Silencing Ringer

Even with my Iphone6 on silent, I still get a ringtone when calls or texts com in. Not sure about other alerts, but possibly. It doesn't matter if they are in my Favorites, or not.The only solution I have is to turn the phone completely off. This has become an annoying inconvenience when I'm in a meeting, at a show or doctor's office, and especially playing golf and I want to use an APP. Any other solutions other than completely shutting phone down?l