A Token-FCM based risk assessment method for complex engineering designs

Guan Wang; Qiang Zou; Rongbin Guo; Yimin Feng; Yusheng Liu

REVIEW 4 major objections 4 minor 36 references

A Token-FCM based risk assessment method for complex engineering designs

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A token-augmented fuzzy cognitive map turns static design-risk models into dynamic simulators that account for time-delayed, two-way causal effects, with a diesel-engine case showing that propagation delays change which components rank as…

desk verdict A genuinely new token-based FCM scheduling idea, but the case-study numbers don't support the headline rankings. read the letter →

arxiv 2501.15406 v1 pith:QWUF43EN submitted 2025-01-26 cs.CE

Guan Wang , Yimin Feng , Rongbin Guo , Yusheng Liu , Qiang Zou This is my paper · ORCID

classification cs.CE

keywords riskassessmentfuzzycognitivemaptokenmechanismtimedelaydynamicprioritynumberprobabilisticlinguistictermsetsgroupdecisionmakingengineeringdesign

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes Token-FCM, an extension of fuzzy cognitive maps in which small 'tokens' carry risk values along arcs and wait out a time delay before activating the target node. The aim is to make risk assessment for engineering designs capture two-way and time-delayed causal relations that static methods such as FMEA, fault trees, and ordinary FCMs ignore. The authors claim that combining this token mechanism with a group-decision initialization based on probabilistic linguistic term sets yields a dynamic risk priority number (DRPN) per component, and that the DRPN ranking is more informative than the static RPN ranking. A real diesel-engine design is used to argue that time delays change which risks dominate during operation, not just the numerical values.

What carries the argument

The central object is the token: a packet carrying five attributes (TokenID, NodeID, NodeValue, ArcTimeDelay, ArcWeight). A node updates its value only when a token arrives, using the weighted-sum update of Eq. (2): $f(A_i) = f(A_i + \sum_j w_j v_j)$, where $w_j$ and $v_j$ are the arc weight and starting-node value carried by token $j$. Arcs are classified into one-to-one, one-to-many, and many-to-one relations; one-to-many duplicates tokens, and many-to-one lets a node be activated several times at different arrival times. The second machinery is the initialization pipeline: expert opinions on occurrence, severity, and detection are collected as linguistic ratings, aggregated through probabilistic linguistic term sets with group decision making, converted to a fuzzy RPN via the weighted geometric-mean rule of Eq. (6), and defuzzified with Eq. (8) to give each node's initial value. Together these parts let the simulation respect time delays and bidirectional influence.

What would settle it

Re-run the diesel-engine case study with a longer simulation horizon (for example 100 minutes instead of 50) and compare the cycle-averaged DRPN values for DR1, DR2, and DR4. If the averages change with the horizon, or if the three-value cycle repeats with a different phase, then the claimed 'stable' DRPN is an artifact of the stopping rule rather than a property of the risk dynamics; that would settle the convergence concern directly.

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Extended reading notes

Core claim

Token-FCM models each design risk as a node in a fuzzy cognitive map and lets an update happen only when a token arrives after a fixed time delay, so the simulation follows a chronological trigger sequence rather than simultaneous updates. The central claim is that this produces a Dynamic Risk Priority Number (DRPN) that reflects both the static risk level (RPN, from occurrence, severity, and detection difficulty) and the two-way, time-delayed propagation of risk through the design. On the diesel-engine case, the authors show that the static ranking (piston > valve > camshaft > big-end bearing > cylinder head > fuel injector) differs from the dynamic ranking (piston > fuel injector > valve > cylinder head > camshaft > big-end bearing), and argue that the dynamic ranking is the one that matters during operation. They also claim that ignoring time delays overestimates the influence of rapid causal chains and misorders the risks.

Load-bearing premise

The load-bearing premise is that when a node's value enters a repeating finite cycle of length three (DR1, DR2, DR4 in the case study), the arithmetic mean of those three values is the correct 'stable' risk index; the paper applies this averaging rule without proving that the cycle average is independent of the simulation horizon, and it concedes that some time-delay assignments never converge.

Editorial extensions

If this is right

If the central claim holds, design reviews should use DRPN rankings rather than RPN rankings, because two components with the same static risk can behave very differently once propagation delays are accounted for.
The 'Most Impact DR' column tells the designer which other component's failure most amplifies each risk; for the diesel engine, piston failure (DR2) is the most influenced node, directing reliability effort to the piston and its physical and energy flow.
Time-delay modeling changes the ordering of risks: without delays the fuel injector (DR4) would appear nearly as risky as the piston, but with delays it drops below it, showing that quick-feedback loops matter more than the number of incoming influences.
The method can be transferred to other engineering designs with bidirectional, time-delayed failure relations, provided experts can agree on arc weights and delays and the simulation converges.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: Token-FCM is effectively a discrete-event simulation, so its convergence question can be reframed as a scheduling problem on token arrival times; a convergence guarantee might come from bounding the set of possible arrival times rather than averaging limit cycles.
Beyond the paper: a direct test of the central claim would compare DRPN-ranked components against observed failure frequencies in field data across many drilling machines; the case study shows plausibility, not predictive advantage.
Beyond the paper: the token mechanism could also be added to other graph-based risk models such as Bayesian networks or Petri nets to give them time-delayed two-way dynamics; the paper does not claim this extension, but the token design does not depend on fuzzy logic alone.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Worth knowing: Token-FCM is a real variation—tokens carry time-delay and weight information and activate node updates asynchronously. That's a concrete way to bring time delays into FCM inference, and the initialization via probabilistic linguistic term sets plus group decision is a sensible pipeline for engineering design risk. The paper is readable and the engine example is a real, non-trivial system.

The problem is the demonstration. The stress-test note is right: the DRPN values in Table 9 cannot be derived from the time series in Table 7. For instance, Table 7 shows DR2 cycling between 0.7412 and 0.7716 after t=40, but Table 9 reports DRPN2=0.8438. DR5's steady values are around 0.777, yet Table 9 gives 0.7020, which is actually DR6's value. The 'average of the three cycle values' is not specified well enough to reproduce any of these entries. Since the ranking in Section 6.4 and the time-delay comparison in Table 11 all rest on these DRPN values, the effectiveness claim is internally unsupported.

Two other soft spots. The threshold function used in the case study is never stated; Eq. 2's f is said to bound [0,1], but the initial RPN values are negative, and the paper doesn't explain how those map in. That alone is fixable, but it's needed for reproducibility. Also, the FMEA comparison in Section 6.4.1 is built from the same expert O/S/D ratings and the same arc weights, so it doesn't validate the method—it just confirms that both methods encode the same input.

What the paper does well: the token concept is clearly explained, the pseudocode is concrete, and the authors honestly flag the possible non-convergence of time-delayed activation in Section 7. That's good practice.

My take: the contribution is a new implementation, not a new conceptual framework. The method is plausible, but the reported results fail an internal consistency check. With corrected numbers, a stated threshold function, and a comparison against generalized/dynamic FCM [6,29], it could be a useful tool. As-is, it needs major revision.

Referee Report

4 major / 4 minor

Summary. The paper proposes Token-FCM, a fuzzy cognitive map augmented with a token mechanism, to model two-way and time-delayed causal-effect risk relations in engineering design. The method uses a fuzzy-set and group-decision-based initialization to compute initial node values (RPNs), then iterates a token-based update rule to obtain dynamic risk priority numbers (DRPNs). The approach is demonstrated on a diesel engine case study and compared with a custom FMEA variant. The authors claim that Token-FCM provides more comprehensive and accurate risk assessments than static methods, and they discuss limitations including potential non-convergence in Section 7.

Significance. If the method were properly validated, it would address a real gap: most existing risk assessment methods cannot handle bidirectional, time-delayed causal-effect relations. The token mechanism is a creative extension of FCM, and the group-decision-based initialization is a useful contribution. However, the case study as reported is internally inconsistent and not reproducible: the reported DRPNs do not follow from the displayed iteration data, the threshold function is never specified, and the 'most impact' analysis appears degenerate. The significance of the empirical demonstration is therefore currently not established. No code, complete parameter set, or formal convergence criterion is provided.

major comments (4)

[Section 6.2, Tables 7 and 9] The DRPN vector reported in Table 9 cannot be reproduced from the iteration values in Table 7. For example, the stable values of DR2 from t=40 to t=50 are 0.7716, 0.7412, 0.7662, 0.7662, 0.7716, 0.7412; neither the mean nor the maximum of these values equals the reported DRPN2=0.8438. Similarly, DRPN5=0.7020 equals the steady value of DR6, not of DR5 whose stable values are about 0.7767-0.7786, and DRPN6=0.7659 lies far above the displayed DR6 values of about 0.7014-0.702. Since the DRPN column is the basis for the rankings and for the comparative claims in Section 6.4, the demonstration of effectiveness as reported is internally unsupported.
[Section 3.3 and Eq. (2)] The threshold function f in Eq. (2) is stated to bound node values into [0,1], but the case-study initial values computed by Eq. (8) are negative (e.g., DR3=-1.3390, DR4=-1.5745). The specific threshold function used for the diesel engine simulation is never given; Section 3.3 mentions 'Sigmoid()' only in a small illustrative example. This makes the reported iteration values irreproducible and leaves the relationship between the negative initial RPNs and the bounded iteration values unexplained.
[Section 6.2 and Section 7] The rule 'take the average of the three cycle values' is not well-defined. In Table 7, DR1, DR2, and DR4 exhibit a four-step period (e.g., DR1: 0.6908, 0.7872, 0.799, 0.8041), not three distinct values, and no average of any three or four consecutive stable values matches the entries in Table 9. A formal convergence criterion and a precise definition of the reported 'stable' value are needed, especially because Section 7 concedes that Token-FCM can fail to converge for some time-delay assignments.
[Section 6.2, Table 8 and Table 9] The independent activation analysis in Table 8 produces nearly identical final vectors for all six initial conditions (e.g., the DR1-init and DR6-init final rows differ only in the third decimal place). The 'Most Impact DR' column in Table 9 is therefore reading noise-level differences as meaningful; the claim that 'five design risks DR1, DR3, DR4, DR5, and DR6 all have a greater influence on DR2' is not supported by the magnitude of these differences.

minor comments (4)

[Table 9 and Section 6.4.1] There are several presentation errors in the comparison text: Table 9 lists 'Cylinder head crackin' instead of 'Cylinder head cracking', and the ranking sentence in Section 6.4.1 contains 'Camshaft failure' twice and appears internally inconsistent.
[Section 6.4.1, Eq. (9a)] The FMEA variant uses a nonstandard hazard index e^(O+S+D) rather than the traditional RPN product O×S×D. The text should clarify that this is a custom variant and justify why it is a fair benchmark for the comparison.
[Algorithm 1 and Eq. (7)] The symbol t is used both for the iteration step size in Algorithm 1 and for the range of linguistic terms in Eq. (7). This is confusing and should be disambiguated.
[Reference [36]] The author name 'Docent, D.' in reference [36] appears to be a title or role rather than a person's name; the reference should be verified and corrected.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: DRPN is a genuine simulation output, not a fitted input; one minor non-load-bearing self-citation and self-referential validation, plus an internal Table 9/Table 7 arithmetic mismatch, explain the low score.

full rationale

The Token-FCM derivation chain is feed-forward: expert O/S/D linguistic ratings (Table 5) are aggregated by group decision-making (Eqs. 3-4), converted to fuzzy RPN values (Eqs. 6-8), used as initial node values, and then propagated through Algorithm 1 / Eq. 2 with expert-supplied arc weights and time delays (Table 6) to obtain the DRPN vector. No parameter is fitted to the reported DRPN values, and no reported output is defined in terms of the quantity it is said to predict, so the central calculation is not circular. The only author self-citation is reference [33] (Wang et al. 2021), which supports the generic statement that individual expert experience can be limited; this is not the load-bearing premise of the method. The FMEA comparison in Section 6.4.1 uses the same O/S/D ratings and arc weights that initialize Token-FCM, so it is a self-referential sanity check rather than an independent validation, but it is not the source of the DRPN values. Two rigor issues are flagged for completeness but are not circularity: (a) Section 6.2 states that the average of the three cycle values is used as the final DRPN, yet Table 9 cannot be reproduced from Table 7; for example, DR2's values at t=40-50 are 0.7716, 0.7412, 0.7662, 0.7662, 0.7716, 0.7412, whose mean is about 0.7597, not the reported 0.8438, and 0.8438 does not appear in the stable cycle at all; and (b) Section 7 concedes that Token-FCM can fail to converge for some time-delay assignments. These problems undermine the demonstration's internal support, but they do not make the stated derivation equivalent to its inputs.

Assumptions & free parameters 6 free parameters · 6 assumptions · 1 invented entities

The central claim rests on expert-chosen weights, time delays, arc weights, and an unspecified threshold function, plus an ad hoc rule for converting limit cycles into stable risk values. None of these are validated against independent data, so the method's quantitative outputs are only as trustworthy as the expert inputs and the unverified convergence assumption.

free parameters (6)

O/S/D risk-index weights (wO, wS, wD) = wO=0.5, wS=0.35, wD=0.15
Used in Eq.6 to aggregate expert opinions into RPN; set by expert judgment, not by data, and no sensitivity analysis is given.
Arc weights W_ij = Table 6 (e.g., DR1->DR2 0.8, DR2->DR4 0.8, DR4->DR3 0.4)
Expert-assigned influence strengths between design risks; they directly determine DRPN values and the final ranking.
Arc time delays = Table 6 (2 to 10 minutes)
Expert-assigned propagation delays; the paper's main claim is that these change the ranking, yet they are subjective inputs.
Threshold function f = Unspecified in case study (example uses Sigmoid)
Eq.2 requires f bounding values into [0,1]; the case study never states which f is used, and negative initial RPN values suggest an inconsistency.
Iteration step size t and horizon T = t=2 min, T=50 min
Simulation parameters chosen by the authors; the final DRPN depends on them because limit-cycle averaging is applied.
Limit-cycle averaging rule = Average of three cycle values
The DRPN for DR1, DR2, DR4 is the mean of one limit cycle's values, an ad hoc summary without a formal justification.

assumptions (6)

standard math Kosko FCM update rule with threshold function f (Eq.1) is a valid model of causal influence propagation
Adopted from Kosko (1986) and Papageorgiou (2013); not re-derived.
standard math Probabilistic linguistic term set operations and g/g^-1 conversion faithfully aggregate expert opinions
Borrowed from Pang et al. [34] and Montserrat-Adell et al. [35] without verification.
domain assumption Expert-supplied O, S, D ratings and RPN aggregation (Eq.6-8) produce meaningful initial risk values
The method assumes that subjective expert scores quantify failure risk; no calibration against historical failure data.
domain assumption The causal graph, arc weights, and time delays in Table 6 correctly represent the diesel engine's failure propagation
The entire case-study output depends on these expert inputs; no empirical failure-propagation data are used.
ad hoc to paper A Token-FCM limit cycle can be summarized by the arithmetic mean of its values as the 'stable' DRPN
Section 6.2 averages the three values of the DR1/DR2/DR4 cycle; Section 7 concedes convergence is not guaranteed.
domain assumption Token movement rules in Section 3.2 correctly model physical failure propagation timing
The token behavior is a modeling choice; no comparison to real failure sequences validates it.

invented entities (1)

Token (Token-FCM)
purpose: Carries time delay and arc weight information to activate node updates asynchronously, implementing time-delayed causal propagation in FCM.
The token is a computational construct with no falsifiable prediction outside the simulation; its correctness rests on the modeler's choices.

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Cite this review

Pith. "Pith review of A Token-FCM based risk assessment method for complex engineering designs." pith.science (2026). https://pith.science/paper/QWUF43EN

@misc{pith2026250115406,
  author       = {Pith},
  title        = {Pith review of: A Token-FCM based risk assessment method for complex engineering designs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QWUF43EN}},
  note         = {Machine review of arXiv:2501.15406}
}

read the original abstract

Engineering design risks could cause unaffordable losses, and thus risk assessment plays a critical role in engineering design. On the other hand, the high complexity of modern engineering designs makes it difficult to assess risks effectively and accurately due to the complex two-way, dynamic causal-effect risk relations in engineering designs. To address this problem, this paper proposes a new risk assessment method called token fuzzy cognitive map (Token-FCM). Its basic idea is to model the two-way causal-risk relations with the FCM method, and then augment FCM with a token mechanism to model the dynamics in causal-effect risk relations. Furthermore, the fuzzy sets and the group decision-making method are introduced to initialize the Token-FCM method so that comprehensive and accurate risk assessments can be attained. The effectiveness of the proposed method has been demonstrated by a real example of engine design for a horizontal directional drilling machine.

Figures

Figures reproduced from arXiv: 2501.15406 by the authors.

**Figure 2.** Internal block diagram of spacecraft power subsystem using the SysML. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** An example of FCM with five nodes and seven arcs. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Two states of the nodes: (a) activated and (b) inactivated. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 6.** Figure 6: Tokens behavior under one-to-many causal-effect rela [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 5.** Figure 5: Tokens behavior under one-to-one causal-effect relation: [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 7.** Figure 7: Tokens behavior under many-to-one causal-effect rela [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: The example of token behavior. 0.677, Arc T ime Delay : 5, Arc W eight : 0.6}, as shown in Figure 8e. 5) After 5 minutes, the token arrives at the node C3 and subsequently activates it. Then the token’s attributes are changed to: {T oken ID : 1, Node ID : 3, Node V al…

**Figure 9.** Figure 9: The cross-section of diesel engine [36]. According to Section 5, first initialize the value for each FCM node, that is, for each design risk index. To obtain a more reliable risk index, subjective evaluations of 20 experts are collected on the O, S, and D indexes of ea…

**Figure 10.** Figure 10: FCM of the diesel engine design risk. After expert review and empirical data analysis, the impact weight of each design risk and the time delay triggered by each design risk event are obtained, as shown in [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

**Figure 11.** Figure 11: Changes in risk index RP Ni of design risks during iteration. In combination with [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]

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Probabilistic linguistic term sets in multi-attribute group decision making,

Pang, Q., Wang, H., and Xu, Z., 2016, “Probabilistic linguistic term sets in multi-attribute group decision making,” Information Sciences, 369, pp. 128–143

2016
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Consensus, dissension and pre- cision in group decision making by means of an al- gebraic extension of hesitant fuzzy linguistic term sets,

Montserrat-Adell, J., Agell, N., S ´anchez, M., and Ruiz, F. J., 2018, “Consensus, dissension and pre- cision in group decision making by means of an al- gebraic extension of hesitant fuzzy linguistic term sets,” Information Fusion, 42, pp. 1–11

2018
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Approximating the condition and maximum load of an engine by comparing en- gine measurements,

Docent, D., 2016, “Approximating the condition and maximum load of an engine by comparing en- gine measurements,” PhD thesis, Aalto University

2016

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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Risk-based resource allocation for collaborative system design in a distributed environment,

Qiu, Y ., Ge, P., and Yim, S. C., 2008, “Risk-based resource allocation for collaborative system design in a distributed environment,” Journal of Mechani- cal Design, 130(6), 04, p. 061403

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Uncertainty quantification in dynamic system risk assessment: a new approach with randomness and fuzzy the- ory,

Abdo, H., and Flaus, J.-M., 2016, “Uncertainty quantification in dynamic system risk assessment: a new approach with randomness and fuzzy the- ory,” International Journal of Production Research, 54(19), pp. 5862–5885

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Petri net extensions for modelling and validating manufacturing systems,

Choi, B. W., KUOJ, W., and Jackman, J., 1994, “Petri net extensions for modelling and validating manufacturing systems,” International Journal of Production Research, 32(8), pp. 1819–1835

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Availability modelling of repairable systems using bayesian net- works,

Neil, M., and Marquez, D., 2012, “Availability modelling of repairable systems using bayesian net- works,” Engineering Applications of Artificial Intel- ligence, 25(4), pp. 698–704

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A framework for building dimensionless behavioral models to aid in function- based failure propagation analysis,

Coatan ´ea, E., Nonsiri, S., Ritola, T., Tumer, I. Y ., and Jensen, D. C., 2011, “A framework for building dimensionless behavioral models to aid in function- based failure propagation analysis,” Journal of Me- chanical Design, 133(12), 12, p. 121001

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Generalised fuzzy cognitive maps: Consid- ering the time dynamics between a cause and an ef- fect,

Nair, A., Reckien, D., and van Maarseveen, M. F., 2020, “Generalised fuzzy cognitive maps: Consid- ering the time dynamics between a cause and an ef- fect,” Applied Soft Computing, 92, p. 106309

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Fuzzy cognitive maps,

Kosko, B., 1986, “Fuzzy cognitive maps,” In- ternational journal of man-machine studies, 24(1), pp. 65–75

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A review of fuzzy cognitive maps research during the last decade,

Papageorgiou, E. I., and Salmeron, J. L., 2012, “A review of fuzzy cognitive maps research during the last decade,” IEEE transactions on fuzzy systems, 21(1), pp. 66–79

work page 2012