Civil Likelihood of Failure (Steps 5 & 7)

A	B	C	D	E
Never heard of in the industry	Heard of in the industry	Has happened in the organization or more than once in the industry	Has happened at the location or more than once in the organization	Has happened more than once in the location
< 0.01%	< 0.1%	<1%	<10%	<100%
Less than once in 10,000 yrs	One in 1,000 to one in 10,000 yrs	One in 100 to one in 1,000 yrs	One in 10 to one in 100 yrs	Annually to once in 10 yrs
We would be greatly amazed to see it happen	We would think it unusual	We would not be surprised to see it happen

Never heard of in the industry

Heard of in the industry

Has happened in the organization or more than once in the industry

Has happened at the location or more than once in the organization

Has happened more than once in the location

< 0.01%

< 0.1%

<1%

<10%

<100%

Less than once in 10,000 yrs

One in 1,000 to one in 10,000 yrs

One in 100 to one in 1,000 yrs

One in 10 to one in 100 yrs

Annually to once in 10 yrs

We would be greatly amazed to see it happen

We would think it unusual

We would not be surprised to see it happen

From the above table, a windstorm resulting in a failure event, has a probability, p, 1%

For the age-related corrosion, we first determine the remnant life, which is assumed to be between 5 -10 years and use the default confidence class as Intermediate. This gives a likelihood rating of C, which translates into a probability p, 0.1%

Likelihood Matrix - to calculate Risk Likelihood class for AR FMs.

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From the expression p(A∩B) = p(A) * p (B) for independent events, we determine that p(A∩B) is < 0.1% which is a likelihood rating of B.

According to the Risk = Likelihood * Consequence relationship, for any scenario, the consequence remains constant while the likelihood is a variable. For the example, we assume that the age-related failure and the event-related failure have a similar medium consequence and thus both have a risk rating of R2. Risk Matrix.With a likelihood rating of B, the risk rating of both A and B occurring together is now R1.

Let C = event that the asset will fail after it reaches a critical point in a particular year. We now pose the question: “What is the probability (or likelihood rating in this context) that the asset will reach the projected critical point in that particular year given that it has experienced a combined Age-Related and event-based failure?

Consider the conditional probability:For the purpose of the example, we assume that joint probability of A, B and C has a likelihood rating of A. We may try to solve p (C∩A∩B) intuitively by equating it to p(A) * p(B) * p(C). This is not correct as while A and B are mutually independent, A, B and C are not.

The probability of C given that A and B has occurred will be <10% which will be a likelihood rating of D and a risk rating of R2, meaning that we would not be surprised to see it happen. An example of this is a storage tank with structural deformities such as corrosion causing a decrease in wall thickness. Such a deformation can reduce the critical wind load that can cause failure to the tank.

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