework Enabled by Complex Repairable Flow Network Simulation

Abstract

This paper presents a simulation-based methodology for evaluating maintainable asset criticality in production systems modelled as complex repairable flow networks (CRFNs). The proposed Flow-Based Asset Criticality Evaluation Methodology (FACE) adopts a consequence-based perspective, assessing criticality according to network-level economic impact rather than probability-weighted risk. FACE introduces two profitability-oriented metrics, the Minimum Consequence of Failure (MCoF) at the maintainable item (MI) and failure mode (FM) levels, computed using multilayered network simulation integrating topology, capacity, failure behaviour, and profitability-driven flow allocation. By directly linking asset unavailability to system-wide gross profitability, the methodology enables objective, data-driven criticality assessment without reliance on subjective inputs, such as guided scoring processes. The approach supports both strategic and operational maintenance decisions by identifying assets and failure modes most consequential to production throughput and profitability.

1. Introduction

Data-driven insights are essential for informing maintenance decisions that sustain the reliability and performance of maintainable assets within flow networks (FNs). These networks underpin complex production systems across energy, logistics, manufacturing, mining, and utilities [1,2]. Within frameworks such as reliability-centred maintenance (RCM), determining what to maintain, how, and when is central to balancing reliability, cost-effectiveness, and performance [3,4,5]. A key supporting process is asset criticality evaluation, which assesses the importance of maintainable items (MIs) and their failure modes (FMs) using multiple performance and risk criteria [4,5,6,7,8].

Asset criticality evaluation supports decision making across the asset lifecycle [9], but current approaches face persistent limitations. These include a narrow focus on individual machines rather than system-level performance [8], static and subjective assessments that inflate the number of critical assets [7], and limited clarity in prioritising evaluation criteria [10]. These limitations are particularly problematic in complex, multisource, multisink FNs, where misidentification of critical assets can misalign scarce resources and maintenance actions with production outcomes and ultimately reduce return on investment (ROI).

In response to calls for more dynamic, systemic, and performance-based criticality evaluation methods and tools [6], this research builds directly on the Complex Repairable Flow Network Modelling Framework (CRFNMF) [11]. Within this framework, production systems are modelled as complex repairable flow networks (CRFNs) to integrate multilayered topology, capacity constraints, and maintainable asset behaviour. Consistent with calls [12] for improved decision support tools that assess maintenance decisions within the context of production profitability, holistic systems, and interdependent components, performance is evaluated in terms of maximising gross profitability at the network level using profitability-driven flow allocation via the Maximised Gross Profit Pathway Ranking Method (MGPRM) [11]. Hence, this research develops the Flow-Based Asset Criticality Evaluation Methodology (FACE), a dynamic, systemic, and performance-based approach to assessing maintainable asset criticality. Building on the CRFNMF, FACE embeds logic that links maintainable item (MI) disruptions directly to profitability outcomes and introduces two flow-based criticality metrics, the Minimum Consequence of Failure (MCoF) at the MI and failure mode (FM) levels, to support strategic and operational maintenance management decisions, respectively. The approach deliberately adopts a consequence-based view of asset criticality, evaluating importance according to the magnitude of network-level performance degradation arising from MI unavailability rather than probability-weighted risk. Probability is treated as a subsequent modelling layer, consistent with the separation of consequence and likelihood in the definition of risk [13].

The remainder of the paper is structured as follows. Section 2 reviews the relevant literature on reliability engineering, criticality assessment, and flow network (FN) modelling. Section 3 introduces the theoretical foundations and methodology underlying FACE. Section 4 demonstrates the application of FACE through applying the simulation process via supporting experiments on an illustrative example CRFN. Section 5 analyses the results and discusses the implications for maintenance management. Section 6 summarises the key findings and outlines directions for future research.

2. Literature Review

Maintaining the performance and profitability of FNs depends on the effective management of the maintainable assets that enable them. Despite decades of development in maintenance methodologies and reliability analysis, asset criticality evaluation remains reliant on subjective inputs and is often weakly connected to the system-level performance objectives these assets support. This section reviews three interrelated research areas that underpin a performance-based and systemically aligned approach to criticality analysis: reliability engineering, RCM and criticality assessment practices, and FN modelling and optimisation. The review identifies a clear gap in the literature, namely the absence of methods and tools capable of linking maintainable asset failures to system-level and economic consequences in a structured, dynamic, and data-driven manner.

2.1. Reliability Engineering and RCM Foundations

Reliability engineering can be framed as the modelling of failure likelihood and consequence across system components, subsystems, and human elements, with the objective of safeguarding system functionality under uncertainty [12]. This perspective has been extended to include the asset lifecycle, emphasising the need to balance reliability with performance and cost [14]. RCM builds on these principles by defining what maintenance should be performed, on which components, and when to sustain system functionality at minimum cost [4,5]. Its emphasis on functional analysis and FM identification has proven effective for guiding targeted interventions and reducing downtime [15,16]. However, RCM practices often rely heavily on assessor experience and judgement [3,4,12], raising concerns about consistency and objectivity when applied across large, complex asset portfolios. As a result, data-driven decision support is increasingly recognised as critical for improving maintenance decision-making efficiency, effectiveness, and scalability [3,17,18,19,20].

2.1.1. Criticality Evaluation

Asset criticality analysis forms a key part of implementing RCM and is commonly framed as a form of risk assessment [4,5]. The objective is to model available information at the component or event level to assess risk at the system level [21]. Consistent with the definition of risk [13], criticality is typically expressed in terms of failure scenarios (s_i is the ith scenario out of N possibilities), their likelihood (p_i is the probability of s_i occurring), and their associated consequences (c_i is the consequence of s_i). Prior reviews indicate that existing approaches assess criticality either through consequence alone or through probability-weighted expected loss [22,23].

From a purpose perspective, existing literature [22,24,25,26] suggests that asset criticality is evaluated to support decisions across the asset lifecycle [9]. This includes assessing design alternatives to maximise system reliability during the pre-acquisition analysis phase, managing maintenance strategy selection and task prioritisation during the operation and maintenance phase, conducting spare parts analysis during the logistics support phase, and guiding equipment replacement and reliability improvement during the business need or opportunity phase.

In terms of evaluation methods, prior reviews report a wide range of approaches, including risk priority number (RPN)-based techniques, multicriteria decision-making methods, AI-based approaches, and simulation-based methods [10,22,24,27]. Several authors have noted that many of these methods rely on subjective inputs or opaque aggregation logic, limiting their transparency and consistency, particularly in complex systems.

With respect to criticality modelling, Ref. [10] reviewed a broad range of criteria and observed substantial divergence in how the consequence component is defined and prioritised across studies. To provide structure, Ref. [10] consolidated these criteria into four overarching categories: production, quality, maintenance, and safety, health, and the environment. Similar classification frameworks have been adopted in other research studies [28,29,30]. Among these, the categorisation proposed in [28,31] offers a particularly simple and practical structure (see Figure 1).

Both Refs. [28,31] define risk in line with Ref. [13] and employ guided scoring processes to assign probability and consequence inputs within their respective evaluation methods. Probability is defined by a single dimension, frequency, and is assessed via a semi-quantitative scale. Consequence is defined across four dimensions: operational impact (OI), operational flexibility (OF), maintenance cost (MC), and safety and environmental impact (SEI), each assessed using qualitative or semi-quantitative scales. Such guided scoring approaches are widely used as a key input to existing criticality evaluation methods.

2.1.2. Limitations of Existing Approaches

Most existing criticality evaluation methods are unable to identify which machines are critical to macro-level system performance [6]. Prior studies highlight that many approaches focus on machine-level availability metrics rather than system productivity or performance outcomes [7,8]. As a result, criticality assessments often lead to poor prioritisation, inefficient allocation of maintenance effort, and overclassification of assets as critical [7]. These methods are further criticised for being static, speculative, and heavily reliant on subjective criteria, with opaque aggregation logic that obscures how individual machines contribute to overall system performance.

The literature suggests organisations will continue to rely on machine-level key performance indicators (KPIs) such as mean time between failure (MTBF) and mean time to repair (MTTR) until decision support tools are developed that explicitly connect machine behaviour to system-level performance indicators [6]. Establishing this linkage is necessary to understand how local asset behaviour influences global system outcomes [6,32].

More broadly, there have been calls for maintenance decision support tools capable of systematically evaluating trade-offs between production profitability, reliability, safety, and compliance by accounting for complex system interactions and uncertainty [12]. While structured approaches such as RCM provide valuable guidance, their limited ability to capture these system-level trade-offs, particularly in the context of FN performance and profitability, highlights the need for more quantitative, system-aware methods.

2.2. Flow Network Modelling and Simulation

FNs provide a powerful framework for modelling systems whose performance depends on the coordinated flow of resources, people, or information. The literature on stochastic flow networks (SFNs), and in particular repairable flow networks (RFNs), offers tools for analysing how failure and repair affect network behaviour under uncertainty [2,33,34]. However, much of this work focuses on capacity and reliability analysis during the pre-acquisition analysis and operation and maintenance phases of the asset lifecycle, with limited attention to maintenance decision making or asset criticality evaluation.

Numerous studies apply simulation to assess FN performance [35,36,37,38,39,40,41,42,43,44,45], yet relatively few extend these approaches to explicitly model maintenance decisions. Where maintenance is considered, the emphasis is typically on budget constraints [46,47,48] or on evaluating the impact of alternative strategies on FN reliability [49,50,51]. These studies generally do not capture the multilayered structure of real production systems at the process and equipment component levels, nor do they dynamically link maintenance decisions to system-level performance or profitability.

Recognising the limitations of existing frameworks, the CRFNMF, which integrates repairable flow network (RFN) simulation with RCM-aligned maintenance strategy analysis, was introduced [11]. Within this framework, CRFNs represent real-world FNs by modelling facilities, processes, MIs, and FMs within an interconnected network structure, evaluated in terms of gross profitability using the MGPRM. As illustrated in Figure 2, CRFNs capture both production and reliability structure and have been shown to effectively simulate the network-level effects of maintenance strategies.

Despite this capability, CRFNs have not yet been applied to the evaluation of asset criticality. In particular, no existing study has demonstrated how MI failures translate into network-level profitability impacts or how this relationship can be used to support more effective maintenance prioritisation through improved criticality evaluation, consistent with recommendations in the literature [6,12].

2.3. Knowledge Gap and Contribution Goals

The preceding review identifies a clear research gap: existing asset criticality evaluation practices lack the systemic, dynamic, and performance-aligned structure required to support effective maintenance management in complex FNs. While RFNs and CRFNs provide tools for simulating FN behaviour under varying conditions, they have not been fully leveraged to support decision making across the asset lifecycle. In particular, the need for an objective, data-driven, and economically grounded approach to criticality evaluation, one that reflects how MIs and their FMs influence system-level profitability, remains unmet.

This research addresses this gap by developing FACE, a simulation-based decision support framework that builds on the CRFNMF. FACE evaluates criticality by modelling multilayered network structure, flow capacities, and quantitative reliability-related inputs (e.g., MC, SEI, MTTR) to simulate FN performance under different scenarios. Criticality is assessed based on how individual MIs and their FMs affect system-wide gross profitability using the MGPRM and in terms of consequence (c_i) only. The methodology supports maintenance strategy selection and planning, including the identification of maintenance-significant items and the prioritisation of maintenance tasks, providing decision-relevant insights at both strategic and operational levels [26].

Specifically, this research:

• Develops FACE by extending the CRFNMF and MGPRM, enabling dynamic, systemic, performance, and consequence-based evaluation of maintainable asset criticality in complex FNs;
• Demonstrates how FACE supports strategic and operational maintenance decision making by objectively identifying the MIs and FMs most critical to the maximisation of gross profitability;
• Validates the methodology through simulation experiments on an illustrative example CRFN, comparing FACE-derived criticality rankings with those obtained using a guided scoring approach in the literature [28,31].

3. Flow-Based Criticality Evaluation Methodology

This section introduces FACE, which builds on the CRFNMF, to provide a dynamic, systemic, and performance-based approach to assessing maintainable asset importance in complex FNs. FACE distinguishes between strategic and operational criticality evaluation through incorporating stochastic FN simulation and profitability-based consequence modelling.

In line with Ref. [26], strategic maintenance management is concerned with identifying the system-wide consequence of MI failures for maintenance strategy development, while operational maintenance management focuses on prioritising, planning, and scheduling tasks to manage risks associated with specific FMs. Following Ref. [13], strategic analysis considers MIL scenarios (s_i), where consequences (c_i) are expressed in terms of OI and OF [28,31]. Operational analysis considers FML scenarios (s_i), where consequences (c_i) are extended to include MC and SEI, and where failure probability (p_i) becomes relevant due to the risk-focused nature of operational decision making. This distinction reflects the established view that MC, SEI, and p_i are most appropriately quantified at the FML [5,52]. Accordingly, this research focuses on consequence-based criticality, treating probabilistic failure modelling as a subsequent extension.

FACE defines systemic consequence using the MCoF, a profit-based measure of disruption impact. The MCoF is defined as the difference between the maximum gross profit achievable by the FN under a best-case baseline scenario, where all MIs are available, and the maximum gross profit achievable when specific MIs are unavailable. At the MIL, the MCoF reflects structural capacity reduction, while at the FML it captures transient capacity reduction over unplanned repair durations. Hence, the MCoF represents a structural lower bound on network-level consequence arising from capacity reduction, computed under optimal flow reallocation relative to the all-MIs-available baseline scenario. Gross profitability is used as the system (economic) performance measure, calculated as total inflow-based revenue minus flow-dependent production, maintenance, safety, and environmental costs. This measure captures both physical flow loss and its economic significance, providing a decision-relevant indicator of system performance that is inherently aligned with what production-focused organisations are trying to maximise [12].

Defining MCoF relative to the maximum gross profit achievable under a given network configuration serves to isolate structural consequence from stochastic variability. Maximum gross profit represents the performance frontier of the flow network, determined by its topology, capacity constraints, and flow allocation logic. Measuring disruption impact relative to this frontier therefore provides a stable and comparable indicator of how MI unavailability constrains the system’s theoretical performance potential. As an example, using expected profit as the reference would embed assumptions regarding failure frequency, repair behaviour, and operating conditions directly into the criticality metric. While such probabilistic considerations are undoubtedly useful, they may obscure the structural determinants of asset importance during early-stage evaluation. By contrast, a maximum-performance reference ensures that criticality reflects the magnitude of achievable performance loss conditional on disruption, independent of likelihood assumptions. This consequence-first formulation establishes a clear separation between structural importance and probabilistic risk.

FACE eliminates reliance on guided scoring processes by using multilayered network topology, capacities, and other quantitative inputs to dynamically evaluate the impact of each MI within the simulation environment. In doing so, it directly reflects how FN structure and interdependencies associated with OI and OF influence failure impact and performance loss. While MC and SEI still require estimation, strategic analysis results can be used to prioritise data collection efforts. Where data are unavailable, guided scoring consistent with [28,31] may be used as a last resort.

For strategic analysis, FACE computes the MCoF by simulating the maximum gross profit generated at the FL when all MIs are available and when each MI is independently removed from service over a fixed iteration period. The MCoF for any MI is defined as:

$${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right)}=\left({\mathrm{m}\mathrm{a}\mathrm{x}(\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s} \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t})}_{\mathrm{F}\mathrm{L}}-{\mathrm{m}\mathrm{a}\mathrm{x}(\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s} \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t})}_{\mathrm{F}\mathrm{L}\left(~{\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right)}\right)$$

(1)

where:

• ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right)}$ is the minimum cost of failure for MI x (mi_x), as measured at the FL sinks;

• ${\mathrm{m}\mathrm{a}\mathrm{x}(\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{s} \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t})}_{\mathrm{F}\mathrm{L}}$ is the maximum gross profit the FN can generate, as measured at the FL sinks, when all MIs are available;

• ${\mathrm{m}\mathrm{a}\mathrm{x}(\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}\mathrm{s} \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t})}_{\mathrm{F}\mathrm{L}\left(~{\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right)}$ is the maximum gross profit the FN can generate, as measured at the FL sinks, when mi_x is unavailable.

By design, this formulation captures OI and OF based solely on FN topology and capacities, without reliance on guided scoring. It ties criticality directly to FN performance by accounting for how all production processes and MIs interact to generate value. This logic is supported by empirical analysis of simulation outputs, which demonstrate a strong relationship between mean gross profit and maximum gross profit (both measured in Monetary Units (MUs)) under simulated MI failures (see Figure 3).

For operational analysis, the MCoF generated for strategic analysis is adjusted using FM-specific inputs, including unplanned mean time to repair (MTTR_u), unplanned maintenance cost (MC_u), and safety and environmental impact cost (SEIC). The MCoF for any FM is defined as:

$${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}=\left({{\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}\times \mathrm{M}\mathrm{T}\mathrm{T}\mathrm{R}}_{\mathrm{u}\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}\right)+{\mathrm{M}\mathrm{C}}_{\mathrm{u}\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}+{\mathrm{S}\mathrm{E}\mathrm{I}\mathrm{C}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$$

(2)

where:

• ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$ is the minimum cost of failure for failure mode y (fm_y) of mi_x, as measured at the FL sinks;

• ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ is the minimum cost of failure for mi_x, as measured at the FL sinks;

• ${\mathrm{M}\mathrm{T}\mathrm{T}\mathrm{R}}_{\mathrm{u}\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$ is the unplanned mean time to repair for fm_y of mi_x;

• ${\mathrm{M}\mathrm{C}}_{\mathrm{u}\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$ is the unplanned maintenance cost for fm_y of mi_x;

• ${\mathrm{S}\mathrm{E}\mathrm{I}\mathrm{C}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$ is the safety and environment impact cost for fm_y of mi_x.

This formulation enables both strategic and operational maintenance decision making by distinguishing the systemic importance of MIs from the risk-driven prioritisation of specific FMs. Unlike conventional approaches such as RPN methods used within RCM, FACE avoids oversimplified aggregation logic and provides a dynamic, data-driven, and economically grounded basis for criticality assessment, supporting more robust and value-aligned maintenance decision making in complex FNs.

4. FACE in Action: Running Simulation Experiments on an Illustrative Example Complex Repairable Flow Network

This section demonstrates the application of FACE within a simulation environment using a series of experiments conducted on an illustrative example CRFN. The experiments are designed to assess whether FACE satisfies the criteria outlined by Ref. [6], namely that a criticality evaluation method should be dynamic, systemic, objective, and performance-based. While illustrative, the example CRFN captures key structural and performance characteristics typical of capital-intensive production environments, including discrete and continuous process systems.

A detailed representation of the CRFN is provided in Figure 4, Figure 5 and Figure 6, which respectively depict the topology of the FL, PL, and MIL, including flow, capacity, revenue, and cost data. The FML is not visualised, as FMs are modelled as stochastic attributes associated with MIs.

Figure 4. Example iteration of simulated operation at the FL displaying flows (numbers on left-hand side of square brackets), revenues (positive numbers within square brackets), and costs (negative numbers within square brackets) as depicted in Ref. [11]. Blue nodes represent simulation start (ssp) and simulation end (sep) points and green nodes represent FL nodes.

Figure 4. Example iteration of simulated operation at the FL displaying flows (numbers on left-hand side of square brackets), revenues (positive numbers within square brackets), and costs (negative numbers within square brackets) as depicted in Ref. [11]. Blue nodes represent simulation start (ssp) and simulation end (sep) points and green nodes represent FL nodes.

To enable demonstration without reliance on confidential engineering data, a synthetic but industrially representative FN was constructed, consistent with the CRFN structure detailed by Ref. [11], with variation limited to FML input parameters. Obtaining complete and integrated datasets across FL, PL, MIL, and FML levels remains challenging in many industrial contexts. The selected topology therefore reflects the structural characteristics of large push-based continuous-process operations commonly found in sectors such as mining and oil and gas, including multiple sources, intermediate handling points, and multiple sinks connected through interdependent assets. By modelling these dependencies across network layers, the CRFN preserves the hierarchical and stochastic behaviour observed in real operations, providing a realistic and generalisable basis for evaluating FACE. By employing a synthetic yet representative CRFN, this research demonstrates a minimum viable dataset that organisations could replicate in practice.

While validation using real industrial datasets represents an important step in demonstrating practical performance, the objective of this study is methodological development and analytical proof-of-concept rather than empirical benchmarking. The synthetic CRFN therefore serves as a structurally representative and reproducible testbed that enables controlled examination of systemic behaviour, clear attribution of consequence effects, and evaluation of the internal coherence of the FACE logic. In particular, the to-be-performed experiments are designed to demonstrate the sensitivity of the MCoF metrics to structural and parametric variation and the consistency of resulting criticality insights with established engineering reasoning. Because FACE evaluates consequence as a function of network topology, capacity structure, and flow allocation logic, its analytical behaviour is expected to generalise across production systems that can be represented as push-based FNs. Real-world validation would require integrated datasets capturing production flows, asset reliability behaviour, and cost structures, which are typically distributed across production, maintenance, and financial systems. The illustrative example should therefore be interpreted as establishing a generalisable minimum viable modelling configuration rather than a context-specific case study, demonstrating how FACE can be applied to large-scale production systems once integrated data environments are available.

Figure 5. Example iteration of simulated operation at the PL displaying flows (numerators within fractions on left-hand side of square brackets), capacities (denominators within fractions on left-hand side of square brackets), and costs (negative numbers within square brackets) as depicted in Ref. [11]. Green nodes represent FL nodes and amber nodes represent PL nodes.

Figure 5. Example iteration of simulated operation at the PL displaying flows (numerators within fractions on left-hand side of square brackets), capacities (denominators within fractions on left-hand side of square brackets), and costs (negative numbers within square brackets) as depicted in Ref. [11]. Green nodes represent FL nodes and amber nodes represent PL nodes.

The simulation process enables analysis of production constraints (e.g., supply limitations, equipment capacity restrictions) and MIL parameters (e.g., FM shape and scale parameters, MTTR). FACE is demonstrated and evaluated through the following four simulation experiments; together, these experiments evaluate FACE under varying structural, capacity, and failure-related conditions within a CRFN:

• Experiment 1 (E1): Baseline configuration in which each supply node produces 1000 flow units per iteration (i.e., per shift), exceeding downstream capacity and removing supply-side constraints.
• Experiment 2 (E2): Flow from supply node s₁ (i.e., FL link s₁_ssp) is set to zero flow units per iteration, effectively removing FL link s₁_f₁, with all other conditions matching E1.
• Experiment 3 (E3): PL link capacities under FL links s₃_f₂ and f₂_t₁ are increased to 300 and 250 flow units per iteration, respectively, representing threefold and tenfold capacity increases, with all other inputs unchanged from E1.
• Experiment 4 (E4): Identical to E1 in topology, supply, and capacity, but with randomly generated FM parameters.

Figure 6. Example iteration of simulated operation at the MIL where thick bold (as opposed to grey thin) lines display the chosen MI pathway between PL (and FL) nodes as depicted in Ref. [11]. Green nodes represent FL nodes, amber nodes represent PL nodes, and red nodes represent MIL nodes.

Figure 6. Example iteration of simulated operation at the MIL where thick bold (as opposed to grey thin) lines display the chosen MI pathway between PL (and FL) nodes as depicted in Ref. [11]. Green nodes represent FL nodes, amber nodes represent PL nodes, and red nodes represent MIL nodes.

4.1. Model Inputs

To implement FACE through simulation for any push-based FN (i.e., consistent with Ref. [11]), model inputs must reflect the layered architecture of the CRFN and be aligned with the logic of the CRFNMF. While these inputs define the technical requirements for implementing FACE within a simulation environment, practical deployment depends on how these data can be assembled and governed in organisational settings. The required inputs include:

• Adjacency matrices at the FL, PL, and MIL;
• Capacity and cost matrices at the PL;
• Source node cost rates and sink node revenue rates;
• Outbound inventory limits at FL or PL nodes (set to zero);
• Inbound inventory limits at MIL nodes (set to infinity);
• For each MI:

  o 

  FMs;

  o 

  Shape and scale parameters for each FM in terms of flow units enabled;

  o 

  MTTR_u, MC_u, and SEIC values for each FM.

The input structure outlined above represents a minimum viable dataset for applying FACE to a push-based FN. Although comprehensive, these data requirements largely correspond to information that exists within typical industrial organisations, albeit distributed across multiple systems and functions. Structural topology and capacity data are usually available through engineering design documentation, process flow diagrams, or production planning systems. Reliability parameters and failure mode information are commonly maintained within maintenance management systems or reliability studies, while cost and revenue parameters are derived from financial or operational reporting. In practice, the primary implementation challenge is not data absence but the integration of heterogeneous engineering, maintenance, and economic datasets into a consistent network representation.

From an implementation perspective, FACE does not require a fully developed digital twin or real-time data infrastructure. Initial models can be constructed using a combination of engineering estimates, historical maintenance records, and structured expert elicitation to establish baseline parameters. As organisations improve data integration and governance, model fidelity can be progressively refined.

Consequently, FACE should be viewed as a scalable decision support capability rather than a methodology that depends on complete data availability at the outset. This scalability enables organisations with varying levels of digital maturity to adopt the framework incrementally, using early insights to guide both maintenance prioritisation and future data improvement efforts.

4.2. Simulation Process

The simulation process enabling FACE follows four core steps (see Figure 7, which provides a high-level visual summary of the overall process):

• Step 1—Simulation Initialisation
  The number of simulation iterations per run is defined and fixed. For each simulation run, all FM-related random variables (e.g., shape, scale, MTTR_u, MC_u, SEIC) are fixed, ensuring consistency across iterations.

• Step 2—Calculate Maximum Gross Profit with All MIs Available
  The simulation is executed over a fixed number of iterations with all MIs operational. Each iteration simulates a single shift. Within each iteration:

  o 

  Determine MIL Pathways

  For each PL link, available MIL pathways are evaluated using reliability block diagram (RBD) logic. The average availability of each MI (${\propto }_{{\mathrm{m}\mathrm{i}}_{\mathrm{x}}}$) is calculated using each comprising FM’s MTBF and MTTR_u:

  $${\propto }_{{\mathrm{m}\mathrm{i}}_{\mathrm{x}}}=\prod _{{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\in {\mathrm{m}\mathrm{i}}_{\mathrm{x}}}\left({\displaystyle \frac{{\mathrm{M}\mathrm{T}\mathrm{B}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}}{{\mathrm{M}\mathrm{T}\mathrm{B}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}+{\mathrm{M}\mathrm{T}\mathrm{T}\mathrm{R}}_{\mathrm{u}\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}}}\right)$$

  (3)

  MIL pathway availability (${\propto }_{{\mathrm{M}\mathrm{I}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}$) is then calculated by chaining individual MI availabilities:

  $${\propto }_{{\mathrm{M}\mathrm{I}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}=\prod _{{\mathrm{m}\mathrm{i}}_{\mathrm{x}}\in {\mathrm{M}\mathrm{I}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}{\propto }_{{\mathrm{m}\mathrm{i}}_{\mathrm{x}}}$$

  (4)

  MIL pathways are constructed between relevant source (s_x) and sink (t_x) nodes using a breadth-first search (BFS) at the MIL. The MIL pathway with the highest average availability is selected to support the PL link. If no viable pathway exists, the PL link is excluded from any potential flow allocation.

  o 

  Construct PL and FL Pathways

  Using the MIL pathway enabled PL links $\left({\mathrm{P}\mathrm{L} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{j}}\right)$, PL flow pathways (${\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}})$ between relevant nodes (treated as source (s_x) and sink (t_x) nodes) are constructed using a BFS. Each PL pathway’s per-unit cost (${\mathrm{C}}_{{\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}$) is evaluated using each comprising PL link per-unit cost ${(\mathrm{c}}_{{\mathrm{P}\mathrm{L} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{j}}})$:

  $${\mathrm{C}}_{{\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}=\sum _{{\mathrm{P}\mathrm{L} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{j}}\in {\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}{\mathrm{c}}_{{\mathrm{P}\mathrm{L} \mathrm{l}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{j}}}$$

  (5)

  FL flow pathways ${(\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}})$ are constructed between the FL source (s_x) node and sink (t_x) nodes by linking relevant and available PL pathways ${(\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}})$ using a BFS. Each FL pathway’s per-unit cost (${\mathrm{C}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}$) is evaluated using each comprising PL pathway’s per-unit cost (${\mathrm{C}}_{{\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}$) and the relevant source node per-unit cost (${\mathrm{c}}_{{\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}}$) for the FL pathway:

  $${\mathrm{C}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}={\mathrm{c}}_{{\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{c}\mathrm{e}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}}+\sum _{{\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{j}}\in {\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}{\mathrm{c}}_{{\mathrm{P}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{j}}}$$

  (6)

  o 

  Apply MGPRM for Flow Allocation

  For each FL pathway ${(\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{j}})$, the per-unit gross profit (${\mathrm{G}\mathrm{P}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}^{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}$) is calculated using the relevant sink t node per-unit revenue rate (${\mathrm{R}}_{\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{k}}$):

  $${\mathrm{G}\mathrm{P}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}^{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}={\mathrm{R}}_{{\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{k}}_{\mathrm{t}}}-{\mathrm{C}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{j}}}$$

  (7)

  FL pathways are ranked in descending order based on the FL pathway per-unit gross profit (${\mathrm{G}\mathrm{P}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}^{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}$) and flow is allocated using the MGPRM, as detailed in Ref. [11], until all process-level capacities are exhausted.

  o 

  Compute Iteration-Level Profit

  The total gross profit per iteration (${\mathrm{G}\mathrm{P}}^{\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}$) is computed using the allocated flow for the FL pathway (${\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}$) and the FL pathway per-unit gross profit (${\mathrm{G}\mathrm{P}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{j}}}^{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}$):

  $${\mathrm{G}\mathrm{P}}^{\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}=\sum _{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}\left({\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{U}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{i}}}\times {\mathrm{G}\mathrm{P}}_{{\mathrm{F}\mathrm{L} \mathrm{p}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{w}\mathrm{a}\mathrm{y}}_{\mathrm{j}}}^{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w} \mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}}\right)$$

  (8)

  After all iterations have been completed, the maximum gross profit is computed.

• Step 3—Simulate MIL Failures and Compute Strategic MCoF
  Each MI is simulated as failed and Step 2 is repeated. Based on the results of this process, the strategic MCoF (${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right)})$ is calculated using Equation (1).

• Step 4—Compute Operational MCoF Using FML Parameters
  For each FM of each MI, the operational MCoF (${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$) is calculated using Equation (2).

4.3. Key Assumptions

The following simplifying assumptions were adopted in implementing FACE simulation framework:

• No outbound inventory: All FL and PL node inventories are set to zero to emphasise the immediate effect of MI failures on flow continuity. This simplification removes buffering effects, ensuring that any reduction in flow is directly attributable to asset availability rather than inventory dynamics. It is introduced for demonstration purposes to isolate immediate systemic consequence.
• Unlimited inbound inventory: MIL nodes assume infinite input availability, ensuring that flow constraints arise only from MI availability rather than equipment supply limitations. By eliminating supply constraints, the analysis focuses exclusively on capacity limitations introduced by MI behaviour. This is a demonstration-oriented assumption that isolates equipment-driven effects.
• Perfect maintenance effectiveness: Repairs are assumed to fully restore failed MIs to a good-as-new condition, with no accumulation of degradation. Assuming good-as-new restoration prevents cumulative degradation from influencing results, providing a clear baseline for evaluating consequence. This simplification supports interpretability rather than defining a methodological requirement.
• Fixed inputs per run: Random variables associated with failure mode behaviour (e.g., shape, scale, MTTR_u, MC_u, SEIC) are sampled once and remain fixed within each simulation run. Holding stochastic parameters constant within each run isolates structural variability from sampling noise, improving comparability between scenarios. This assumption supports methodological clarity in consequence estimation.
• Deterministic and optimal flow allocation: Flow allocation within each iteration is performed deterministically and optimally using the MGPRM. Ensuring optimal allocation establishes a performance frontier against which consequence is measured, making this a methodological assumption inherent to the FACE logic rather than a case-specific simplification.
• Isolated failures: Each simulation evaluates the failure of a single MI at a time when computing MCoF values, avoiding compounding failure effects. Evaluating one MI at a time enables marginal consequence attribution without interaction effects. This is a methodological design choice that defines how MCoF is computed.
• Fixed topology: The structural topology of the CRFN is held constant across all experiments. Maintaining a constant network structure ensures that performance variation reflects parameter changes rather than redesign effects. This assumption supports controlled evaluation within the illustrative case.
• Push-based flow logic: Simulations mimic push-based flow driven by source availability. Modelling push-based operation aligns the example with capacity-driven production systems and reflects the current scope of the methodology. Extension to pull-based systems driven by sink demand represents a future methodological development.
• Unconstrained maintenance resources: Maintenance actions are assumed to have sufficient labour and budget availability. Assuming sufficient maintenance capacity removes scheduling constraints, allowing consequence to be evaluated independently of organisational limitations. This is primarily a demonstration simplification to isolate failure impact.

Collectively, these assumptions enable the illustrative example to focus on structural consequence mechanisms while maintaining a clear distinction between core methodological features and case-specific simplifications. Additionally, these assumptions define the analytical boundary conditions of the illustrative example and provide a basis for interpreting the sensitivity of the results. Relaxing these assumptions represents a natural direction for future research.

5. Analysis of the Illustrative Example Study Simulation Results

FACE has been used to generate results that support the analysis of systemic criticality across all MIs and FMs, measured in terms of MU. This analysis is critical to demonstrating that FACE is dynamic, systemic, and performance-based, with criticality assessed in terms of impact to the maximised gross profitability of the illustrative example CRFN. It also confirms that OI, OF, MC, and SEI are considered.

5.1. Strategic Maintenance Analysis: MI Criticality

To ensure meaningful simulation outputs, particularly when calculating and utilising the mean gross profit, the number of iterations per simulation run needed to be large enough to ensure stability but small enough to minimise computational cost. Figure 8 displays the moving average of gross profit across iterations for selected MIs (mi₁₅, mi₃₅, mi₅₅, mi₇₅, and mi₉₅) when independently unavailable. Stability is reached around the 2000-iteration mark, a pattern observed across all MIs. For the purposes of this research, the simulation process was conducted over a 5000-iteration runtime (equivalent to approximately seven years of operation, assuming two 12-h shifts per day across 365 days per year). This runtime is less relevant to ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ values, as these are based on the network properties that determine the maximum gross profit achievable by the system for a given scenario (s_i).

Analysing Figure 9 and Figure 10, which show the relationship between mean gross profit and ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ (i.e., Equation (1)) across the simulation experiments, confirms that ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ is sensitive to changes in simulation inputs. This clearly demonstrates that FACE brings a dynamic dimension to asset criticality evaluation. Moreover, the results objectively highlight the most critical MIs in the FN; a higher ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ value indicates a higher systemic criticality. The results confirm that FACE captures the full structure of the multilayered network (i.e., FL, PL, and MIL as depicted in Figure 4 and Figure 5, and 6), meaning that OI and OF are considered quantitatively based on FN topology and capacities, without reliance on guided scoring processes. Furthermore, the results demonstrate a performance-based evaluation, where MI criticality is measured by the impact of unavailability on gross profit generation at the FN sink nodes (i.e., FL nodes t₁ and t₂).

A good example of FACE’s capability can be seen through analysing Figure 9 and Figure 10 alongside Figure 4 and Figure 6. In E1, the MIs enabling FL link f₁_t₁ are more critical than those enabling FL link s₁_f₁, due to capacity redundancy provided by FL link s₂_f₁. Furthermore, the MIs enabling FL links s₃_f₂ and f₂_t₂ are less critical than those enabling s₁_f₁ and f₁_t₁, based on the capacity of their respective child PL links. However, in E2, supply from source node s₁ is removed (effectively eliminating s₁_f₁), and the MIs enabling s₃_f₂ and f₂_t₂ become more critical to the FN, as their flow contribution becomes essential to the CRFN’s ability to generate gross profit.

Comparing E1 and E3 further confirms this capability under different input conditions. In E1, the MIs enabling s₃_f₂ and f₂_t₁ are again less critical than those enabling s₁_f₁ and f₁_t₁, based on the limited capacity of their child PL links. However, in E3, when the child PL links under s₃_f₂ and f₂_t₁ are increased threefold and tenfold respectively, the MIs associated with these links become more critical to the FN than those associated with s₁_f₁ and f₁_t₁.

When comparing E1 and E4, although MI and FM parameter changes have some impact on the mean gross profit generated, the overall effect is relatively small and subject to the inherent variance of the stochastic simulation process. This outcome was expected, given that MI parameters primarily influence the ability of an FN to sustain generating its maximum gross profit, rather than the maximum gross profit achievable by the FN. While mean gross profit may improve over time, maximum achievable gross profit is constrained by FN network properties, not by MI parameter variation.

These examples demonstrate how FACE dynamically analyses changes in topology, capacities, and other parameters at the FL, PL, MIL, and FML levels, and their effects on MI criticality and FN performance measured in gross profitability.

Another important aspect of FACE’s capability relates to its sensitivity to multilayered network parameters (specifically, the PL and MIL) and its impact on gross profit generated at the FN sink nodes (i.e., FL nodes). Through analysing Figure 11, which displays the relationship between mean gross profit and ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ for FL links s₁_f₂ and f₁_t₂, alongside Figure 5 and Figure 6, it can be seen that, when comparing the criticality of mi₄ (enabling PL link p₁_p₂) with mi₇ and mi₈ (both enabling PL link p₂_f₁), mi₄ is more critical to the FN, as there is no redundancy at either the PL or MIL. In contrast, mi₇ and mi₈ provide redundancy for one another.

A similar pattern is observed when comparing mi₄₇ and mi₄₈ (enabling PL link f₁_p₁₀) with mi₅₀ and mi₅₁ (enabling PL link p₁₀_p₁₁). In this case, mi₄₇ and mi₄₈ are more critical to the FN, as there is no redundancy at either the MIL or PL levels, whereas for mi₅₀ and mi₅₁, redundancy exists at the PL through link p₁₀_p₁₂.

These examples further demonstrate FACE’s ability to dynamically analyse how changes in redundancy, whether through additional PL capacity (e.g., parallel process components) or MIs (e.g., parallel equipment components), affect MI criticality and system-level economic performance.

5.2. Operational Maintenance Analysis: FM Criticality

A significant part of this research involves examining FM criticality through the calculation of ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$, a metric specifically designed to support operational maintenance decision making. Figure 12 displays the ranked criticality of FMs within the FN (i.e., linked to the MIs presented in Figure 6) for E1.

Crucially, Figure 12 confirms that FMs can be individually ranked in terms of systemic criticality, measured objectively by impact on the maximised gross profitability as measured at the FN sink nodes. Although only results linked to E1 are shown, because the calculation method draws on ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right)}$ (defined by Equation (1)), FM criticality is inherently sensitive to changes in simulation inputs and network topology. Thus, OI and OF are again quantitatively incorporated without the use of a guided scoring process.

Additionally, the FM criticality evaluation process incorporates sensitivity to MC and SEI through their inclusion in Equation (2), further strengthening the economic dimension of operational maintenance prioritisation.

It is important to acknowledge the potential impact the MC_u and SEIC components can have on FM rankings and this holds particularly true where these values are significant relative to the flow disruption-based component (i.e., with OI and OF only). As an example, in the case of mi₉₁_fm₁, when the MC_u and SEIC are considered, the FM is ranked as the fifth most critical to FN performance. However, when the MC_u and SEIC are not considered, it is ranked last equally, as it has no impact from an OI and OF perspective. Interestingly, when the additive values associated with the MC_u and SEIC components are removed from the gross profitability impact scores, 81 out of a total 186 FMs have an impact score of 0; meaning almost half of the FMs have no impact on the performance of the FN when independently active and considering OI and OF only.

A closer examination of Figure 9 (specifically E1 and MIs associated with FL links f₁_t₁ and s₁_f₁) and Figure 12 highlights the influence of MTTR_u on FM criticality rankings. Although the MIs (e.g., mi₄₇ and mi₄₈) enabling FL link f₁_t₁ are more critical to the FN than the MIs (e.g., mi₁, mi₂, and mi₆) enabling FL link s₁_f₁, not all associated FMs are ranked higher in terms of their criticality to FN performance. Specifically, FMs mi₁_fm₁, mi₄₇_fm₂, mi₂_fm₂, mi₆_fm₂, and mi₄₈_fm₁ are ranked sixth, tenth, eighteenth, twenty-second, and forty-sixth respectively (see Figure 12).

These findings demonstrate FACE’s value for operational maintenance prioritisation. They also demonstrate the potential strategic value of FML insights, particularly in contexts where the MTTR_u and other (current and future potential) simulation input parameters materially affect FN performance.

5.3. Comparison of Application Outputs: FACE vs. Guided Scoring Process

The guided scoring process used by Refs. [28,31] to generate consequence-specific input values (e.g., OI, OF, MC, SEI) for their subsequent criticality evaluation methods was adopted as a benchmark for comparing the criticality outputs generated by FACE. This comparison is presented for E1, noting that consistent patterns were observed across all simulation experiments. The illustrative example CRFN used throughout this research (see Figure 4, Figure 5 and Figure 6 and associated supporting details) was employed for both approaches.

The process was applied in a manner representative of common industrial practice in large, complex FNs, whereby each FL component is assessed individually based on its associated PL, MIL, and FML elements by teams of operators, technicians, and engineers. As part of this, consequence assessment reflects the influence of series and parallel configurations at the PL and MIL, consistent with the framing provided by [28,31]. Such approaches rely on localised expertise and are constrained by the analytical and organisational complexity of performing fully systemic evaluations across large, complex, and often global FNs.

FACE is explicitly designed to address this limitation by evaluating consequence through integrated analysis across all network layers. When comparing the consequence-based outputs generated by FACE with those produced using guided scoring approaches, clear alignment is observed at both the MIL (${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$) and FML (${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$). In both cases, MIs and FMs identified as highly consequential by guided scoring are similarly ranked by FACE. While both the MIL and FML results exhibit comparable patterns of alignment, the FML results provides greater granularity by explicitly differentiating the contribution of individual FMs.

Figure 12. Example (from E1) of ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{({\mathrm{m}\mathrm{i}}_{\mathrm{x}},{\mathrm{f}\mathrm{m}}_{\mathrm{y}})}$ output for the top 50 (out of 186) FMs.

Figure 12. Example (from E1) of ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{({\mathrm{m}\mathrm{i}}_{\mathrm{x}},{\mathrm{f}\mathrm{m}}_{\mathrm{y}})}$ output for the top 50 (out of 186) FMs.

Figure 13 presents the FML comparison alongside the operational maintenance discussion associated with Figure 12. Across the OI, OF, MC, and SEI dimensions, both approaches clearly differentiate between more and less consequential FMs, with a Pearson correlation of approximately 0.65, indicating a moderate to moderately strong positive relationship. This suggests that, despite being derived from fundamentally different logic, FACE produces rankings broadly consistent with established guided scoring methods, thereby supporting its validity.

The differences in relative ordering arise from FACE’s explicit modelling of consequence propagation through network topology and its direct linkage to gross profitability, rather than reliance on predefined consequence categories or static weighting schemes. As such, FACE provides a system-aware and economically grounded alternative that supports more transparent maintenance prioritisation based on network-level impact.

5.4. Soundness of Consequence-Based Criticality Without Probability

Asset criticality evaluation is fundamentally concerned with understanding the relative importance of assets to system performance. In complex production systems, this importance is often dominated by the magnitude of consequence associated with asset unavailability rather than by failure likelihood alone. Assets whose unavailability produces negligible impact on production system throughput or economic performance remain non-critical regardless of how frequently they fail. Whereas assets whose failure induces substantial loss of system capacity or profitability warrant attention even when failure likelihood is low. Accordingly, consequence-based evaluation provides a sufficient and analytically robust basis for relative criticality ranking within the scope of structural performance assessment of production systems.

In complex production systems, failure probability is not an intrinsic or stable property of MIs or their FMs. Rather, it is highly sensitive to operating conditions, maintenance policies, environmental factors, and modelling assumptions. At the FML, probability estimation is further constrained by limited data availability, evolving degradation mechanisms, and feedback between maintenance actions and system usage. As a result, probability is inherently time-varying and context-dependent, making it an unstable foundation for primary criticality evaluation and a potential source of noise in early-stage decision making.

By contrast, the consequences of reduced system capacity are largely determined by the topology, redundancy, and flow allocation structure of the production system. FACE therefore isolates consequence as a first-order system property by evaluating the impact of MI unavailability and FM-induced capacity reductions under optimal flow reallocation. The resulting MCoF metrics represent a structural lower bound on consequence conditional on failure, providing a stable and comparable measure of MI and FM criticality that is independent of probabilistic assumptions.

Beyond its independence from probabilistic assumptions, the stability of consequence-based criticality can also be considered with respect to variation in economic parameters. Because MCoF is derived from optimal flow reallocation across the network, changes in revenue or cost inputs primarily rescale the magnitude of consequence values rather than fundamentally altering the relative ordering of MI and FM criticality, unless such variations materially change the profitability ranking of alternative flow pathways. This indicates that rankings are structurally driven by network topology, capacity constraints, and redundancy and are therefore expected to remain relatively stable under moderate economic variation. A more formal sensitivity analysis across broader price regimes represents a useful direction for future research.

Separating consequence from probability improves decision transparency by clearly distinguishing impact magnitude from likelihood. Consequence-based metrics quantify the severity of production system performance degradation resulting from asset failures, whereas probabilistic metrics characterise the likelihood of such events. Combining these dimensions prematurely can obscure the structural determinants of criticality and hinder effective decision making. A consequence-first approach therefore supports clearer and more interpretable prioritisation.

From an optimisation perspective, consequence-based ranking identifies the marginal impact of asset availability on system performance. Maintenance decision variables influence expected outcomes through their effect on FMs, and FACE isolates the performance loss associated with these states independently of probability assumptions. As such, the resulting consequence structure forms the baseline upon which probabilistic risk models and optimisation algorithms operate, providing a theoretically consistent foundation for maintenance prioritisation.

Finally, FACE establishes the system-level consequence surface upon which probabilistic analysis and maintenance optimisation can subsequently operate. By identifying the MIs and FMs that are structurally most consequential to production throughput and profitability, FACE defines where probabilistic modelling effort is likely to yield the greatest decision value. Integration of failure probability is therefore a natural extension of the methodology rather than a prerequisite, enabling estimation of expected loss and maintenance optimisation once consequence has been structurally characterised.

5.5. Computational Considerations and Scalability

The computational effort associated with FACE arises primarily from repeated pathway generation and flow allocation across simulation iterations. For the illustrative example CRFN, simulation runs comprising 5000 iterations with sequential evaluation of each MI were completed within typical desktop computing environments, indicating that the methodology is tractable for networks of comparable scale. Each 5000-iteration run performed per MI took approximately 7 min to complete, translating to an approximate runtime of 11 h when analysing all 96 MIs in the system.

Computational complexity increases with the number of nodes and links, as pathway enumeration and profit calculations must be repeated for each simulated scenario. However, the simulation structure is inherently parallelisable, as each failure scenario can be evaluated independently. This characteristic suggests strong scalability for larger industrial networks when implemented using distributed computing or cloud-based environments. Consequently, computational requirements are not expected to be a limiting factor for practical deployment, particularly as industrial analytics platforms increasingly support parallel simulation workflows. However, runtime will depend on network complexity and the granularity of the simulation design. Furthermore, FACE can be applied to large industrial networks using modular decomposition without necessarily altering the underlying evaluation logic.

6. Conclusions and Recommendations for Future Work

This research developed a methodology for evaluating maintainable asset criticality based on network-level economic consequence, with the goal of supporting both strategic and operational maintenance decision-making. To this end, FACE was developed as a transdisciplinary, multilayered, network-based approach building on the CRFNMF and MGPRM. Following suggestions in the literature [6,32], two novel flow-based criticality metrics were introduced that combine discrete-level KPIs, such as MTBF and MTTR, with system-level performance indicators: the ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$, which informs strategic maintenance decisions at the MIL; and the ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$, which extends the analysis to the FML to support operational decision-making.

Simulation experiments were conducted to demonstrate the FACE methodology. Results confirmed that ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ effectively identifies strategically critical MIs, while ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$ provides operationally relevant insights at the FML. Together, these metrics offer an integrated framework for aligning maintenance strategy, planning, and prioritisation with system-level performance outcomes. For practitioners, FACE provides a quantitative basis for assessing which assets most significantly influence throughput, recovery, and profitability, enabling genuine alignment between maintenance and production decisions.

The metrics also connect naturally to resilience-oriented perspectives on production systems. By quantifying the best achievable system performance under reduced network capacity and optimal flow reallocation, FACE implicitly evaluates two key dimensions of system resilience: robustness and adaptive capacity, that is, the ability of a system to absorb disruption and sustain function through reconfiguration, rather than simply characterising the likelihood of disruption itself. In this respect, consequence-based criticality establishes a structural lower bound on performance loss under disruption, providing a principled foundation for subsequent resilience and risk analysis.

Several directions for future research emerge from this work. The most immediate extension involves incorporating failure probability at the FML to enable risk estimation, or expected loss, over defined planning horizons, building directly on the consequence surface established here. Closely related is the task of operationalising ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{{(\mathrm{m}\mathrm{i}}_{\mathrm{x}})}$ and ${\mathrm{M}\mathrm{C}\mathrm{o}\mathrm{F}}_{\left({\mathrm{m}\mathrm{i}}_{\mathrm{x}}\right.,\left.{\mathrm{f}\mathrm{m}}_{\mathrm{y}}\right)}$ within practical maintenance strategy formulation and maintenance planning processes. Beyond these near-term developments, future work could enhance FACE to evaluate joint failure states and cascading disruptions, sampling combinations of MI and FM events to analyse system behaviour under compounding disturbances. Extending FACE to incorporate interdependencies between MIs and FMs would complement this direction, providing a structured representation of how correlated failure states arise and enabling more realistic assessment of interacting disruptions. Further extensions include adapting the framework for pull-based networks and alternative operational strategies, testing it across different network structures and industrial sectors, and investigating the sensitivity of simulation outcomes to modelling assumptions such as inventory constraints. Finally, with increasing sensorisation across industrial systems, there is clear potential to integrate real-time data streams into FACE simulations, refining failure modelling and enhancing predictive maintenance capabilities.

FACE provides a platform for bridging strategic and operational maintenance decisions through a dynamic, systemic, and economically grounded approach. It should be interpreted as a decision-support methodology that complements, rather than replaces, probabilistic risk modelling within maintenance management frameworks, and one that will benefit from further empirical application across diverse industrial contexts to strengthen confidence in its practical performance.