If you have a fid who is not used to sudden loud noises and is easily spooked, it would not be a bad idea keep your bird in its cage while you have energetic or very young children at your home.
I very nearly had a disaster here. My cockatiel and I live in a small apartment. The only kid who ever really visits here often is my nephew when my sister and her husband stop by. He is 11 months old.
Anyways, he is learning how to walk. I was sitting in the kitchen with my tiel Lucky sitting on my shoulder while I was chatting with my sister. My nephew was in the living room bracing himself on the coffee table while "walking". He lost his balance as babies his age usually do while learning to walk, and bumped his head on the table. My nephew is alright (he was clapping his hands and giggling moments later), but it made a loud noise which startled my cockatiel and sent him flying to the carpet. My brother-in-law did what any concerned parent would do and came running from the other room to make sure the baby was okay.
But Lucky had landed right in the path where my brother-in-law was running! Luckily, he saw my bird at the last moment, and leaped over him. As it turns out, my bird has lived up to his name. He was lucky..this time. He could have been seriously injured, or worse.
To wrap this up, I'd just like to sum this up by saying that disaster can strike within only a few seconds. So be careful.