Q: iphone 6  auto shutsdown when i go to notification centre

Try to reset your device. This won't delete your data stored on device.

• Press and hold the Sleep/Wake button
• Press and hold on the Home button
• Keep holding both buttons until the display turns off and back on with Apple logo on it.

Alternatively, you may go to Settings - General - Reset - Reset All Settings

If your iOS device restarts, displays the Apple logo, or powers off while you're using it - Apple Support

sometimes, my iphone 6  automatically shutdown when I go to see notifications. but was overcome

If so, I think you should buy one other iphone

I would not be so categorical as jaikapok.

I would try the steps in this article(backup the phone with iTunes  and restore it to factory settings): Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support

If this will not help you always have the option  to take your iPhone to the Apple Store. They would offer you the best solution.