Toyota Production System is a manufacturing system that is often used as inspiration for modern lean manufacturing. It's not just "Toyota's production system," it's a proper noun, "Toyota Production System." You could spend a lifetime learning the philosophy behind it. If you find yourself so inclined to learn, you'll find many things at odd with TPS in the video posted above. The study of TPS can be life changing, as it modifies your view on everything you do. There is a great little book that plants the seed, it can be found here: http://www.amazon.com/Need-About-Manufacturing-Learned-Garage/dp/0963043935
My first reaction to the i3 video is it's over automated by a long shot.