Have you got 'alarm in silent mode' checked under alarms>settings?
You can also set your alarm volume here too.
It's also worth setting the alarm itself to vibrate too.
edit: just to add I set my phone to silent each night when I go to bed. I've never had an alarm fail to go off in around 3 weeks of use.
#6077644, By rutter Android hardware
rutter 1,919 posts
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