Sequences and frequencies
How the visual numbers each event tree sequence, works out its path probability and frequency, where the results appear, the settings that control them, and the rules the numbers must follow.
Sequence identifiers
Every path from the initiating event to an outcome is a sequence. Its identifier starts with the initiating event's Node ID, then adds a part for each split the path passes through: S for a success branch, F for failure or C for conditional, followed by the branch's position at that split. A step that is the only way on from a node adds nothing.
In the example, IE-S1-F2-S1 reads: from IE, the first branch at Gas detected? (success), the second at Ignition avoided? (failure), then the first at Fire suppressed? (success).
Positions follow Order, then success before conditional before failure. If Order puts a failure branch first, the identifiers change to match, such as IE-F1 and IE-S2, while the drawing still shows success above failure. Number success branches first to keep the two in step.
Path probability and frequency
| Value | Worked out as |
|---|---|
| Path probability | The branch probabilities along the path, multiplied together. |
| Sequence frequency | The initiating event's Frequency multiplied by the path probability. |
Units are never converted. If the initiating frequency is per year, so is every sequence frequency.
A step that is the only way on from a node needs no probability and counts as 1. If it does have a probability, that is multiplied in like any other branch.
Where the results appear
On each outcome, as its secondary line, such as IE-S1-F2-S1 · f = 1.98e-3. When the initiating event has no Frequency, the path probability is shown instead: IE-S1-F2-S1 · p = 7.60e-2. An outcome at the end of several sequences lists each one, separated by |.
Because the results are written as the secondary line, they need Labels → Secondary label turned on, as it is by default. An outcome that already has a secondary label keeps it, with the sequence after it.
Settings
These settings are in the Sequence quantification group on the Labels tab.
| Setting | Options | Default |
|---|---|---|
| Sequence identifier | Show on outcome, Hide | Show on outcome |
| Sequence frequency | Show on outcome, Hide | Show on outcome |
| Quantity format | Scientific, Decimal, Percentage | Scientific |
| Quantity format | Controlled fire in the example |
|---|---|
| Scientific | f = 1.98e-3 |
| Decimal | f = 0.001977 |
| Percentage | f = 0.198% |
These formats belong to the visual and apply only to the sequence values. Values in tooltips and the Node Inspector use the Power BI format of their column.
Rules the numbers must follow
| Rule | Severity | Message |
|---|---|---|
| A branch probability is from 0 to 1 | Error | A branch probability of 98 is outside 0 to 1. Every sequence through this branch is quantified from it. |
| The branches leaving a split add up to 1 | Error | The branches leaving this event sum to 1.0100, not 1. They are meant to be exhaustive and mutually exclusive, so every downstream frequency is wrong until they complete. |
| Every branch of a split has a probability, or none does | Warning | One branch of 2 leaving this event has no probability, so every sequence through it is left uncounted while the rest of the tree is quantified. Supply the missing value, or remove the others to keep the tree qualitative. |
| The initiating frequency is a number of 0 or more | Error | An initiating frequency of -1 is not a finite value of zero or more. |
A split that adds up to within 0.000001 of 1 is accepted. A probability entered as a percentage, 98 instead of 0.98, breaks both of the first two rules.
Trees without all the numbers
- No probabilities at all. A qualitative tree. It draws, each outcome shows its sequence identifier, and the Validation tab notes that no sequence can be quantified.
- Probabilities but no initiating Frequency. Outcomes show p, the path probability, instead of f, and the Validation tab notes that no frequency is mapped.
- One split missing a probability. The sequences through it show only their identifier. The rest of the tree is still quantified.