Postgres 12

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CREATE TABLE monitoring_engine
(
    cell_id character varying(1024) COLLATE pg_catalog."default",
    monitoring_started_at timestamp without time zone,
    gap character varying(1024) COLLATE pg_catalog."default",
    status character varying(1024) COLLATE pg_catalog."default"
);
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_A', '2020-09-15', NULL, 'Monitor');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_A', '2020-09-16', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_A', '2020-09-17', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_A', '2020-09-18', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_A', '2020-09-20', '2 days', 'Monitor');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-15', NULL, 'Monitor');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-17', '2 days', 'Monitor');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-18', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-20', '2 days', 'Monitor');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-21', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-23', '2 days', 'Monitor');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-24', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-25', '1 day', 'Action');
INSERT INTO public.monitoring_engine(cell_id, monitoring_started_at, gap, status) VALUES ('Cell_B', '2020-09-26', '1 day', 'Action');
1 rows affected

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select 
	cell_id, 
	monitor_date, 
	min(monitoring_started_at) filter(where status = 'Action') first_action_date,
	max(monitoring_started_at) filter(where status = 'Action') last_action_date
from (
	select me.*,
		max(monitoring_started_at) 
			filter(where status = 'Monitor') 
			over(partition by cell_id order by monitoring_started_at) 
			as monitor_date
	from monitoring_engine me
) t
group by cell_id, monitor_date
order by cell_id, monitor_date


cell_id
monitor_date
first_action_date
last_action_date


Cell_A
2020-09-15 00:00:00
2020-09-16 00:00:00
2020-09-18 00:00:00

Cell_A
2020-09-20 00:00:00
null
null

Cell_B
2020-09-15 00:00:00
null
null

Cell_B
2020-09-17 00:00:00
2020-09-18 00:00:00
2020-09-18 00:00:00

Cell_B
2020-09-20 00:00:00
2020-09-21 00:00:00
2020-09-21 00:00:00

Cell_B
2020-09-23 00:00:00
2020-09-24 00:00:00
2020-09-26 00:00:00

cell_id	monitor_date	first_action_date	last_action_date
Cell_A	2020-09-15 00:00:00	2020-09-16 00:00:00	2020-09-18 00:00:00
Cell_A	2020-09-20 00:00:00	null	null
Cell_B	2020-09-15 00:00:00	null	null
Cell_B	2020-09-17 00:00:00	2020-09-18 00:00:00	2020-09-18 00:00:00
Cell_B	2020-09-20 00:00:00	2020-09-21 00:00:00	2020-09-21 00:00:00
Cell_B	2020-09-23 00:00:00	2020-09-24 00:00:00	2020-09-26 00:00:00