Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
|
| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.20093192 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866901923082272768 |
|---|---|
| author | Zafar, Usman |
| author_facet | Zafar, Usman |
| contents | <p>This paper introduces the DeBruijn functional Λ(T,H) as a mathematically rigorous operator<br>theoretic framework for the analysis and assurance of Safety Instrumented Systems (SIS), Safety<br>Instrumented Functions (SIF), and Safety Integrity Level (SIL) performance. The proposed<br>functional defines a localized, positive, self-adjoint quadratic form capable of quantifying unsafe<br>deviation, fault intensity, degradation accumulation, and consequence-weighted hazard exposure<br>within a unified analytical structure.</p> <p>Three physically meaningful realizations of the safety signal Z(t) are developed. The first<br>interprets Z(t) as closed-loop control deviation from a prescribed safe operating manifold, yield<br>ing a direct measure of accumulated unsafe process excursion. The second interprets Z(t) as<br>a diagnostic residual generated from model–plant disagreement, thereby capturing latent fault<br>growth, sensor degradation, actuator inconsistency, and structural anomalies. The third ex<br>tends the framework to risk-weighted safety analysis by embedding spatially and operationally<br>dependent hazard severity kernels into the functional, allowing the metric to distinguish between<br>benign deviations and deviations with catastrophic consequence potential.</p> <p>Under suitable kernel regularity conditions, the resulting DeBruijn functional admits a<br>compact spectral representation and possesses strong stability, localization, and monotonic<br>ity properties relevant to SIL verification. The framework naturally unifies time-domain safety<br>monitoring, frequency-domain degradation characterization, and consequence-sensitive hazard<br>quantification within a single mathematically closed formalism. Unlike conventional SIL metrics<br>based solely on probabilistic averages such as PFDavg and PFH, the proposed approach pro<br>vides a continuous analytical measure of dynamic safety integrity capable of resolving localized<br>unsafe behavior, transient degradation phenomena, and evolving fault structures. The resulting<br>theory establishes a forward-looking foundation for mathematically rigorous functional safety<br>assessment, real-time safety intelligence, and next-generation operator-theoretic SIL assurance<br>methodologies.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20093192 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The De Bruijn Functional: Enhanced Metric for Safety Intelligence Systems. Zafar, Usman Functional analysis functional safety sil sis failure rate <p>This paper introduces the DeBruijn functional Λ(T,H) as a mathematically rigorous operator<br>theoretic framework for the analysis and assurance of Safety Instrumented Systems (SIS), Safety<br>Instrumented Functions (SIF), and Safety Integrity Level (SIL) performance. The proposed<br>functional defines a localized, positive, self-adjoint quadratic form capable of quantifying unsafe<br>deviation, fault intensity, degradation accumulation, and consequence-weighted hazard exposure<br>within a unified analytical structure.</p> <p>Three physically meaningful realizations of the safety signal Z(t) are developed. The first<br>interprets Z(t) as closed-loop control deviation from a prescribed safe operating manifold, yield<br>ing a direct measure of accumulated unsafe process excursion. The second interprets Z(t) as<br>a diagnostic residual generated from model–plant disagreement, thereby capturing latent fault<br>growth, sensor degradation, actuator inconsistency, and structural anomalies. The third ex<br>tends the framework to risk-weighted safety analysis by embedding spatially and operationally<br>dependent hazard severity kernels into the functional, allowing the metric to distinguish between<br>benign deviations and deviations with catastrophic consequence potential.</p> <p>Under suitable kernel regularity conditions, the resulting DeBruijn functional admits a<br>compact spectral representation and possesses strong stability, localization, and monotonic<br>ity properties relevant to SIL verification. The framework naturally unifies time-domain safety<br>monitoring, frequency-domain degradation characterization, and consequence-sensitive hazard<br>quantification within a single mathematically closed formalism. Unlike conventional SIL metrics<br>based solely on probabilistic averages such as PFDavg and PFH, the proposed approach pro<br>vides a continuous analytical measure of dynamic safety integrity capable of resolving localized<br>unsafe behavior, transient degradation phenomena, and evolving fault structures. The resulting<br>theory establishes a forward-looking foundation for mathematically rigorous functional safety<br>assessment, real-time safety intelligence, and next-generation operator-theoretic SIL assurance<br>methodologies.</p> |
| title | The De Bruijn Functional: Enhanced Metric for Safety Intelligence Systems. |
| topic | Functional analysis functional safety sil sis failure rate |
| url | https://doi.org/10.5281/zenodo.20093192 |