# Time Series in Fault Tree

The probability and cost data of an event can be defined as a function of time. This is accomplished via a two stage process. First, time series intervals for the fault tree must be defined.

__Defining Time Series Intervals__

Series are comprised of intervals, e.g., from 1 to 4, 5 to 6, etc. Intervals are comprised of elements. Since series are often used to define time series, elements are often referred to as periods.

Define the time series intervals for the fault tree via FAULT TREE | Alter | Define Intervals.

- Click on FAULT TREE | Alter | Define Intervals. The Define Intervals dialog appears.
- Click Add to add a new interval.
- Enter the From value for each defined interval.
- Enter the To value for the last interval.
- Click OK.

Note: interval boundaries must be contiguous; hence, the To value is only necessary for the last interval. If the first interval goes from 0 and the second goes from 5, then the first interval goes to 4. The From value of the first interval can be any non-negative integer. All From values must be increasing over the intervals. The To value of the last interval must be greater than or equal to its From value.

__Creating Time Series Nodes__

__Defining a Time Series__

- Double-click the binary event or value node for which you wish to enter a series.
- Switch to the General tab.
- Check Time series event (or value).
- Switch back to the Data tab.
- Enter data to define the series. For events, this may be probability, true state cost, or false state cost data.
- Click OK.

Note: there will be a vector symbol (rightward pointing arrow) displayed near the top, left corner of the node to indicate it is a series. Also note that a time series node cannot be a predecessor to a scalar node. Once you turn a scalar node into a time series node, DPL turns all successors of that node into time series nodes. A scalar can be a predecessor to a time series node. In this situation, the scalar is a predecessor of the first interval of the time series node.

__Editing Time Series Intervals__

- Click on FAULT TREE | Alter | Define Intervals. The Define Intervals dialog appears.
- Modify the From values of any existing intervals as desired.
- Modify the To value of the last interval as desired.
- Add/delete intervals as desired.
- Click OK.

The interval boundaries of all time series nodes will be modified to match the edits you made. If you deleted intervals, those intervals will be deleted from time series nodes as well. If you added intervals, you will need to edit the time series nodes in the fault tree to provide data for the new intervals.

__Defining Series Recursively__

To define the expression as a function of the time period, you need to use the relative subscript [$]. This takes on the value of the period that the variable is in. For example, if a value series node is called "sample" and subsequent intervals are 80% of the previous value, the expression would read: "sample[$-1] * 0.8".

* Versions:* DPL Fault Tree

*See Also*