Life-Support Standby Switchover Reliability (2D)

A single standby life-support unit only protects a crew if its automatic switchover actually works. This 2D companion simulator strips the model down to its cleanest form — one primary unit, one cold standby — so the standby-redundancy-with-imperfect-switchover math is fully visible: a real Monte Carlo engine samples exponential failure times for the primary and, on failure, a real coin flip for the switchover, then an exponential failure time for the standby if it engages. A live single-mission trace animates one such run while a 20,000-trial batch builds an empirical mission-success-vs-duration curve that is checked, live, against the closed-form formula R(t) = e^(−λt) + p·λt·e^(−λt).