Unconditional Failure Intensity
For each possible outcome of the event tree, unconditional failure intensity (w) estimates the probability that the sequence leading to that outcome experiences a failure per time unit at time t. This is also the expected number of failures per time unit at time t. For a given sequence at time t, this calculation is performed by doing the following:
1. Compute for each column the unconditional failure intensity, wk(t), for the k th column along the sequence.
2. Compute w(t) for the possible outcome by combining these columnwise w k (t) values
For the k th column, wk(t) is computed by the following set of formulae:
• For a column linked to a fault tree gate or event, wk(t) is equal to the failure rate for that gate or event.
• For a constant probability column, wk(t) is equal to 0.
• For a frequency column, failure rate/MTBF column, or failure with repair column with instantaneous repair (mean corrective time = 0), wk(t) =λ, where λ is the conditional failure intensity derived from frequency, failure rate, or MTBF.
• For a failure with repair column with non-instantaneous repair (mean corrective time > 0) and a failure with periodic inspection column, wk (t) =λ*(1−Qk(t)), where λ is the conditional failure intensity derived from frequency, failure rate, or MTBF and Qk(t) is the column unavailability at time t.
The calculation of w(t) for the possible outcome uses the formula:
Where K is the collection of active columns along the sequence.
By assumption, the product in this formula excludes the possibility of simultaneous failures of multiple columns.