$47.$ Consider a LOPA scenario where a temperature control loop failure is the initiating event, the time at risk is $0\mathrm{.}2,$ and an operator is always present during operation. The final event is an overpressure that leads to a catastrophic vessel failure. Safeguards present are a properly sized pressure relief valve, a pressure control loop that closes the same steam valve that the temperature control loop operates, and a pressure control loop that operates from the same pressure sensor but opens a vent valve from the vessel. Remembering that not all safeguards are necessarily IPLs, what is the final event frequency for the scenario?

a$.0\mathrm{.}0002$

b$.0\mathrm{.}00002$

c$.0\mathrm{.}000002$

d$.0\mathrm{.}0000002$