**Probability of Failure Based on Basic Engineering Principles**

All plausible failure mechanisms must be included in the assessment of PoF. Every failure mechanism must be properly measured by independently measuring the following three elements:

(attack) – The unmitigated aggressiveness of the force or process that may precipitate failure. This includes external forces, corrosion, cracking, human error, and all other failure mechanisms. Example measurement units are ‘events per mile-year’ or ‘mils per year (mpy) metal loss’.*Exposure*(defense) – The effectiveness of every mitigation measure designed to block or reduce an exposure. The benefit from each independent mitigation measure, coupled with the combined effect of all mitigations, is to be estimated. There are numerous common mitigations including depth of cover, patrol, coatings, inhibitors, training, and procedures, to name but a few.*Mitigation*(survivability) – The ability of the system to withstand forces that are not fully mitigated.*Resistance*

Assessment of the first two, exposure and mitigation, produces the probability of ‘damage without failure’ while all three produce an estimate of ‘damage resulting in failure’.

For each time-dependent failure mechanism, a theoretical remaining life estimate must be produced and expressed as a function of time.

The process is intuitive and comprehensive. Equations used can (and ‘should’) be simple and grounded in sound engineering principles. For instance:

Time-independent failure mechanisms include third party damages; geohazards; human error; sabotage; theft

They can each be efficiently modeled as:

(failure probability, PoF) = [unmitigated event frequency] x (1 – [mitigation effectiveness]) x (1 – [resistance])

For example,

0.5 excavations/km-yr x (1- [90% mitigation]) x (1-[80% resistance])

= 0.01 failures/km-year

= 1% probability of failure per km-year

Time-dependent failure mechanisms include corrosion; fatigue, and environmentally-assisted-cracking (EAC)

They can each be efficiently modeled as

(failure probability, PoF) = f (time-to-failure,TTF)

where, in a simple and conservative application:

TTF = [*available** pipe wall] / ([wall loss rate] x (1 – [mitigation effectiveness]))

For example, an effective remaining wall thickness of 10 mm exposed to a potential corrosion rate of 0.5 mmpy, but which is mitigated 97%, shows:

TTF = 10mm / [0.5 mmpy x (1-97%mitigation)] = 167 years

PoF = <1% probability of failure per year**

**Uses a pipe (or component) wall thickness adjusted for previous wall loss—measured or estimated—and other possible weaknesses from any source including manufacturing and construction*

* **using a simple and conservative relationship between TTF and PoF; other relationships are often more appropriate*