sql query to sum the total count - sql-server

Question

I have to calculate the sum of total count value for each distinct arrival_time (column in database table) corresponding to column system_name. My sql query is:
SELECT system_name, COUNT(distinct arrival_time) AS c
FROM i2alarmlog
WHERE Ack_status = 0
AND Direction='CAME'
AND system_name in('I2-tciu database',
'i2-vcs logging',
'Indus1 Vacuum',
'Indus2 TCIU',
'Indus2 Vacuum',
'Septum_SIP2',
'TL3 Vacuum')
GROUP BY system_name
UNION ALL
SELECT 'sum' system_name,
Count(distinct arrival_time)
FROM i2alarmlog
WHERE Ack_status=0
AND Direction='CAME'
AND system_name in( 'I2-tciu database'
,'i2-vcs logging',
'Indus1 Vacuum',
'Indus2 Vacuum',
'Septum_SIP2',
'TL3 Vacuum')
When I run this sql query then sum is shown as 1841 but actually its 1845.
i2-vcs logging 2
I2-tciu database 2
Indus1 Vacuum 19
Indus2 TCIU 120
Indus2 Vacuum 1691
Septum_SIP2 8
TL3 Vacuum 3
sum 1841

Answer 1

In your second query, the distinct part is applied to all data. That means, if you have the same arrival time for 2 different products, it will only be counted once, and not once for each product. That would explain the difference between your expected and actual results.
What you could do instead is this:
;with cte as
(SELECT system_name, COUNT(distinct arrival_time) AS c
FROM i2alarmlog
WHERE Ack_status = 0
AND Direction='CAME'
AND system_name in('I2-tciu database','i2-vcs logging','Indus1 Vacuum','Indus2 TCIU','Indus2 Vacuum','Septum_SIP2','TL3 Vacuum')
GROUP BY system_name )
select system_name, c
from cte
union
select 'sum', sum(c) as c
from cte
Demo

Answer 2

One solution is by using an inline view and calculate the total sum like so:
SELECT system_name, COUNT(distinct arrival_time) AS c
FROM i2alarmlog
WHERE Ack_status = 0
AND Direction='CAME'
AND system_name in('I2-tciu database','i2-vcs logging','Indus1 Vacuum','Indus2 TCIU','Indus2 Vacuum','Septum_SIP2','TL3 Vacuum')
GROUP BY system_name
UNION ALL
select 'TotalSum' as TotalSum, sum(s.c) as TotalValue
from
(
SELECT system_name, COUNT(distinct arrival_time) AS c
FROM i2alarmlog
WHERE Ack_status = 0
AND Direction='CAME'
AND system_name in('I2-tciu database','i2-vcs logging','Indus1 Vacuum','Indus2 TCIU','Indus2 Vacuum','Septum_SIP2','TL3 Vacuum')
GROUP BY system_name
) s
With this solution the maximum agregation level (2) was reached ( sum(count(value)) ).