When
Functional Safety Math Equals Signal Integrity Math

This is a high-level summary. The full paper — with all
derivations, the 17-tool cross-domain transfer matrix, and four worked
examples translating FMEDA tables into jitter budgets — is on Zenodo.

The observation

Functional safety (ISO 26262, IEC 61508) and high-speed signal
integrity are usually treated as entirely separate engineering
disciplines. One is reliability engineers writing FMEDAs at ASIL-D. The
other is signal-integrity engineers fighting jitter at 25 Gbps SerDes
lanes.

But both rest on the same mathematical structure:
decompose total failure probability into systematic (bounded) and random
(unbounded) contributions, then quantify how much of each is covered by
detection or margin mechanisms.

The paper makes the correspondence precise and shows how to use
it.

The master equation

Both fields compute, in the end, the same kind of integral: a bounded
distribution convolved with a sub-Gaussian distribution, evaluated at a
threshold.

In functional safety, that integral is the residual
hardware failure probability — the leftover risk after you’ve accounted
for safety mechanisms. The standard reports it as PMHF (Probabilistic
Metric for Hardware Failures), broken down via SPFM (Single-Point Fault
Metric) and LFM (Latent-Fault Metric).

In signal integrity, the same integral is the bit
error rate at a target eye opening. Total jitter (TJ) decomposes into
deterministic jitter (DJ — bounded) and random jitter (RJ — Gaussian).
The dual-Dirac model picks a BER target, the convolution gives you the
eye margin you need, and the design either makes that margin or it
doesn’t.

The paper writes down the mappings explicitly:

Functional safety	Signal integrity
Single-Point Fault Metric (SPFM)	Deterministic jitter margin ratio
Latent-Fault Metric (LFM)	Correlated-jitter coverage
PMHF	Bit error rate (BER)
Diagnostic coverage (DC)	Equalisation effectiveness
FMEDA	Jitter budget
Common-cause / dependent failure	Correlated jitter

Why it matters

For safety engineers: Signal-integrity engineers
have spent decades developing tools — eye diagrams, dual-Dirac
decomposition, jitter-tolerance curves — for exactly the kind of
bounded-plus-Gaussian convolution problem you face when computing PMHF.
You can borrow their visualisations and their decomposition methods
directly.

For signal-integrity engineers: Reliability
engineers have spent decades developing tools — FMEDA, FTA, Markov
models, common-cause analysis — for exactly the kind of failure-mode
bookkeeping you face when allocating a jitter budget across a serial
channel. You can borrow their hierarchical decomposition and their
coverage frameworks directly.

For project leads: Knowing the duality lets you
transfer expertise across teams that usually don’t talk to each other.
The senior safety engineer can review your jitter budget. The senior SI
engineer can review your FMEDA. They’ll both find different things,
because they bring different vocabulary to the same underlying
mathematics.

Cross-domain tool transfer

The 17-tool transfer matrix in §8 is the practical core of the paper.
For each tool from one domain, it lists how to apply it in the
other:

FMEDA → jitter budgeting
FTA → root-cause for jitter excursions
Markov models → jitter accumulation across serial channels
Common-cause analysis → correlated jitter on shared clock trees
Eye diagrams → safety margin visualisation
Dual-Dirac decomposition → SPFM/LFM split
Jitter tolerance curves → diagnostic-coverage characterisation

Four worked examples in §7 walk through the translation in both
directions: an ISO 26262 FMEDA reframed as a jitter budget, and a 25
Gbps SerDes margin analysis reframed as a safety case.

This paper is a companion to Hardware Safety
Methodology for Electronic Systems: A Practitioner’s Guide,
which covers the practitioner side of FMEDA in depth. Read them together
if you want both the methodology and the deeper mathematical
connection.

Get the full paper

Probabilistic Fault
Metrics and Signal Jitter: A Unified Mathematical Framework
— Zenodo, 2026. DOI: 10.5281/zenodo.19349165. Open access.

Working at the intersection of functional safety and high-speed
signal integrity? Get in touch.

#FunctionalSafety #SignalIntegrity #ISO26262 #Jitter #SerDes
#Reliability #HighSpeed #Mathematics

When Functional Safety Math Equals Signal Integrity Math