For this I am going to assume there are 12 disks in the array, and each are 1TB big.

That means there is 10TB of storage. This is for example, provided you are not using more than 6 disks (6TB) worth of storage, then it doesn't matter what size they are.

Oblig disclaimer: None of this may be supported by Synology, so I would check with them if this approach can cause problems, backup beforehand, and shutdown any synology services beforehand. Synology use standard md raid arrays as far as I know, and they are accessible if the disk are moved to a standard server that supports md - so there should be no problems.

Overview

The sequence goes like this:

1. Reduce the filesystem size
2. Reduce the logical volume size
3. Reduce the array size
4. Resize the file system back
5. Convert the spare disks into hot spares

File system

Find the main partition, using df -h, it should look something like:

Filesystem                Size      Used Available Use% Mounted on
/dev/vg1/volume_1         10T       5T   5T         50% /volume1 

Use this command to resize to the maximum it needs and no more:

umount /dev/vg1/volume_1
resize2fs -M /dev/vg1/volume_1 

Now check:

mount /dev/vg1/volume_1 /volume1
df -h  Filesystem                Size      Used Available Use% Mounted on
/dev/vg1/volume_1         5T       5T    0T        100% /volume1 

Volume

To reduce the volume size, use lvreduce (make it a bit bigger just in case):

umount /dev/vg1/volume_1
lvreduce -L 5.2T /dev/vg1/volume_1 

Now that the logical volume has been reduced, use pvresize to reduce the physical volume size:

pvresize --setphysicalvolumesize 5.3T /dev/md0 

If the resize fails, see this other question for moving the portions of data that were allocated at the end of the physical volume towards the beginning.

Now we have a 5.3T volume on a 10T array, so we can safely reduce the array size by 2T.

Array

Find out the md device:

pvdisplay -C

PV         VG      Fmt  Attr PSize   PFree
/dev/md0   vg1     lvm2 a--  5.3t    0.1t 

The first step is to tell mdadm to reduce the array size (with grow):

mdadm --grow -n10 /dev/md0

mdadm: this change will reduce the size of the array.
        use --grow --array-size first to truncate array.
        e.g. mdadm --grow /dev/md0 --array-size 9683819520 

This is saying that in order to fit the current array onto 10 disks, we need to reduce the array size.

mdadm --grow /dev/md0 --array-size 9683819520 

Now it is smaller, we can reduce the number of disks:

mdadm --grow -n10 /dev/md0 --backup-file /root/mdadm.md0.backup 

This will take a loong time, and can be monitored here:

cat /proc/mdstat

Personalities : [raid6] [raid5] [raid4]
md4 : active raid6 sda4[0] sdb4[1] sdc4[2] sdd4[3] sde4[4] sdf4[5] sdg4[6] sdh4[7] sdi4[1] sdj4[1]        [>....................]  reshape =  1.8% (9186496/484190976)                               finish=821.3min speed=9638K/sec [UUUUUUUUUU__] 

But we don't need to wait.

Resize the PV, LV and filesystem to maximum:

pvresize /dev/md0
lvextend -l 100%FREE /dev/vg1/volume_1
e2fsck -f /dev/vg1/volume_1
resize2fs /dev/vg1/volume_1 

Set spare disks as spares

Nothing to do here, any spare disks in an array are automatically spares. Once your reshaping is complete, check the status:

cat /proc/mdstat

Personalities : [raid6] [raid5] [raid4]
md4 : active raid6 sda4[0] sdb4[1] sdc4[2] sdd4[3] sde4[4] sdf4[5] sdg4[6] sdh4[7] sdi4[S] sdj4