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Likelihood Evaluation

15.5 Interactions Between Hardware or System Components

Incidents in chemical facilities are often the result of complex interactions of process components. In some cases, this
interaction requires the simultaneous failure of a number of components. This parallel structure is often depicted by a logical
“AND” with the failure probability of the individual components multiplied to obtain an overall failure probability. Process
components may also interact in series which is often depicted by a logical “OR” with failure probability of the individual
components added to obtain an overall failure probability.

Process components interact in two different fashions. In some cases a process failure requires the simultaneous
failure of a number of independent components in parallel. This parallel structure is represented by a logical "AND" function
which means that the failure probabilities for the individual components must be multiplied.

P =  Pi = P1 P2 P3 …
Process components also interact in series. This means that a failure of any single component in the series of
components will result in failure of the process. The logical OR function represents this case. For series components the
overall failure probabilities is approximately the summation of failure probabilities for the individual components (which
assumes an interaction probability - or both components in series fail – is small).

P =  Pi = P1 + P2 + P3 …

A Common Cause Failure is a single event that affects a number of systems simultaneously and may significantly
increase overall failure probability. Common cause failures include events such as loss of utilities such as electricity or
instrument air. These failure probabilities are typically addressed via OR logic within a summation of component failure
probabilities. One needs to deliberately design systems to minimum common cause failures.

15.6 Probability of Failure on Demand
The probability of failure on demand is the probability that a system will fail to perform a specified function on demand
(i.e., when challenged or needed). Simple failure probability equations assumed failures are immediately obvious and
corrected in a negligible amount of time. For many components (particularly emergency interlocks), failure may not be
obvious without regular and reliable testing.

For an unrevealed failure, the failure becomes obvious only upon regular inspection. For example (Figure 15-2): a flat
tire on a car is immediately obvious to the driver (revealed failure). However, the spare tire may also be flat without the
driver being aware until the spare is needed (unrevealed failure).

Figure 15-2 Changing a Tire

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