Sí, eso es simple:
SELECT id, part, value,
row_number() OVER (PARTITION BY grp ORDER BY id) - 1 AS number
FROM (SELECT id, part, value,
sum(part) OVER (ORDER BY id) AS grp
FROM mytable
) AS q;
id | part | value | number
----+------+-------+--------
1 | 0 | 8 | 0
2 | 0 | 3 | 1
3 | 0 | 4 | 2
4 | 1 | 6 | 0
5 | 0 | 13 | 1
6 | 0 | 4 | 2
7 | 1 | 2 | 0
8 | 0 | 11 | 1
9 | 0 | 15 | 2
10 | 0 | 3 | 3
11 | 0 | 2 | 4
(11 rows)