Suppose a pressure vessel in a manufacturing facility has four main components that keep it from exploding when IAoperating under pressure. The pressure sensor triggers the pressure regulator to automatically reduce pressure. If the pressure senor or rAgo,thitgata, then an overpressure relief valve (primary) automatically expels excessive pressure. There’s a backup overpressure relief valve in case the primary overpressure relief valve fails. In essence, if dtkeakearganggya (thgatlaqgflusjaagIthen both the primary and backup overpressure valves fail, an explosion could occur. Below are the failure rates (probabilities) for each of the four componen s.I
Component Failure Rate/ Probability Over Pressure Relief Valve 0.005 Over Pressure Backup Relief Valve 0.05 Pressure Sensor 0.001 Pressure Regulator 0.002
What is the probability of an explosion occurring should excessive pressure start building up during operation of the vessel? Show your work.




Sample Solution