Вот два способа сделать это. Я уверен, что SUM CASE будет лучше, но вы можете проверить это сами
Использование SUM CASE
select person.first_name,
SUM(case when incident.incident_id =1 THEN 1 ELSE 0 END) as Active,
SUM(case when incident.incident_id =2 THEN 1 ELSE 0 END) AS NonActive,
FROM incident, person
where person.PERSON_ID = incident.OWNER_ID
AND (incident.dept_id = 111 OR incident.dept_id = 222)
AND incident.incident_id IN (1,2)
GROUP BY person.first_name;
Использование JOIN
SELECT DISTINCT
p.First_name,
Acive.Active,
NonActive.NonActive
FROM
PERSON p
LEFT JOIN
(
select person.first_name, COUNT(person.PERSON_ID) as Active
FROM incident, person
where person.PERSON_ID = incident.OWNER_ID
and incident.incident_id = 1
AND (incident.dept_id = 111 OR incident.dept_id = 222)
GROUP BY person.first_name;
) Active
ON p.first_name = active.first_name
LEFT JOIN
(
select person.first_name, COUNT(person.PERSON_ID) as NonActive
FROM incident, person
where person.PERSON_ID = incident.OWNER_ID
AND incident.incident_id = 2
AND (incident.dept_id = 111OR incident.dept_id = 222)
GROUP BY person.first_name
) NonActive
ON p.first_name = NonActive.first_name
where Active.First_name is not null
and NonActive.First_name is not null