I’m an engineer on the PagerDuty mobile team. Firstly, thanks for using the PagerDuty mobile app
Unfortunately, right now Apple’s APIs do not allow our app to override Do Not Disturb mode or the system volume on iOS. If this changes in the future and Apple exposes public APIs for this, we can investigate ways to implement the feature to override system volume for push notifications.
As a workaround, if you are on iOS 10, each individual contact in the Contacts app has a dedicated switch, called Emergency Bypass, which overrides the Do Not Disturb feature for that person. You could add PagerDuty numbers (you can find these here) as a contact and enable this bypass mode. This feature lets you permit sound for phone and text notifications even when Do Not Disturb is enabled globally in your Settings. You can enable it by going to a Contact -> Edit -> Ringtone -> Toggle Emergency Bypass.
Hope this helps!