Drawing on Song & Zhang [33] and Brunel et al. [34], the evaluation subjects, including the general public (non-specialist personnel), on-site frontline operational workers, and industry safety domain experts, were stratified into three cohorts based on professional competency and hazard perception. Out of 500 distributed questionnaires, a rigorous screening process yielded 120 valid responses. To ensure data reliability and eliminate arbitrary scoring, incomplete or logically inconsistent submissions were excluded, ultimately retaining 20 valid questionnaires from safety domain experts, 40 from on-site frontline operational workers, and 60 from the general public.

As shown in Table 2, although the SDE sample size (n = 20) is relatively small compared with the FOW (n = 40) and NSP (n = 60) cohorts, the SDE group represents a highly filtered, homogeneous tier of certified senior engineers and safety directors. Statistical dispersion metrics in this study indicate high intra-group consensus among SDEs, which suppresses outlier susceptibility and ensures the robustness of the reference metric despite the imbalanced cohort sizes.

Table 2. Profiles of the 8 representative high-frequency construction cases and the research design framework.

Note: SDE = Safety Domain Experts (n = 20); FOW = Frontline Operational Workers (n = 40); NSP = Non-Specialist Personnel (n = 60). Note: All 120 validated respondents provided complete empirical LEC risk ratings across all 8 cases (CASE-1 to CASE-8). CASE-1 to CASE-4 correspond directly to the focal operations mentioned in the study design, while CASE-5 to CASE-8 complete the comprehensive operational spectrum of high-risk site activities.

Referring to the previous study of Al-Bayati & Chellappa [35], such as senior engineers, engineers, certified constructors, safety supervisors, and qualified surveyors, the expert cohort was defined as professionals holding relevant industry certifications with a minimum of three years of active domain experience. Specifically, this expert sample is predominantly composed of individuals born between 1980 and 1989 (13 individuals, accounting for 65%). The remaining age distribution includes 4 individuals born between 1970 and 1979 (20%), 2 individuals born between 1990 and 1999 (10%), and 1 individual born between 2000 and 2009 (5%).

Also, to comprehensively represent the complex risk landscape of modern construction environments, the survey in this study evaluated eight high-frequency, typical on-site operational cases as shown in Table 2.

The foundational analytical model employed in this study is the LEC operational condition hazard evaluation method, while the mathematical framework is expressed as:

where the variables are formally defined as follows:

1) L(Likelihood): Represents the probability of an accident occurring, defined on a continuous scale with discrete reference values ranging from 0.1 to 10.

2) E(Exposure): Denotes the frequency of human exposure to the hazardous environment, with values ranging from 0.5 to 10.

3) C(Consequence): Indicates the severity of the consequences should an accident occur, with values ranging from 1 to 100.

4) D(Danger/TotalRiskScore): Represents the cumulative hazard score. Based on the calculated magnitude of D, occupational hazards are classified into five distinct risk levels, where a higher value strictly correlates with a greater operational risk.

Furthermore, referring to GB/T 33000-2025 (Requirements of work safety management system for large and medium-sized enterprises), T/XZBX 0154-2025 (Code for safety risk classification management and control of construction engineering site), and T/CCPITBSC 096-2025 (Specifications for safety risk prevention and control in high-rise building construction), this study applies the adopted L, E, and C grading tables and corresponding common risk classification standards, which are shown in Table 3.

Table 3. Standardized LEC valuation matrix.

To systematically elucidate the domain-specific subjective evaluation bias inherent in the traditional Likelihood-Exposure-Consequence (LEC) safety assessment framework, including safety domain experts ( N = 20 ), frontline operational workers ( N = 40 ), and non-specialist personnel ( N = 60 ), raw metric scores assigned by three distinct evaluator cohorts were processed using four scaling adjustment coefficients ( k = 0.8 , 1.0 , 1.2 , 1.4 ). As shown in Figure 2, including the arithmetic mean ( μ ) and standard deviation ( σ ), statistical metrics were synthesized across eight representative construction operational cases to characterize score hierarchies and inter-group dispersions.

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Figure 2. Mean scores analysis of the operational condition risk assessment. (a) High-altitude operations, (b) Temporary electrical works, (c) Scaffold erection and dismantling, (d) Trench excavation and earthworks, (e) Tower crane lifting and hoisting operations, (f) Confined space operations, (g) Hot works, (h) Heavy mobile machinery operations.

3.1.1. Dimensional Hierarchies & Quantitative Magnitude Distribution

Referring to Kokangül et al. [36], raw metric scores were first transformed using the scaling coefficient k to evaluate the dimensional characteristics without confounding mathematical domain bounds with cognitive risk weights. Let x m , s , i r a w denote the raw metric score assigned for dimension m ∈ { L , E , C } by individual i in scenario s ∈ { 1 , 2 , ⋯ , 8 } . The adjusted score x m , s , i ( k ) under scaling factor k is formulated as:

Because the baseline assignment domains defined by the traditional LEC lookup framework are inherently non-uniform, where L ∈ [ S L m i n , S L m a x ] = [ 0.1 , 10 ] , E ∈ [ S E m i n , S E m a x ] = [ 0.5 , 10 ] , C ∈ [ S C m i n , S C m a x ] = [ 1 , 100 ] , direct numerical comparisons of raw averages ( x ¯ C > x ¯ E > x ¯ L ) induce a deceptive scalar artifact. To decouple the intrinsic domain boundary effects from genuine subjective risk weights, a dimensionless normalized metric x ˜ m , s , i ( k ) is established via min-max domain mapping:

Furthermore, the relative partial elasticity ϵ m of the risk score D = L ⋅ E ⋅ C with respect to each metric dimension m demonstrates equal mathematical weighting in logarithmic derivative space:

As shown above, Equation (4) proves that the multiplicative structure of the LEC model imparts identical relative sensitivity ( ϵ L = ϵ E = ϵ C = 1 ) to all three parameters. Consequently, any observed raw absolute dominance of C over L and E is purely an artifact of scale allocation bounds ( S C m a x / S L m a x = 10 ) rather than an inherent structural priority of risk severity over likelihood or exposure.

Across all eight construction operational cases in Figure 2, raw score averages exhibit a persistent numerical hierarchy where x ¯ C ∈ [ 3.68 , 33.50 ] significantly exceeds x ¯ E ∈ [ 2.19 , 7.21 ] and x ¯ L ∈ [ 0.44 , 3.58 ] . In high-hazard operations such as High-altitude Work (Figure 2(a)) and Scaffolding Erection (Figure 2(h)), raw mean scores for Consequence Severity ( C ) reach peak values exceeding 30.0 under k = 1.4 . Conversely, in lower-severity tasks like Ground Material Handling (Figure 2(e)) and Mechanical Cutting (Figure 2(c)), raw C scores drop to lower ranges ( x ˜ C = 3.68 ~ 11.38 ). However, when evaluated through the dimensionless normalized metric x ˜ m , s , i ( k ) , the apparent dominance of C diminishes substantially. In routine handling operations (Figure 2(e)), normalized exposure frequency x ˜ E = 0.28 ~ 0.45 actually surpasses normalized consequence severity x ˜ C = 0.03 ~ 0.08 , demonstrating that risk magnitude in non-catastrophic tasks is primarily driven by exposure persistence rather than extreme loss potential.

An analytical difference in this study revealed by the four scaling coefficients ( k = 0.8 , 1.0 , 1.2 , 1.4 ) is the non-linear compound expansion of the total risk score D . Since D ( k ) = k 3 ⋅ D r a w , applying scalar multipliers linearly expands individual parameters but exponentially inflates total risk scores. In high-consequence cases (e.g., High-altitude Work in Figure 2(a) and Trench Edge Protection in Figure 2(f)), this multiplicative amplification magnifies initial raw evaluation discrepancies by up to 1.4 3 ≈ 2.744 times. This exponential scaling underscores the vulnerability of traditional uncalibrated LEC scoring, as small subjective variance in high-bounded dimensions ( C ) disproportionately skews final risk classification thresholds ( D ).

3.1.2. Dimension-Specific Cognitive Dispersions & Scale Range Effects

As noted in Bedeian & Mossholder [37], to quantify inter-group evaluation dispersion independent of scalar magnitude, the dimensionless Coefficient of Variation ( C V m , i , s ) is formulated for each dimension m , cohort i , and situation s :

where σ m , i , s represents the sample standard deviation. Equation(5) confirms that C V is invariant under linear scaling factors k , rendering it a robust metric for cross-cohort reliability analysis. To capture the extent to which baseline metric scale ranges ( S m m a x − S m m i n ) distort absolute variance perception, the Scale Range Effect ( S R E m , i , s ) is defined as:

In addition, referring to Xu [38], the Inter-Cohort Discrepancy Index ( D I m , s ) measures the standardized distance between non-expert cohorts ( i ∈ { W o r k e r s , O r i d i n a r y } ) and the safety domain experts ( i = E x p e r t ):

Empirical observations across Figures 2(a)-(h) reveal a stark dichotomy between absolute standard deviation ( σ ) and relative dispersion ( C V ). Across all cases, Likelihood ( L ) and Exposure ( E ) display tight absolute error bars ( σ L ∈ [ 0.47 , 3.58 ] , σ E ∈ [ 1.73 , 4.57 ] ), whereas Consequence Severity ( C ) exhibits massive absolute standard deviations ( σ C ∈ [ 2.51 , 42.69 ] ). However, evaluating relative dispersion via Equation(5) reverses this visual impression: C V L ( 0.42 ~ 0.85 ) and C V E ( 0.38 ~ 0.62 ) exhibit higher relative dispersion than C V C ( 0.25 ~ 0.55 ) in routine tasks. The discussions in this study prove that while evaluators reach numerical convergence on L and E due to constrained baseline options ( [ 0.1 , 10 ] and [ 0.5 , 10 ] ), their underlying relative cognitive uncertainty regarding event probability remains substantial.

The vast absolute standard deviation observed in Consequence Severity ( σ C ) is predominantly driven by the Scale Range Effect ( S R E C ). Because the scoring bounds for C span across two orders of magnitude (1~100), discrete leaps between rating anchors (e.g., jumping from 15 “single fatality” to 40 “multiple fatalities”) generate huge statistical variance. In High-altitude Work (Figure 2(a)), Confined Space Inspection (Figure 2(d)), and Scaffolding Erection (Figure 2(h)), Non-specialist personnel and Workers exhibit extreme variance ( σ C > 30.0 under k = 1.4 ). The wide spread in this study reflects divergent cognitive interpretations of worst-case accident outcomes versus nominal operational incidents among non-expert personnel.

As scaling coefficients increase from k = 0.8 to k = 1.4 , absolute error bar spans in Figures 2(a)-(h) dilate proportionally ( σ ( k ) = k ⋅ σ r a w ), while the visual widening of error bars in this study must not be misinterpreted as deteriorating evaluation consensus at higher scaling factors. Because C V remains perfectly constant across all k values, linear scaling alters only the visual metric resolution without changing the underlying stochastic consistency of cohort perceptions. Nevertheless, the Inter-Cohort Discrepancy Index ( D I C , s ) confirms that inter-group divergence is highest in Consequence Severity ( C ), pinpointing C as the primary source of subjective bias in multi-cohort safety risk assessment.

3.1.3. Situation-Dependent Risk Perception Patterns across Evaluator Cohorts

According to Zhao et al. [39] and Sjöberg [40], to model cohort-specific cognitive bias across varying operational contexts, the Cohort Perception Bias ( Δ μ m , i , s ) relative to the safety domain experts is defined as:

To evaluate how each evaluator cohort perceives relative risk severity across the spectrum of operational cases, the Situation Risk Sensitivity Index ( R S I i , s ) is established:

Furthermore, the overall Cognitive Divergence Metric ( C D M s ) synthesizes multi-dimensional perceptual variance across all three parameters for a given situation s :

Analysis of Figure 2(a) to Figure 2(b) demonstrates distinct, situation-dependent cognitive patterns among the three evaluator cohorts. The safety domain experts ( N = 20 ) display structured, risk-discriminative behavior, assigning high risk scores ( D ) exclusively to high-consequence, structurally complex operations, such as High-altitude Work in Figure 2(a), Trench Edge Protection in Figure 2(f), and Scaffolding Erection in Figure 2(h). In the critical operations above, safety domain experts maintain conservative scoring on Consequence Severity ( C ), recognizing secondary risks such as structural instability and cave-ins. On the other hand, for standardized or low-energy tasks like Ground Material Handling in Figure 2(e) and Conventional Hot Work in Figure 2(g), safety domain experts consistently assign low likelihood ( L ) and severity ( C ) scores, reflecting a highly calibrated risk perception anchored in technical standards and historical failure experiences.

Frontline operational workers ( N = 40 ) display a dual cognitive bias characterized by “Operational Habituation” and “Immediate Hazard Sensitivity.” In routine high-risk environments such as Trench Edge Protection in Figure 2(f) and Scaffolding Erection in Figure 2(h), workers consistently underestimate Likelihood ( L ) and Exposure ( E ) compared to safety domain experts ( Δ μ L , W o r k e r < 0 ). Long-term exposure to site hazards induces psychological desensitization (“risk numbness”), leading workers to perceive frequent hazardous exposures as acceptable baseline conditions. However, for tasks such as Temporary Electrical Work in Figure 2(b) and Mechanical Cutting in Figure 2(c), frontline operational workers assign elevated severity scores ( C ) in tasks involving immediate mechanical or electrical contact hazards, driven by direct first-hand exposure to personal injuries and acute operational mishaps.

Non-specialist personnel ( N = 60 ) exhibit maximum cognitive divergence ( C D M s ), driven by systemic information asymmetry and a lack of engineering expertise. The analysis in this study indicates that non-specialist personnel suffer from severe “Cognitive Polarization,” resulting in overestimation of visible, high-profile hazards and underestimation of complex, hidden risks. Such as High-altitude Work in Figure 2(a) and Confined Space Inspection in Figure 2(d), non-specialist personnel overestimate risk scores ( D ), yielding peak values far exceeding those of safety domain experts ( Δ μ > 0 ), which stems from dread-risk anxiety associated with height and asphyxiation. Conversely, in tasks such as Trench Edge Protection in Figure 2(f) and Scaffolding Erection in Figure 2(h), non-specialist personnel fail to recognize latent geotechnical and structural stability hazards, yielding severe risk underestimation, which underscores the critical necessity of introducing cohort-specific calibration coefficients ( k ) to reconcile subjective evaluation discrepancies in site safety management.

Building upon the foundational parameter comparisons, this study advances to a deeper cognitive evaluation of the aggregated risk score ( D ) within the Likelihood-Exposure-Consequence (LEC) framework. To systematically decode the compounding mechanisms of subjective bias across the three distinct stakeholder safety domain experts ( N = 20 ), frontline operational workers ( N = 40 ), and non-specialist personnel ( N = 60 ), the raw evaluation metrics were subjected to a dynamic calibration matrix utilizing four scaling coefficients ( k = 0.8 , 1.0 , 1.2 , 1.4 ). As shown in the statistical trajectories from Figures 3(a)-(h), which synthesize arithmetic means ( μ ) and standard deviations ( σ ) across eight representative construction cases, this analysis moves from descriptive data to cognitive-behavioral diagnostics. By reflecting shifting score hierarchies and inter-group dispersions across varied k -values [41]-[44], such as workers’ operational habituation and laypersons’ risk polarization, this study elucidates cohort-specific perceptual disparities, demonstrating the efficacy of targeted calibration in bridging multi-stakeholder consensus gaps.

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Figure 3. Assignment analysis of the operational condition risk assessment. (a) High-altitude operations, (b) Temporary electrical works, (c) Scaffold erection and dismantling, (d) Trench excavation and earthworks, (e) Tower crane lifting and hoisting operations, (f) Confined space operations, (g) Hot works, (h) Heavy mobile machinery operations.

3.2.1. Cognitive Modeling & Sensitivity Decomposition

According to Man et al. [45] and Pinto et al. [46], this study derives the aggregated operational risk score D is derived via the multiplicative synthesis formulation D = L × E × C to eliminate random observational noise and subjective cognitive discrepancies across evaluator cohorts. The weighted mean risk score evaluated by the expert cohort is established as the professional consensus proxy ( D j * = D ¯ E , j ) for each operational case of the situation j ∈ { 1 , 2 , ⋯ , 8 } . To quantify the parametric sensitivity and risk distortion among non-expert stakeholders (on-site frontline operational workers W and non-specialist personnel P ), a coefficient-scaling transformation function is introduced as below:

where D i j represents the raw weighted average risk score of stakeholder cohort i ∈ { W , P } under situation j . The linear response gradient of the risk score with respect to the scaling coefficient k is given by:

To avoid the epistemological misconception that Consequence Severity ( C ) dictates risk magnitude over Likelihood ( L ) or Exposure ( E ) solely due to its larger numerical bounds ( C ∈ [ 1 , 100 ] vs. L ∈ [ 0.1 , 10 ] , E ∈ [ 0.5 , 10 ] ) [47][48], a logarithmic additive decomposition framework is formulated in this study. Taking the natural logarithm of the risk synthesis function yields:

The logarithmic cognitive deviation ( Δ ln D i j ) of a non-expert cohort relative to the expert reference ( D j * ) is expressed as:

where δ ln X i j = ln X ¯ i j − ln X E , j * for X ∈ { L , E , C } . Equation(14) proves that the proportional variation in the aggregated risk score D is an isotropic, scale-invariant sum of the relative logarithmic cognitive discrepancies of the individual indicators [49].

Furthermore, the Relative Cognitive Distortion Index ( R C D I i j ) and the optimal stakeholder calibration coefficient ( k i , j * ) required to harmonize non-expert risk ratings with expert references are defined as:

When R C D I i j > 0 , the stakeholder group overestimates the operational risk, necessitating a reductive calibration factor ( k * < 1.0 ); conversely, when R C D I i j < 0 , the operational risk is underestimated, requiring an amplificative calibration factor ( k * > 1.0 ).

Within the calculation above, this study formally defines the SDE weighted mean risk score as a heuristic reference baseline ( D j * = D ¯ E , j ) rather than asserting the expert cohort as an infallible or absolute physical standard. Based on the specific calculated approach above, the operational definition posits that while expert perception is not immune to epistemic uncertainty, it represents the most robust, normatively calibrated professional consensus available for cross-cohort risk harmonization.

3.2.2. High-Consequence Structural & Elevation Hazards

1) High-Altitude Operations (CASE-1, Figure 3(a))

For high-altitude operations, the safety domain experts were established at D 1 * = 111.31 . As illustrated in Figure 3(a), non-specialist personnel demonstrated an acute risk overestimation trend, yielding a raw score of D ¯ P , 1 = 306.42 ( R C D I P , 1 = + 1.753 ). The response trajectory for non-specialist personnel exhibits the steepest response gradient ( d D P , 1 / d k = 306.42 ), rising rapidly from 245.14 ( k = 0.8 ) to 428.99 ( k = 1.4 ), and this stems from severe psychological dread and a lack of engineering context regarding fall-arrest protections. Frontline operational workers yielded a moderately elevated rating ( D ¯ W , 1 = 144.15 , R C D I W , 1 = + 0.295 ). To reconcile these evaluations with the safety domain experts D 1 * , the optimal calibration factors were computed as k W , 1 * = 0.772 ≈ 0.8 for frontline operational workers and k P , 1 * = 0.363 < 0.8 for non-specialist personnel.

2) Scaffolding Erection Operations (CASE-8, Figure 3(h))

Scaffolding erection represents a complex elevation hazard with a safety domain experts of D 8 * = 248.52 . In stark contrast to CASE-1, both non-expert groups exhibited significant risk underestimation, as depicted in Figure 3(h). Frontline operational workers evaluated the raw risk at D ¯ W , 8 = 150.13 ( R C D I W , 8 = − 0.396 ), while non-specialist personnel recorded an even lower rating of D ¯ P , 8 = 82.46 ( R C D I P , 8 = − 0.668 ). Frontline scaffolders suffer from operational risk habituation, underestimating structural instability and dynamic load risks, whereas non-specialist personnel lack awareness of temporary structure failure mechanics. Because no intersection with the safety domain experts occurs within k ∈ [ 0.8 , 1.4 ] , both cohorts require strong amplificative calibration coefficients: k W , 8 * = 1.655 > 1.4 and k P , 8 * = 3.014 ≫ 1.4 .

3) Trench and Foundation Pit Edge Protection (CASE-6, Figure 3(f))

As shown in Figure 3(f), trench and foundation pit edge protection exhibited the most pronounced multi-stakeholder risk underestimation among all evaluated cases. While safety domain experts assigned a high baseline score of D 6 * = 96.74 due to soil collapse and slope instability hazards, frontline operational workers ( D ¯ W , 6 = 32.94 , R C D I W , 6 = − 0.659 ) and non-specialist personnel ( D ¯ P , 6 = 33.55 , R C D I P , 6 = − 0.653 ) produced nearly identical, suppressed evaluations. The response curves for both non-expert cohorts remain positioned far below the expert reference across the entire range of k ∈ [ 0.8 , 1.4 ] . This convergence highlights that non-experts intuitively perceive trench edges as static ground terrain, failing to comprehend subsurface geomechanical failure modes. Due to this, both groups require an aggressive scaling correction factor of k W , 6 * = 2.937 > 1.4 and k P , 6 * = 2.883 > 1.4 .

3.2.3. Process & Environmental Hazards

1) Temporary Electrical Operations (CASE-2, Figure 3(b))

Temporary site power distribution shows an expert-reference baseline of D 2 * = 33.53 . Figure 3(b) indicates that frontline operational workers assigned the highest raw risk score ( D ¯ W , 2 = 75.50 , R C D I W , 2 = + 1.252 ), demonstrating a response gradient of d D W , 2 / d k = 75.50 , which reflects workers’ direct operational encounters with electrical hazards, cable wear, and wet ground conditions. Non-specialist personnel evaluated the risk as moderately higher than safety domain experts ( D ¯ P , 2 = 47.03 , R C D I P , 2 = + 0.403 ). Reconciling these evaluations requires reductive calibration parameters as k W , 2 * = 0.444 < 0.8 for frontline operational workers and k P , 2 * = 0.713 ≈ 0.7   -   0.8 for non-specialist personnel.

2) Routine Inspection in Confined Spaces (CASE-4, Figure 3(d))

Atmospheric hazards in confined spaces resulted in a safety domain experts of D 4 * = 21.22 . As displayed in Figure 3(d), frontline operational workers demonstrated high-degree cognitive alignment with safety domain experts, scoring a raw value of D ¯ W , 4 = 20.26 ( R C D I W , 4 = − 0.045 ), which intersects the safety domain experts at k W , 4 * = 1.047 ∈ [ 1.0 , 1.2 ] . Conversely, non-specialist personnel exhibited cognitive inflation ( D ¯ P , 4 = 27.75 , R C D I P , 4 = + 0.308 ) due to claustrophobic anxiety and heightened perception of toxic gas hazards, requiring a reductive factor of k P , 4 * = 0.765 < 0.8 .

3) Conventional Hot Work Without Surrounding Flammables (CASE-7, Figure 3(g))

For conventional hot work, safety domain experts set the reference at D 7 * = 60.13 . As Figure 3(g) shows, risk perceptions diverged significantly. Frontline welders and cutters underestimated the risk ( D ¯ W , 7 = 31.04 , R C D I W , 7 = − 0.484 ), as routine exposure breeds complacency regarding thermal radiation and stray sparks. In contrast, non-specialist personnel overestimated the risk ( D ¯ P , 7 = 96.98 , R C D I P , 7 = + 0.613 ) due to visual fear of open flames. Neither the non-expert curve intersects the safety domain experts within k ∈ [ 0.8 , 1.4 ] . Alignment requires an amplificative correction for workers ( k W , 7 * = 1.937 > 1.4 ) and a reductive correction for non-specialist personnel ( k P , 7 * = 0.620 < 0.8 ).

3.2.4. Low-Consequence Routine Operational Hazards

1) Mechanical Cutting Operations (CASE-3, Figure 3(c))

Mechanical cutting represents a low-to-moderate physical hazard with a safety domain experts of D 3 * = 30.05 . As shown in Figure 3(c), both non-expert groups overestimated operational risks. Non-specialist personnel produced the highest evaluation ( D ¯ P , 3 = 59.66 , R C D I P , 3 = + 0.985 ), driven by visceral apprehension of high-speed blade contact and flying debris. Frontline operators yielded a moderately inflated rating ( D ¯ W , 3 = 43.06 , R C D I W , 3 = + 0.433 ). Consequently, reductive calibration parameters are required for both groups, as k W , 3 * = 0.698 < 0.8 and k P , 3 * = 0.504 < 0.8 .

2) Ground Material Handling Operations (CASE-5, Figure 3(e))

Ground material handling represents a high-frequency, low-severity routine activity ( D 5 * = 21.95 ). Figure 3(e) demonstrates that frontline operational workers accurately calibrated the operational risk ( D ¯ W , 5 = 20.55 , R C D I W , 5 = − 0.064 ), yielding an ideal calibration coefficient near unity ( k W , 5 * = 1.068 ≈ 0.8   -   1.0 ). Conversely, non-specialist personnel dramatically inflated the risk ( D ¯ P , 5 = 54.30 , R C D I P , 5 = + 1.474 ) due to subjective overestimation of physical exertion and manual lifting risks. Aligning non-specialist personnel evaluation requires a reductive factor of k P , 5 * = 0.404 < 0.8 .

3.2.5. Operational Calibration Matrix ( k ∗ ) & Multi-Stakeholder Risk Alignment

To synthesize the empirical findings across all eight construction scenarios, Table 4 compiles the expert reference values ( D * ), raw non-expert ratings ( D ¯ ), Relative Cognitive Distortion Indices ( R C D I ), and optimal calibration coefficients ( k * ).

Table 4. Operational calibration matrix (k*) and multi-stakeholder risk alignment across 8 reference construction cases.

Note: D^*: Expert Baseline; D ¯ W : On-Site Workers Raw; RCDIW: Worker Distortion; kW^*: Worker Calibration; D ¯ P : Ordinary Public Raw; RCDIP: Public Distortion; k P * : Public Calibration.

The systematic analysis of Table 4 reveals three fundamental cognitive mechanisms governing subjective safety evaluation as below:

1) UniversalNon-ExpertBlindSpots(SevereUnderestimation, k ≫ 1 . 4 ):

In cases involving complex structural or geotechnical failure mechanisms (S6: Trench Protection, S8: Scaffolding Erection), both workers and non-specialist personnel severely underestimate risk ( R C D I ≈ − 0.40 ~ − 0.66 ), which establishes an urgent imperative for site safety management to deploy dynamic amplification factors ( k * > 1.4 ) rather than relying on uncalibrated survey averages.

2) RoutineOperationalHabituation( k > 1 . 4 ):

Frontline operational workers exhibit pronounced risk habituation in high-frequency hazardous tasks such as Hot Work (S7, R C D I W = − 0.484 ), necessitating upward calibration ( k W * = 1.937 ) to correct for workplace complacency.

3) VisceralRiskInflation( k < 0 . 8 ):

Non-experts without a technical engineering background consistently over-evaluate highly visual or high-dread hazards (S1: High Altitude, S3: Cutting, S5: Material Handling), generating positive cognitive distortion ( R C D I P up to +1.753). These scores require aggressive scaling compression ( k * < 0.8 ) to prevent false positives and misallocation of operational resources in risk management.

The quantitative assessment of accident likelihood ( L ) across the eight baseline construction cases demonstrates a high degree of convergence among distinct evaluation cohorts for routine, localized operations, contrasted by pronounced divergence in dynamic, structural hazard environments (AppendixTable A2).

Under standard scaling conditions ( k = 1.0 ), baseline likelihood mean scores ( μ L ) across all evaluators remained restricted within a low-amplitude range of 0.57 to 2.10.

SafetyDomainExperts(SDE): Safety domain experts exhibited superior hazard discrimination sensitivity. The mean likelihood values reached peak magnitude in high-altitude operations (CASE-1: μ L = 1.69 , σ L = 2.55 ) and trench edge protection (CASE-6: μ L = 2.10 , σ L = 1.70 ), while yielding minimum values for mechanical cutting (CASE-3: μ L = 0.64 , σ L = 0.59 ). The elevated standard deviations observed in expert evaluations for gravity-related hazards reflect a highly differentiated risk perspective grounded in dynamic site conditions and regulatory compliance standards.FrontlineOperationalWorkers(FOW): Operational frontline personnel displayed systematically lower mean likelihood ratings ( μ L ∈ [ 0.57 , 1.62 ] ) and reduced variance relative to safety domain experts. This attenuation is primarily attributable to operational habituation and spatial familiarity bias, wherein continuous exposure to structural hazards induces an underestimation of potential accident initiation probabilities.Non-SpecialistPersonnel(NSP): Non-expert evaluators demonstrated erratic scoring dispersion ( σ L reaching up to 3.25 under k = 1.4 in CASE-3). Lacking contextual safety knowledge, their L -value assignments fluctuated widely, overestimating probabilities in visually striking operations (e.g., CASE-3 Mechanical Cutting: μ L = 1.66 , σ L = 2.32 at k = 1.0 ) while underestimating latent dynamic risks.

As many previous studies have shown [50]-[53], parameter L serves as a relatively stable baseline metric for low-complexity task evaluations; however, subjective probability assessment in non-linear dynamic construction environments necessitates expert-calibrated reference coefficients to eliminate cognitive optimism bias.

The analysis of risk exposure frequency ( E ) quantifies the temporal and spatial involvement of personnel within hazardous operational zones (AppendixTable A3). Across all cohorts, E -metric scoring spanned a moderate numerical band ( μ E ∈ [ 2.19 , 7.21 ] across all k factors).

OccupationalPatterning: Scaffolding erection (CASE-8) registered the highest continuous exposure indices across all three cohorts ( μ E = 5.15 for safety domain experts; μ E = 4.86 for frontline operational workers; μ E = 4.12 for non-specialist personnel at k = 1.0 ). This reflects a shared consensus regarding the sustained, multi-phase spatial vulnerability inherent in structural scaffold assembly. Conversely, confined space inspection (CASE-4) yielded the lowest exposure averages ( μ E = 3.70 for safety domain experts; μ E = 2.74 for frontline operational workers at k = 1.0 ), aligning with its characterization as an intermittent, highly controlled operational task.Inter-CohortDispersion: Safety domain experts demonstrated slightly higher exposure estimates ( μ E ) and moderate standard deviations ( σ L ∈ [ 2.67 , 3.27 ] at k = 1.0 ), evaluating exposure from a strict normative framework that considers environmental variability and secondary containment duties. Frontline operational workers displayed remarkably stable intra-group variance ( σ E ), reflecting direct empirical awareness of physical shift durations and site throughput schedules. Non-specialist personnel, while tracking general operational trends, exhibited elevated relative variance ( σ E / μ E ), underscoring an inability to differentiate between active task execution and passive environmental exposure.

In summary, parameter E exhibits stronger cross-cohort evaluation consistency than likelihood ( L ) or consequence severity ( C ), as temporal exposure is more readily anchored to observable physical durations on-site.

Accident consequence severity ( C ) was identified as the predominant source of subjective dispersion and variance within the LEC evaluation system (AppendixTable A4). Mean consequence scores exhibited extreme scalar stratification ( μ C ∈ [ 3.68 , 57.13 ] across scaling factors), driving the overall magnitude of the composite risk index.

High-SeverityDomainCharacteristics: For high-fatality-risk operations such as high-altitude work (CASE-1), trench edge protection (CASE-6), and scaffolding erection (CASE-8), all cohorts yielded elevated C -scores. However, the internal logic of scoring diverged significantly between groups, as shown below:

1) SafetyDomainExperts(SDE): Assigned conservative severity values (e.g., CASE-1: μ C = 17.55 , σ C = 23.29 at k = 1.0 ), reflecting comprehensive risk modeling that accounts for regulatory penalties, structural damage, and multi-casualty disaster thresholds.

2) FrontlineOperationalWorkers(FOW): Exhibited elevated consequence ratings for immediate, explicit physical injuries (e.g., CASE-1: μ C = 23.93 at k = 1.0 ), driven by direct peer exposure to major injury events. However, they significantly underestimated consequences for insidious hazards, such as trench edge collapses (CASE-6: μ C = 6.38 vs. Expert μ C = 13.95 at k = 1.0 ).

3) Non-SpecialistPersonnel(NSP): Displayed non-Gaussian scoring distributions. Notably, in temporary electrical operations (CASE-2), novice evaluations showed severe statistical dispersion ( σ C = 18.75 at k = 1.0 and σ C = 68.56 at k = 1.2 ), indicating severe cognitive polarization due to a lack of technical comprehension regarding electrical shock mechanisms and systemic arc-flash hazards.

Low-SeverityDomainCharacteristics: Ground material handling (CASE-5) consistently anchored the lower bound of consequence metrics across all groups ( μ C ∈ [ 3.68 , 5.83 ] at k = 1.0 ), confirming strong broad consensus regarding lower-tier physical trauma hazards (e.g., minor contusions, localized strains).

The empirical data demonstrate that C -value subjective bias constitutes the primary driver of risk misclassification in traditional LEC applications, requiring targeted mathematical adjustment based on evaluator background.

The empirical data demonstrate that C -value subjective bias constitutes the primary driver of risk misclassification in traditional LEC applications, requiring targeted mathematical adjustment based on evaluator background. Also, to verify that the SDE represents true objective risk rather than mere subjective groupthink, the expert evaluations were corroborated against macro-level historical accident databases. Based on the analytical results, SDEs anchored peak Consequence Severity ( C ) and total risk ( D ) values to High-altitude Operations (CASE-1) and Scaffolding Erection (CASE-8), which impeccably mirror empirical industry fatality statistics, where falls from height and structural collapses dominate historical construction site mortalities, accounting for over 60% of total annual fatalities [54]-[57]. Such alignment with empirical historical reality confirms that the SDE cohort serves as a mathematically rigorous and historically grounded reference baseline for subsequent model calibration.

The compound risk score, defined by the non-linear multiplicative formulation D = L × E × C , synthesizes individual parameter uncertainties into an integrated hazard index (AppendixTable A5). The quantitative findings highlight a critical mathematical vulnerability in the traditional LEC method due to multiplicative error propagation.

Under first-order error approximation and relative variance expansion, the compound perturbation follows:

As demonstrated by the compounded metric dynamics across adjustment factors k ∈ { 0.8 , 1.0 , 1.2 , 1.4 } :

CompoundedVarianceAmplification: While individual parameter variations ( L , E , C ) remained within modest bounds, the resulting composite risk scores ( D ) expanded exponentially. For instance, in safety domain experts’ evaluations of trench edge protection (CASE-6), the mean risk score inflated from D = 137.66 ( σ D = 533.38 ) at k = 0.8 to D = 1291.08 ( σ D = 5002.54 ) at k = 1.4 , which confirms that minor subjective variations in primary scoring inputs undergo severe non-linear amplification in high-hazard situations.CognitiveAsymmetry&RiskMisclassification:

1) Over-OptimisminHigh-RiskSituations: Field workers (GW) and non-specialist personnel (GP) exhibited severe risk underestimation in critical structural tasks. In CASE-6 (trench edge protection), worker-assigned risk values D = 32.94 at k = 1.0 ) were over an order of magnitude lower than expert references ( D = 336.08 ). A similar habituation deficit was observed in scaffolding erection (CASE-8: Worker D = 150.13 vs. Expert D = 248.52 at k = 1.0 ). The findings in this study emphasize that a habituation-driven deficit creates catastrophic management blind spots if uncorrected.

2) Hyper-InflationinLow-to-ModerateHazards: Non-specialist personnel significantly overestimated hazards in visible operational tasks, such as mechanical cutting (CASE-3: Worker D = 145.66 vs. Expert D = 30.05 at k = 1.0 ), leading to potential resource misallocation in routine site safety enforcement.

Domain-SpecificCalibrationRequirements: The linear scaling factor k effectively shifts non-expert evaluation distributions toward the reference expert envelope ( D E x p e r t ). However, because cognitive bias varies non-linearly across distinct hazard domains, a universal adjustment coefficient is mathematically invalid. Field worker inputs for scaffold and trench hazards require upward scaling ( k > 1.4 ) to compensate for risk habituation, whereas novice inputs for mechanical cutting require downward suppression ( k < 0.8 ).

In conclusion, implementing multi-subject correction coefficients within the LEC framework mitigates individual subjective bias and provides a quantitatively grounded foundation for classifying construction safety risks. However, using a simple linear scalar multiplier ( k ) to adjust the aggregated hazard score ( D ) has an inherent mathematical limitation. Given the non-linear error propagation innate to the D = L × E × C structure, applying a terminal linear adjustment compresses the macroscopic disparity without rectifying the root-cause variations residing unevenly within the individual parameters L , E , and C . The deployment of a unified scalar k in this study serves as a pragmatic operational compromise to ensure computational feasibility and ease of implementation for frontline site management. While future iterations of this framework are expected to transition from a scalar multiplier to parameter-decoupled calibration vectors ( k L , k E , k C ) to achieve authentic source-level correction, the current unified calibration proxy effectively counteracts severe multiplicative error expansion, establishing a calculational first step toward dynamic cross-cohort risk harmonization.