My first experience was when my mom bought me a new digital watch in the mid 1970s. She had set it to the correct date and time. Within about 30 minutes the watch's display was 01-01 1:11. I reset it and once again, it reverted back to those numbers. We put a new battery in it and the same thing happened. My mom reset i and wore it for a couple of days while it kept perfect time. Once I put it on again, within 30 minutes it was back to 01-01 1:11. I gave the watch to my mom.
More recently, more often than not, when I check the time, it is 11:11, or it is 11 minutes after the hour. I just giggle to myself and presume I'm on the right path.