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Since 1.15.0 Calculate the total duration in a given state. Unlike duration_in, you can use this function across multiple state aggregates that cover multiple time buckets. Any missing values at the time bucket boundaries are interpolated from adjacent state aggregates. 
interpolated_duration_in(
  agg StateAgg,
  state {TEXT | BIGINT},
  start TIMESTAMPTZ,
  interval INTERVAL
  [, prev StateAgg]
) RETURNS DOUBLE PRECISION

​
Arguments

NameTypeDefaultRequiredDescription
aggStateAgg-✔A state aggregate created with state_agg
stateTEXT | BIGINT-✔The state to query
startTIMESTAMPTZ-✔The start of the interval to be calculated
intervalINTERVAL-✔The length of the interval to be calculated
prevStateAgg-The state aggregate from the prior interval, used to interpolate the value at start. If NULL, the first timestamp in aggregate is used as the start of the interval

​
Returns

ColumnTypeDescription
interpolated_duration_inINTERVALThe total time spent in the queried state. Displayed as days, hh:mm:ss, or a combination of the two

​
Samples

Create a test table that tracks when a system switches between starting, running, and error states. Query the table for the time spent in the running state. Use LAG and LEAD to get the neighboring aggregates for interpolation. If you prefer to see the result in seconds, EXTRACT the epoch from the returned result. 
SELECT
  time,
  interpolated_duration_in(
    agg,
    'running',
    time,
    '1 day',
    LAG(agg) OVER (ORDER BY time)
) FROM (
  SELECT
    time_bucket('1 day', time) as time,
    state_agg(time, state) as agg
  FROM
    states
  GROUP BY time_bucket('1 day', time)
) s;
Returns: 
time                    | interpolated_duration_in
------------------------+--------------------------
2020-01-01 00:00:00+00  | 13:30:00
2020-01-02 00:00:00+00  | 16:00:00
2020-01-03 00:00:00+00  | 04:30:00
2020-01-04 00:00:00+00  | 12:00:00