I spent most of my career as an architect for large embedded systems. I did some of the initial architecture for one of the LHC experiments that discovered the Higs Boson at CERN.
Systems like this are implemented with a certified reliable RTOS. LHC used LynxOS.
Just to present a counter-argument, I spent most of my career as a developer at cisco Systems, which helped create The Internet As We Know It Today. A cisco router is a fairly large embedded system that uses a home-built OS that is not certified, not realtime, and not particularly (certainly not inherently) reliable. I remember way back when BBN announced that they had gotten their fancy multicore "butterfly" router to reliably switch packets within 1ms. At the time, cisco routers were switching most of the packets in about 12 us... (but we couldn't do ALL of them within 1ms.)
The other interesting part involved cisco's experiments (and products) that WERE/ARE based on real-time kernels. It turns out that effectively using a modern RT kernel is a pretty complex undertaking, and it's really easy to shoot yourself in the foot...