Counting minutes in arduino
Your method is completely wrong.

You need a variable that contains the value of millis() at the start of your period, whenever that may be (when the switches change? when a button is pressed? since the Arduino was powered up?) and compare that value to the current value of millis().  When the difference between them is greater than or equal to 60000 * 15 then 15 minutes have passed.

Look at BlinkWithoutDelay in the Examples menu in the IDE - it showcases the technique for you.