From HRN to HRNt

From HRN to HRNt

Why Steel's classic model needed — and now has — an extension that reads what the modern plant already records.

Thirty-five years of the Hazard Rating Number. Nearly four decades since Steel published the formula that reshaped quantitative risk appreciation in machinery.

GS × FE × PO × NP. Severity × frequency × probability × number of people exposed. Clean, comparable, defensible. There's a reason it stuck.

But the 2025 plant doesn't look like the 1990 plant. We now log proof tests with dates, near-misses with traceability, accidents with digital history. Valuable information the classic model simply wasn't designed to read.

The natural extension

The HRNt model, published in Revista ISTL, proposes exactly the extension the discipline needed. It does not replace the classic HRN — it extends it with two multiplicative factors:

φ(t) — temporal degradation. Penalises the reliability of a safeguard based on the months elapsed since its last proof test, against the approved Proof Test Interval. Smooth growth up to expiry, sharper growth thereafter.

ψ — operational evidence. Weights accidents and near-misses registered on the equipment over a rolling four-year window.

HRNt = √(HRN × HRP) × φ(t) × ψ Backward-compatible: if the machine is up to date and incident-free, HRNt = HRN

The technical elegance lies in the backward-compatible design: if the machine is up to date with its proof tests and incident-free, φ(t) ≈ 1 and ψ = 1. HRNt converges to the classic HRN and historical comparability is preserved. Otherwise, the model automatically broadens the assessment — never inventing risk where none exists, only where operational evidence justifies it.

Empirical validation

Three deliberately heterogeneous sectors:

Sector Classic HRN HRNt Reading

Food & beverage 200 162.48 Downward recalibration by controlled evidence

Paper & cardboard 400 404.77 Confirmation with severity/avoidability balance

Metalworking 600 652.52 Increase due to insufficient testing and near-misses

In all three cases, HRNt reduced statistical dispersion against the classic HRN, increased sensitivity to real operational conditions, and improved the prioritisation of preventive measures.

What this changes for the engineer

1. Plant inspection ceases to be purely visual. Proof-test dates and incident records become formal model inputs, not marginal notes.

2. The defence before an auditor becomes dual. Every appreciation can be contrasted with its classic HRN reading.

3. Prioritisation gains resolution. Equipment formerly classed as equivalent can now be distinguished by real maintenance state.

Normative alignment

HRNt breaks nothing — it extends. Its principles respond to ISO 12100:2010, ISO 13849-1/-2, IEC 62061:2015, IEC 61511:2016, ANSI B11.0:2023 and B11.19:2019, and OSHA 29 CFR 1910.147. Normative convergence without requiring modification.

From theory to practice

A mathematical model without implementation is an academic exercise. There are already industrial platforms running classic HRN and HRNt in parallel on every piece of equipment, governed under ISO/IEC 42001 and with inviolable human validation. One reference implementation is @AI-SAFE, which has operated under that hybrid architecture since 2025.

REFERENCES

Aguirre Andrade, J. & Cañizalez de Aguirre, B. (2025). Mathematical HRNt model for risk estimation in industrial machinery. Revista ISTL — Instituto Tecnológico Superior Libertad. revistaistl.itslibertad.edu.ec

ISO 12100:2010 · ISO 13849-1:2023 · IEC 62061:2015 · IEC 615