Most fields require very high probabilities of safety, even when the stakes are much lower than the extinction of humanity.^[1] Here are a few examples with risk thresholds expressed in Log Odds (base 10).

Intro to Log Odds

Instead of writing probabilities like 0.9999 which is hard to read, I'll use log odds.

$LogOdds (p) = {log}_{10} (\frac{p}{\neg p}) = {log}_{10} (\frac{p}{1 - p})$

So LogOdds $(0.9999) \approx 4$

Conversion Trick: rounding LogOdds towards zero^[2] roughly corresponds to the number of nines/zeros after the dot in the probability. Conveniently, the complementary probability in log space is just negative. LogOdds $(1 - p) = -$ LogOdds(p)

Civil Engineering

United States

General Structural Design (ASCE/SEI 7-22)^[3]

Target Reliability Table (excluding earthquake, tsunami, and extraordinary events) Annual probability of various types of failure.

$S =$ sudden, $W =$ widespread progression of damage

Types of Failure	Risk Categories
Types of Failure	I^[4]	II^[5]	III^[6]	IV^[7]
$\neg S \land \neg W$	-3.90	-4.52	-4.90	-5.30
$S \lor W$	-4.52	-5.30	-5.70	-6.15
$S \land W$	-5.30	-6.15	-6.60	-7.00

Bridges (AASHTO LRFD)

Lifetime Reliability Target ( $β = 3.5$ )

LogOdds: -3.63 lifetime reliability (-5.51 annual, for a typical 75 year service life)

Dams (Bureau of Reclamation Public Protection Guidelines)

Piecewise log-log fatality-probability guidelines. (-1 slope represents constant Annualized Life Loss)

ALARP = As Low As Reasonably Practicable

"ALARP is now considered to apply anywhere on the risk portrayal chart"

Case Study: Citicorp Center^[8]

1/16 annual chance of collapse was unacceptable

LogOdds: -1.18

Europe

Building Minimum Reliability^[9] (EN 1990)

Reference Periods	Reliability Classes
Reference Periods	RC1^[10]	RC2^[11]	RC3^[12]
1 year	-4.87	-5.89	-7.00
50 years	-3.32	-4.14	-5.07

Netherlands - Fundamentals of Flood Protection (2017)

Log-log death-frequency target for 2050

China

Building Annual Reliability Index (GB 50153‑2008)

Type of failure	Safety Class
Type of failure	Class III^[13]	Class II^[14]	Class I^[15]
Ductile (gradual)	-2.46	-3.16	-3.97
Brittle (sudden)	-3.16	-3.97	-4.87

Highway Bridges, Culverts, and Tunnels (JTG 2120‑2020)

Type of failure	Safety Class
Type of failure	Class III^[16]	Class II^[17]	Class I^[18]
Ductile (gradual)	-3.97	-4.87	-5.89
Brittle (sudden)	-4.87	-5.89	-7.00

Automotive

International

Random Hardware Failures (ISO 26262)

ASIL	Examples	Target Failure Rate per Hour
B	Headlights, Brake Lights	-7
C	Cruise Control, Rear Wheel Brakes	-7
D	All Wheel Brakes	-8

Aerospace

United States

Airplane Failure Probability-Severity per flight-hour (AC 25.1309-1)

Effects

Severity (LogOdds Range)

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